A Complete Resource Book in Physics for JEE Main 2017

Sanjeev Kumar

Chapter 9

Oscillations and Waves - all with Video Answers

Educators

Chapter Questions

Problem 1

A simple harmonic motion (SHM) has an amplitude $A$ and time period $T$. The time required by it to travel from $x=A$ to $x=A / 2$ is
(A) $7 / 6$
(B) 714
(C) $T / 3$
(D) $T / 2$

Dharmendra Jain

Dharmendra Jain

Numerade Educator

Problem 2

A mass $m$ is suspended from two springs of spring constant $k_1$ and $k_2$ as shown in Fig. 9.23. The time period of vertical oscillations of the mass will be
(A) $2 \pi \sqrt{\left(\frac{k_1+k_2}{m}\right)}$
(B) $2 \pi \sqrt{\frac{m}{\left(k_1+k_2\right)}}$
(C) $2 \pi \sqrt{\frac{m\left(k_1 k_2\right)}{\left(k_1+k_2\right)}}$
(D) $2 \pi \sqrt{\frac{m\left(k_1+k_2\right)}{\left(k_1 k_2\right)}}$
(FIGURE CAN'T COPY)
Fig. 9.23

Dheeraj Sharma

Numerade Educator

Problem 3

Two SHMs are represented by the equations $Y_1=10$ $\sin \left(3 \pi t+\frac{\pi}{4}\right)$ and $Y_2=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$. Their amplitudes are in the ratio of
(A) $2: 1$
(B) $3: 1$
(C) $1: 3$
(D) $1: 4$

Dheeraj Sharma

Numerade Educator

Problem 4

A mass $M$ attached to a spring oscillates with a period of 2 seconds. If the mass is increased by 2 kg the period increases by 1 second. The initial mass $M$ will be
(A) 1.6 kg
(B) 1 kg
(C) 1.5 kg
(D) 2 kg

Dheeraj Sharma

Numerade Educator

Problem 5

The ratio of kinetic energy at mean position to the potential energy when the displacement is half of the amplitude is
(A) $\frac{4}{1}$
(B) $\frac{2}{3}$
(C) $\frac{4}{3}$
(D) $\frac{1}{2}$

Dheeraj Sharma

Numerade Educator

Problem 6

If the displacement ( $x$ ) and velocity ( $v$ ) of a particle executing SHM are related through the expression $4 v^2=25-x^2$, then its time period is
(A) $\pi$
(B) $2 \pi$
(C) $4 \pi$
(D) $6 \pi$

Ankur S

Numerade Educator

Problem 7

In a simple pendulum at mean position,
(A) KE is maximum and PE is minimum.
(B) KE is minimum and PE is maximum.
(C) Both PE and KE are maximum.
(D) Both PE and KE are minimum.

Dheeraj Sharma

Numerade Educator

Problem 8

Maximum velocity in SHM is $v_{\text {wer }}$. The average velocity during the motion from one extreme point to the other extreme point will be
(A) $\frac{\pi}{2} v_n$
(B) $\frac{2}{\pi} v_n$
(C) $\frac{4}{\pi} v_n$
(D) $\frac{\pi}{4} v_w$

Dheeraj Sharma

Numerade Educator

Problem 9

When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is $n$, the frequency of the kinetic energy is
(A) $n / 2$
(B) $n$
(C) $2 n$
(D) $4 n$

Dheeraj Sharma

Numerade Educator

Problem 10

A mass $M$ suspended from a spring of negligible mass. The spring is pulled a little and then released, so that the mass executes SHM of time period $T$. If the mass is increased by $m$, the time period becomes $5 T / 3$. The ratio of $m / M$ is
(A) $\frac{5}{3}$
(B) $\frac{3}{5}$
(C) $\frac{16}{9}$
(D) $\frac{25}{9}$

Dheeraj Sharma

Numerade Educator

Problem 11

What will be the displacement of a particle in SHM when its velocity is half the maximum velocity ( $A=$ amplitude)
(A) $\frac{3}{\sqrt{2}} A$
(B) $\sqrt{2} A$
(C) $\frac{3}{4} A$
(D) $\frac{\sqrt{3}}{2} A$

Dheeraj Sharma

Numerade Educator

Problem 12

Two blocks of mass $m_1$ and $m_2$ are kept on a smooth horizontal table as shown in Fig. 9.24. Block of mass $m_1$ but not $m_2$ is fastened to the spring. If now both the blocks are pushed to the left so that the spring is compressed a distance $d$. The amplitude of oscillation of block of mass $m_1$, after the system is released is
(FIGURE CAN'T COPY)
(A) $d \sqrt{\frac{m_1}{m_1+m_2}}$
(B) $d \sqrt{\frac{m_2}{m_1+m_2}}$
(C) $d \sqrt{\frac{2 m_2}{m_1+m_2}}$
(D) $d \sqrt{\frac{2 m_1}{m_1+m_2}}$

Dheeraj Sharma

Numerade Educator

Problem 13

Displacement-time graph of a particle executing SHM is shown.
The corresponding force-time graph of the particle is
(GRAPH CAN'T COPY)

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 14

A particle starts executing SHM of amplitude $a$ and total energy $E$. At the instant, its kinetic energy is $\frac{3 E}{4}$ and its displacement $y$ is given by
(A) $y=\frac{a}{\sqrt{2}}$
(B) $y=\frac{a}{2}$
(C) $y=\frac{a \sqrt{3}}{2}$
(D) $y=a$

Dheeraj Sharma

Numerade Educator

Problem 15

The periodic time of a mass suspended by a spring (force constant $k$ ) is $T$. If the spring is cut in three equal pieces, the force constant of each part and the periodic time if the same mass is suspended from one piece are
(A) $k, \pi \sqrt{3}$
(B) $3 k, T$
(C) $3 k, \sqrt{3} T$
(D) $3 k, T \sqrt{3}$

Dheeraj Sharma

Numerade Educator

Problem 16

$x=A \sin \omega t$, represents the equation of a SHM. If displacements of the particle are $x_1$ and $x_2$ and velocities are $v_1$ and $v_2$, respectively, then amplitude of SHM is
(A) $\left[\frac{\left(v_2-v_1\right)\left(x_2-x_1\right)}{v_2^2-v_1^2}\right]^{\frac{1}{2}}$
(B) $\left[\frac{\left(v_2 x_1\right)^2-\left(v_1 x_2\right)^2}{v_2^2-v_1^2}\right]^{\frac{1}{2}}$
(C) $\frac{v_1 x_2}{\left(v_2-v_1\right)^2}$
(D) $\left[\frac{v_1 x_2-v_2 x_1}{v_1^2-v_2^2}\right]^{\frac{1}{2}}$

Dheeraj Sharma

Numerade Educator

Problem 17

On smooth inclined plane, a body of mass $m$ is attached between two massless springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $k$, the period of oscillation of the body is
(A) $2 \pi \sqrt{\frac{m}{2 k}}$
(B) $2 \pi \sqrt{\frac{2 m}{k}}$
(C) $2 \pi \sqrt{\frac{m g \sin \theta}{2 k}}$
(D) $2 \pi \sqrt{\frac{2 m g \sin \theta}{k}}$

Dheeraj Sharma

Numerade Educator

Problem 18

A person measures the time period of a simple pendulum inside a stationary lift and finds it to be $T$. If the lift starts accelerating upwards with an acceleration of $\mathrm{g} / 3$, the time period of the pendulum will be
(A) $\sqrt{3} T$
(B) $\frac{\sqrt{3}}{2} T$
(C) $T / \sqrt{3}$
(D) $T / 3$

Ajay Singhal

Numerade Educator

Problem 19

The displacement $x$ (in centimeters) of an oscillating particle varies with time $t$ (in seconds) as $x=2 \cos \left(0.5 \pi t+\frac{\pi}{3}\right)$. The magnitude of the maximum acceleration of the particle in $\mathrm{cms}^{-2}$ is
(A) $\frac{\pi}{2}$
(B) $\frac{\pi}{4}$
(C) $\frac{\pi^2}{2}$
(D) $\frac{\pi^2}{4}$

Dheeraj Sharma

Numerade Educator

Problem 20

A particle is executing SHM with an amplitude of 4 cm . At the mean position, velocity of the particle is $10 \mathrm{~cm} / \mathrm{s}$. The distance of the particle from the mean position when its speed becomes $5 \mathrm{~cm} / \mathrm{s}$ is
(A) $\sqrt{3} \mathrm{~cm}$
(B) $\sqrt{5} \mathrm{~cm}$
(C) $2 \sqrt{3} \mathrm{~cm}$
(D) $2 \sqrt{5} \mathrm{~cm}$

Dheeraj Sharma

Numerade Educator

Problem 21

A source $x$ of unknown frequency produces 8 beats with a source of 250 Hz and 12 beats with a source of 270 Hz . The frequency of source $x$ is
(A) 258 Hz
(B) 242 Hz
(C) 262 Hz
(D) 282 Hz

Dheeraj Sharma

Numerade Educator

Problem 22

A sonometer wire of density $d$ and radius $r$ is held between two bridges at a distance $L$ apart. The wire has a tension $T$. The fundamental frequency of the wire will be
(A) $f=\frac{1}{2 L r} \sqrt{\frac{T}{\pi d}}$
(B) $f=\frac{r}{2 L} \sqrt{\frac{\pi d}{T}}$
(C) $f=\frac{1}{2 L r} \sqrt{\frac{d}{\pi T}}$
(D) $f=\frac{1}{2 L} \sqrt{\frac{d}{T}}$

Dheeraj Sharma

Numerade Educator

Problem 23

The amplitude of a wave disturbance propagating in the positive $y$-direction is given by $y=\frac{1}{1+x^2}$ at $t=$ 0 and $y=\frac{1}{\left[1+(x-1)^2\right]}$ at $t=2$ second, where $x$ and $y$ are in $m$. If the shape of the wave disturbance does not change during the propagation, what is the velocity of the wave?
(A) $1 \mathrm{~m} / \mathrm{s}$
(B) $1.5 \mathrm{~m} / \mathrm{s}$
(C) $0.5 \mathrm{~m} / \mathrm{s}$
(D) $2 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 24

Two sinusoidal plane waves of the same frequency having intensities $I_0$ and $4 I_0$ are traveling in the same direction. The resultant intensity at a point at which waves meet with a phase difference of zero radian is
(A) $I_0$
(B) $5 I_6$
(C) $9 I_0$
(D) $3 I_0$

Ajay Singhal

Numerade Educator

Problem 25

An open pipe is suddenly closed which results in the second overtone of the closed pipe to be higher in frequency by 100 Hz than the first overtone of the original pipe. The fundamental frequency of open pipe will be
(A) 100 Hz
(B) 300 Hz
(C) 150 Hz
(D) 200 Hz

Dheeraj Sharma

Numerade Educator

Problem 26

A fast train moving at $40 \mathrm{~m} / \mathrm{s}$ passes by a stationary observer, emitting a whistle of frequency 300 Hz . If the velocity of sound waves is $340 \mathrm{~m} / \mathrm{s}$, then the change in the apparent frequency of the sound, just before and just after the train passes by the observer, will be nearly
(A) 32 Hz
(B) 40 Hz
(C) 72 Hz
(D) 8 Hz

Yuva S

Numerade Educator

Problem 27

Which of the following represents a standing wave?
(A) $y=A \sin (e x-k x)$
(B) $y=A \sin k x \sin (a r-\theta)$
(C) $y=A e^{-k x} \sin (\omega x-k x+\alpha)$
(D) $y=(a x+b) \sin (a x-k x)$

Mahendra K

Numerade Educator

Problem 28

A man on the platform is watching two trains, one leaving and the other entering the station with equal speed of $4 \mathrm{~m} / \mathrm{s}$. If they sound their whistles each of natural frequency 240 Hz , the number of beats heard by the man (velocity of sound in air $=320 \mathrm{~m} / \mathrm{s}$ ) will be
(A) 6
(B) 3
(C) 0
(D) 12

Dheeraj Sharma

Numerade Educator

Problem 29

The two waves having intensities in the ratio $1: 9$ produce interference. The ratio of the maximum to the minimum intensities is equal to
(A) $10: 8$
(B) $9: 1$
(C) $4: 1$
(D) $2: 1$

Dheeraj Sharma

Numerade Educator

Problem 30

A train moves towards a stationary observer with speed $34 \mathrm{~m} / \mathrm{s}$. The train sounds a whistle and its frequency registered is $f_1$. If the train's speed is reduced to $17 \mathrm{~m} / \mathrm{s}$, the frequency registered is $f_2$. If the speed of sound is $340 \mathrm{~m} / \mathrm{s}$ then the ratio $\frac{f_1}{f_2}$ is
(A) $\frac{18}{19}$
(B) $\frac{1}{2}$
(C) 2
(D) $\frac{19}{18}$

Dheeraj Sharma

Numerade Educator

Problem 31

A uniform cord has a mass of 0.3 kg and length of 6 m . (see Fig. 9.25). The speed of a pulse on this cord is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$
(A) $20 \mathrm{~m} / \mathrm{s}$
(B) $10 \mathrm{~m} / \mathrm{s}$
(C) $40 \mathrm{~m} / \mathrm{s}$
(D) $5 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 32

A closed-organ pipe of length $L$ is placed in a container having gas of density $\rho_1$ and an open organ pipe is placed in another container having gas of density $\rho_2$, both the gases are of same compressibility. If the frequency of tirst overtone for both the pipes is same, the length of open organ pipe is
(A) $L$
(B) $\frac{4 L}{3} \sqrt{\frac{\rho_1}{\rho_2}}$
(C) $L \sqrt{\frac{\rho_1}{\rho_2}}$
(D) $\frac{4 L}{3} \sqrt{\frac{\rho_2}{\rho_1}}$

Dheeraj Sharma

Numerade Educator

Problem 33

The frequency of sound emitted from a source in water is 600 Hz . If speed of sound in water is $1500 \mathrm{~m} / \mathrm{s}$ and in air is $300 \mathrm{~m} / \mathrm{s}$, then the frequency of sound heard above the surface of water is
(A) 300 Hz
(B) 750 Hz
(C) 600 Hz
(D) 1200 Hz

Dheeraj Sharma

Numerade Educator

Problem 34

An organ pipe opens at both ends and another organ pipe closed at one end will resonate with each other if their lengths are in the ratio of
(A) $1: 1$
(B) 1:4
(C) $2: 1$
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 35

If $n_1, n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by
(A) $n=n_1+n_2+n_3$
(B) $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$
(C) $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$
(D) $\sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}$

Dheeraj Sharma

Numerade Educator

Problem 36

A longitudinal wave sent by a ship to the bottom of the sea returns after a lapse of 2.64 s . Elasticity of water is $220 \mathrm{~kg} / \mathrm{mm}^2$ and density of sea water is $1.1 \mathrm{gm} / \mathrm{cc}$. The depth of the sea is (in metres)
(A) 1400
(B) 1848
(C) 924
(D) 700

Dheeraj Sharma

Numerade Educator

Problem 37

When the speed of sound in air is $330 \mathrm{~m} / \mathrm{s}$, the shortest air column, closed at one end that will respond to a tuning for $k$ with a frequency of 440 vibs/s has a length of (approximately).
(A) 19 cm
(B) 33 cm
(C) 38 cm
(D) 67 cm

Dheeraj Sharma

Numerade Educator

Problem 38

The speed of a longitudinal wave in a gas is given by
(A) $v=\sqrt{p / d}$
(B) $v=(1 / \gamma) \sqrt{p / d}$
(C) $v=\sqrt{\gamma_p / d}$
(D) $v=\sqrt{p / \gamma d}$

Dheeraj Sharma

Numerade Educator

Problem 39

For a wave displacement amplitude is $10^{-3} \mathrm{~m}$, density of air $1.3 \mathrm{~kg} \mathrm{~m}^{-3}$, velocity in air $340 \mathrm{~ms}^{-1}$, and frequency is 2000 Hz The intensity of wave is
(A) $5.3 \times 10^{-4} \mathrm{~W} / \mathrm{m}^{-2}$
(B) $5.3 \times 10^{-6} \mathrm{~W} / \mathrm{m}^{-2}$
(C) $3.5 \times 10^{-5} \mathrm{~W} / \mathrm{m}^{-2}$
(D) $3.5 \times 10^{-6} \mathrm{~W} / \mathrm{m}^{-2}$

Dheeraj Sharma

Numerade Educator

Problem 40

The displacement of a particle is represented by the equation $y=3 \cos \left(\frac{\pi}{2}-2 \omega t\right)$. The motion of the particle is
(A) simple harmonic with period $2 \pi / \omega$.
(B) simple harmonic with period $\pi / \omega$.
(C) periodic but not simple harmonic.
(D) non-periodic.

Dheeraj Sharma

Numerade Educator

Problem 41

The displacement of a particle is represented by the equation $y=\sin ^3$ or
The motion is
(A) non-periodic.
(B) periodic but not simple harmonic.
(C) simple harmonic with periodic $2 \pi / \omega$.
(D) simple harmonic with periodic $\pi / \omega$.

Dheeraj Sharma

Numerade Educator

Problem 42

The relation between acceleration and displacement of four particles are given below.
(A) $a_x=+2 x$
(B) $a_x=+2 x^2$
(C) $a_x=-2 x^2$
(D) $a_x=-2 x$

Dheeraj Sharma

Numerade Educator

Problem 43

Motion of an oscillating liquid column in an U-tube is
(A) periodic but not simple harmonic.
(B) non-periodic.
(C) simple harmonic and time period is independent of the density of the liquid.
(D) simple harmonic and time period is directly proportional to the density of the liquid.

Dheeraj Sharma

Numerade Educator

Problem 44

A particle is acted simultaneously by mutually perpendicular SHM $x=a \cos \omega t$ and $y=a \sin \omega x$ The trajectory of motion of the particle will be.
(A) An ellipse
(B) A parabola
(C) A circle
(D) A straight line

Dheeraj Sharma

Numerade Educator

Problem 45

The displacement of a particle varies with time according to the relation. $y=a \sin \omega t+b \cos \omega \mathrm{r}$
(A) The motion is oscillatory but not SHM
(B) The motion is SHM with amplitude $a+b$
(C) The motion is SHM with amplitude $a^2+b^2$
(D) The motion is SHM with amplitude $\sqrt{a^2+b^2}$

Dheeraj Sharma

Numerade Educator

Problem 46

For pendulums $A, B, C$, and $D$ are suspended from the same
(FIGURE CAN'T COPY)
Fig. 9.26
elastic support as shown in Fig. 9.26. $A$ and $C$ are of the same length, while $B$ is smaller than $A$, and $D$ is larger than $A$. If $A$ is given a transverse displacement,
(A) $D$ will vibrate with maximum amplitude.
(B) C will vibrate with maximum amplitude.
(C) $B$ will vibrate with maximum amplitude.
(D) All four will oscillate with equal amplitude.

Dheeraj Sharma

Numerade Educator

Problem 47

Figure 9.27 shows the circular motion of a particle. The radius of the circle, the period, sense of revolution, and the initial position are indicated in the Fig. 9.27. The SHM of the $x$-projection of the radius vector of the rotating particle $P$ is
(FIGURE CAN'T COPY)
Fig. 9.27
(A) $x(t)=B \sin \left(\frac{2 \pi t}{30}\right)$
(B) $x(t)=B \cos \left(\frac{\pi t}{15}\right)$
(C) $x(t)=B \sin \left(\frac{\pi t}{15}+\frac{\pi}{2}\right)$
(D) $x(t)=B \cos \left(\frac{\pi t}{15}+\frac{\pi}{2}\right)$

Yuva S

Numerade Educator

Problem 48

The equation of motion of a particle is $x=a \cos (\alpha t)^2$. The motion is
(A) periodic but not oscillatory.
(B) periodic and oscillatory.
(C) oscillatory but not periodic.
(D) neither periodic nor oscillatory.

Dheeraj Sharma

Numerade Educator

Problem 49

A particle executing SHM has a maximum speed of $30 \mathrm{~cm} / \mathrm{s}$ and maximum acceleration of $60 \mathrm{~cm} / \mathrm{s}^2$. The period of oscillation is
(A) $\pi \mathrm{s}$
(B) $\frac{\pi}{2}$ s
(C) $2 \pi \mathrm{~s}$
(D) $\frac{\pi}{t} \mathrm{~s}$

Dheeraj Sharma

Numerade Educator

Problem 50

In a common base mode of a transistor, the collector current is 5.488 mA for an emitter current of 5.60 mA . The value of the base current amplification factor ( $\beta$ ) will be
(A) 48
(B) 49
(C) 50
(D) 51

Dheeraj Sharma

Numerade Educator

Problem 51

Doppler effect can be observed for the following case (s)
(A) Supersonic speed
(B) Ultrasonic waves
(C) Both of these
(D) None of these

Yuva S

Numerade Educator

Problem 52

Transverse waves are generated in two uniform wires $A$ and $B$ of the same material by attaching their free ends to a vibrating source of frequency 200 Hz . The cross-section of $A$ is half that of $B$ while the tension on $A$ is twice that on $B$. The ratio of wavelengths of the transverse waves in $A$ and $B$ is
(A) $1: \sqrt{2}$
(B) $\sqrt{2}: 1$
(C) $1: 2$
(D) $2: 1$

Dheeraj Sharma

Numerade Educator

Problem 53

A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
(A) 261 Hz
(B) 258 Hz
(C) 254 Hz
(D) 251 Hz

Dheeraj Sharma

Numerade Educator

Problem 54

Two waves having the intensities in the ratio of $9: 1$ produce interference. The ratio of maximum to minimum intensity is equal to
(A) $10: 8$
(B) $9: 1$
(C) $4: 1$
(D) $2: 1$

Dheeraj Sharma

Numerade Educator

Problem 55

Velocity of sound at $0^{\circ} \mathrm{C}$ is $330 \mathrm{~m} / \mathrm{s}$. When pressure increases by 1 atmosphere and temperature increases by $1^{\circ} \mathrm{C}$, the velocity of sound
(A) Increases by $0.6 \mathrm{~m} \mathrm{~s}^{-1}$
(B) Decreases by $0.6 \mathrm{~m} \mathrm{~s}^{-1}$
(C) Increases by $60 \mathrm{~m} \mathrm{~s}^{-1}$
(D) Decreases by $60 \mathrm{~m} \mathrm{~s}^{-1}$

Dheeraj Sharma

Numerade Educator

Problem 56

A tuning fork of frequency 256 Hz is excited and held at the mouth of resonance column of frequency 254 Hz . Choose the correct statement;
(A) 2 beats per second will be heard
(B) 4 beats per second will be heard
(C) 1 beat per second will be heard
(D) No beat will be heard

Yuva S

Numerade Educator

Problem 57

The frequency of sound emitted from a source in water is 600 Hz . If speed of sound in water is $1500 \mathrm{~m} / \mathrm{s}$ and in air is $300 \mathrm{~m} / \mathrm{s}$, then the frequency of sound heard above the surface of water is
(A) 300 Hz
(B) 750 Hz
(C) 600 Hz
(D) 1200 Hz

Dheeraj Sharma

Numerade Educator

Problem 58

The equation $y=a \sin \frac{2 \pi}{\lambda}(v t-x)$ is expression for
(A) Stationary wave of single frequency along $x$-axis.
(B) A simple harmonic motion.
(C) A progressive wave of single frequency along $x$-axis.
(D) The resultant of two SHMs of slightly different frequencies.

Dheeraj Sharma

Numerade Educator

Problem 59

A SHW is represented by the equation $y(x, t)=a_0 \sin 2 \pi\left(v t-\frac{x}{\lambda}\right)$. If the maximum particle velocity is three times the wave velocity, the wavelength $\lambda$ of the wave is
(A) $\frac{\pi a_0}{3}$
(B) $\frac{2 \pi a_0}{3}$
(C) $\pi a_0$
(D) $\frac{\pi a_0}{2}$

Dheeraj Sharma

Numerade Educator

Problem 60

Two waves are represented by the equations $y_1=A \sin \left(10 \pi x-15 \pi t+\frac{\pi}{2}\right)$ and $y_2=2 A \sin (30 \pi x$ $+45 \pi t$ ). Which of the following statements is correct?
(A) The maximum particle velocity of the second wave is twice that of first.
(B) Their superposition will produce a standing wave.
(C) Maximum particle acceleration for the second wave is eighteen times that of the first wave.
(D) Their wave velocities are different.

Dheeraj Sharma

Numerade Educator

Problem 61

The equation of stationary wave in a stretched string is given by $y=5 \sin (\pi x / 3) \cos (40 \pi x)$, where $x$ and $y$
are in cm and $t$ is in sec. The separation between two adjacent nodes is
(A) 1.5 cm
(B) 3 cm
(C) 6 cm
(D) 4 cm

Yuva S

Numerade Educator

Problem 62

A string of mass $m$ and length $L$ is hung vertically from a ceiling, and a mass $M$ is attached at its lower end. A wave pulse is generated at the lower end. The velocity of the generated pulse as it moves up towards the ceiling will
(A) remain constant.
(B) increase.
(C) decrease linearly.
(D) decrease non-linearly.

Dheeraj Sharma

Numerade Educator

Problem 63

When two tuning forks $A$ and $B$ sounded together produce 4 beats per second. After filing of $A$ and waxing of $B$, the number of beats remains unaltered. If initial frequency of $A$ is 250 Hz , then the initial frequency of $B$ is
(A) 246 Hz
(B) 250 Hz
(C) 254 Hz
(D) 242 Hz

Dheeraj Sharma

Numerade Educator

Problem 64

A whistle giving out 450 Hz approaches a stationary observer at a speed of $33 \mathrm{~m} / \mathrm{s}$. The frequency heard by the observer in Hz is (speed of sound $=330 \mathrm{~m} / \mathrm{s}$ )
(A) 409
(B) 429
(C) 517
(D) 500

Dheeraj Sharma

Numerade Educator

Problem 65

Two waves represented by $y_1=10 \sin 2000 \pi t$, $y_2=20 \sin \left(2000 \pi t+\frac{\pi}{2}\right)$ are superimposed at any point at a particular instant. The amplitude of the resultant wave is
(A) 200
(B) 30
(C) $10 \sqrt{5}$
(D) $10 \sqrt{3}$

Dheeraj Sharma

Numerade Educator

Problem 66

Which of the following is wrong?
(A) Velocity of sound is more in denser medium.
(B) Sound propagation is an adiabatic process.
(C) Frequencies of standing wave and its constituent wave are same.
(D) Frequency of resonance tube will change if we change the liquid maintaining same level.

Nidhi Singhi

Numerade Educator

Problem 67

The ratio of maximum to minimum intensity at a place due to superposition of two waves represented by $y_1=3 \sin (200 t) \mathrm{cm}$ and $y_2=4 \cos (208 t) \mathrm{cm}$ will be
(A) $7: 1$
(B) $49: 1$
(C) $4: 3$
(D) $16: 9$

Dheeraj Sharma

Numerade Educator

Problem 68

2nd overtone of an open organ pipe resonates with 3rd harmonics of a closed organ pipe. The ratio of their length will be
(A) $\frac{2}{1}$
(B) $\frac{1}{2}$
(C) $\frac{6}{5}$
(D) $\frac{5}{6}$

Dheeraj Sharma

Numerade Educator

Problem 69

If $\lambda_1, \lambda_2$, and $\lambda_3$ are the wavelengths of the waves giving resonance with the fundamental, first and second overtones, respectively, of a closed organ pipe, then the ratio of wavelengths $\lambda_1: \lambda_2: \lambda_3$ is
(A) $1: 2: 3$
(B) $1: \frac{1}{3}: \frac{1}{5}$
(C) $1: 3: 5$
(D) $5: 3: 1$

Dheeraj Sharma

Numerade Educator

Problem 70

A transverse wave is described by the equation $y=y_0 \sin 2 \pi\left(f t-\frac{x}{\lambda}\right)$. The maximum particle velocity is equal to four times the wave velocity if
(A) $\lambda=\frac{\pi y_0}{4}$
(B) $\lambda=\frac{\pi y_0}{2}$
(C) $\lambda=\pi y_0$
(D) $\lambda=2 \pi y_0$

Dheeraj Sharma

Numerade Educator

Problem 71

Two waves are represented by the following equations $y_1=5 \sin 2 \pi(10 t-0.1 x) ; y_2=10 \sin 2 \pi(20 t-0.2 x)$ Ratio of intensities $I_2 / I_1$ will be
(A) 1
(B) 2
(C) 4
(D) 16

Dheeraj Sharma

Numerade Educator

Problem 72

For the stationary wave $y=4 \sin \left(\frac{\pi x}{15}\right) \cos (96 \pi t)$, ( $x$ and $y$ are in cm and $t$ in second) the distance between a node and the next anti-nodes is
(A) 7.5 cm
(B) 15 cm
(C) 22.5 cm
(D) 30 cm

Dheeraj Sharma

Numerade Educator

Problem 73

The equation of a plane progressive wave is $y=0.09 \sin 8 \pi\left(t-\frac{x}{20}\right)$. When it is reflected at rigid support, its amplitude becomes two-third of its previous value. The equation of the reflected wave is
(A) $y=-0.09 \sin 8 \pi\left(t-\frac{x}{20}\right)$
(B) $y=-0.06 \sin 8 \pi\left(t-\frac{x}{20}\right)$
(C) $y=0.06 \sin 8 \pi\left(t+\frac{x}{20}\right)$
(D) $y=-0.06 \sin 8 \pi\left(t+\frac{x}{20}\right)$

Yuva S

Numerade Educator

Problem 74

If the temperature is raised by 1 K from 300 K the percentage change in the speed of sound in a gaseous mixture is ( $R=8.31 \mathrm{~J} / \mathrm{mole}-\mathrm{K}$ )
(A) $0.167 \%$
(B) $2 \%$
(C) $1 \%$
(D) $0.334 \%$

Ajay Singhal

Numerade Educator

Problem 75

A wave is represented by the equation: $y=0.1 \sin (100 \pi t-k x)$. If wave velocity is $100 \mathrm{~m} / \mathrm{s}$, its wave number is equal to
(A) $1 \mathrm{~m}^{-1}$
(B) $2 \mathrm{~m}^{-1}$
(C) $\pi \mathrm{m}^{-1}$
(D) $2 \pi \mathrm{~m}^{-1}$

Yuva S

Numerade Educator

Problem 76

A racing car moving towards a cliff sounds its hom. The driver observes that the sound reflected from the cliff has a frequency one octave higher than the actual frequency of the horn. If $v$ is the velocity of sound, then the velocity of the car is
(A) $\frac{v}{2}$
(B) $\frac{v}{\sqrt{2}}$
(C) $\frac{v}{4}$
(D) $\frac{v}{3}$

Dheeraj Sharma

Numerade Educator

Problem 77

The power of sound from the speaker of a radio is 20 mW . By turning the knob of volume control, the power of sound is increased to 400 mW . The power increase in dB as compared to the original power is $\left(\log _{10} 2=0.3\right)$
(A) 1.3 dB
(B) 3.1 dB
(C) 13 dB
(D) 30.1 dB

Dheeraj Sharma

Numerade Educator

Problem 78

For a carrier frequency of 100 kHz and a modulating frequency of 5 kHz , what is the band width of AM transmission?
(A) 5 kHz
(B) 10 kHz
(C) 20 kHz
(D) 200 kHz

Dheeraj Sharma

Numerade Educator

Problem 79

The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is $0.5 \pi$. The wave velocity is
(A) $144 \mathrm{~m} / \mathrm{s}$
(B) $256 \mathrm{~m} / \mathrm{s}$
(C) $384 \mathrm{~m} / \mathrm{s}$
(D) $720 \mathrm{~m} / \mathrm{s}$

Ajay Singhal

Numerade Educator

Problem 80

The end correction of a resonance column is 1.0 cm . If the shortest length resonating with a tuning fork is 14.0 cm , the next resonating length is
(A) 44 cm
(B) 45 cm
(C) 46 cm
(D) 47 cm

Dheeraj Sharma

Numerade Educator

Problem 81

A ball is dropped into a well in which the water level is at a depth $h$ below the top $(t=0)$. If the speed of sound be $c$, then the time after which the splash is heard will be given by
(A) $h\left[\sqrt{\frac{2}{g h}}+\frac{1}{c}\right]$
(B) $h\left[\sqrt{\frac{2}{g h}}-\frac{1}{c}\right]$
(C) $h\left[\frac{2}{g}+\frac{1}{c}\right]$
(D) $h\left[\frac{2}{g}-\frac{1}{c}\right]$

Dheeraj Sharma

Numerade Educator

Problem 82

A sonometer wire is in unison with a tuning fork in fundamental mode. Keeping the same tension, the length of wire between the bridges is doubled. The tuning fork can still be in resonance with the wire, provided the wire now vibrates in
(A) 4 segments
(B) 6 segments
(C) 3 segments
(D) 2 segments

Dheeraj Sharma

Numerade Educator

Problem 83

The driver of a car approaching a vertical wall notices that the frequency of the horn of his car changes from 400 Hz to 450 Hz after being reflected from the wall. Assuming speed of sound to be $340 \mathrm{~ms}^{-1}$, the speed of approach of car towards the wall is
(A) $10 \mathrm{~ms}^{-1}$
(B) $20 \mathrm{~ms}^{-1}$
(C) $30 \mathrm{~ms}^{-1}$
(D) $40 \mathrm{~ms}^{-1}$

Dheeraj Sharma

Numerade Educator

Problem 84

Following are equations of four waves:
(i) $y_1=a \sin \omega\left(t-\frac{x}{v}\right)$
(ii) $y_2=a \sin \omega\left(t+\frac{x}{v}\right)$
(iii) $\mathrm{z}_1=a \sin \varphi\left(t-\frac{x}{v}\right)$
(iv) $z_2=a \cos \omega\left(t+\frac{x}{v}\right)$

Which of the following statement is correct?
(A) On superposition of waves (i) and (iii), a traveling wave having amplitude $a$ will be formed.
(B) Superposition of waves (ii) and (iii) is not possible.
(C) On superposition of (i) and (ii), a stationary wave having amplitude $a \sqrt{2}$ will be formed.
(D) On superposition of (iii) and (iv), a transverse stationary wave will be formed.

Nidhi Singhi

Numerade Educator

Problem 85

A wave is represented by the equation: $y=0.1 \sin (100 \pi t-k x)$. If wave velocity is $100 \mathrm{~m} / \mathrm{s}$, its wave number is equal to
(A) $1 \mathrm{~m}^{-1}$
(B) $2 \mathrm{~m}^{-1}$
(C) $\pi \mathrm{m}^{-1}$
(D) $2 \pi \mathrm{~m}^{-1}$

Yuva S

Numerade Educator

Problem 86

A stretched wire of some length under a tension is vibrating with its fundamental frequency. Its length is decreased by $45 \%$ and tension is increased by $21 \%$. Now its fundamental frequency (assuming linear mass density remains the same)
(A) increases by $50 \%$
(B) increases by $100 \%$
(C) decreases by $50 \%$
(D) decreases by $25 \%$

Dheeraj Sharma

Numerade Educator

Problem 87

Two trains, one coming towards and another going away from an observer both at $4 \mathrm{~m} / \mathrm{s}$ produce a whistle simultaneously of frequency 300 Hz . The number of beats heard by observer will be (velocity of sound = $340 \mathrm{~m} / \mathrm{s}$ )
(A) 5
(B) 6
(C) 7
(D) 12

Dheeraj Sharma

Numerade Educator

Problem 88

Speed of sound wave is $v$. If a reflector moves towards a stationary source emitting waves of frequency $f$ with speed $u$, the frequency of reflected wave will be
(A) $\frac{v-u}{v+u} f$
(B) $\frac{v+u}{v} f$
(C) $\frac{v+u}{v-u} f$
(D) $\frac{v-u}{v} f$

Dheeraj Sharma

Numerade Educator

Problem 89

The intensity of sound after passing through a slab decreases by $20 \%$. On passing through two such slabs, the intensity will decrease by
(A) $50 \%$
(B) $40 \%$
(C) $36 \%$
(D) $30 \%$

Dheeraj Sharma

Numerade Educator

Problem 90

The length of a sonometer wire $A B$ is 110 cm . Where should the two bridges be placed from $A$ to divide the wire in three segments whose fundamental frequencies are in the ratio of $1: 2: 3$ ?
(A) $30 \mathrm{~cm}, 90 \mathrm{~cm}$
(B) $60 \mathrm{~cm}, 90 \mathrm{~cm}$
(C) $40 \mathrm{~cm}, 70 \mathrm{~cm}$
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 91

A sound wave of wavelength $\lambda$ travels towards the right horizontally with a velocity $v$. It strikes and reflects from a vertical plane surface, traveling at a speed v towards the leff. The number of positive crests striking in a time interval of three seconds on the wall is
(A) $3(V+v) / \lambda$
(B) $3(V-v) / \lambda$
(C) $(V+v) / 3 \lambda$
(D) $(V-v) / 3 \lambda$

Dheeraj Sharma

Numerade Educator

Problem 92

A stationary source of sound is emitting waves of frequency 30 Hz towards a stationary wall. There is an observer standing between the source and the wall. If the wind blows from the source to the wall with a speed $30 \mathrm{~m} / \mathrm{s}$, then the number of beats heard by the
observer is (velocity of sound with respect to wind is $330 \mathrm{~m} / \mathrm{s}$ )
(A) 10
(B) 3
(C) 6
(D) Zero

Dheeraj Sharma

Numerade Educator

Problem 93

The driver of a car traveling with speed $30 \mathrm{~m} / \mathrm{s}$ towards a hill sound a horn of frequency 600 Hz If the velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$, the frequency of reflected sound as heard by the driver is
(A) 720 Hz
(B) 555.5 Hz
(C) 550 Hz
(D) 500 Hz

Dheeraj Sharma

Numerade Educator

Problem 94

A wave disturbance in a medium is described by $y(x, t)=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)$
where $x$ and $y$ are in meter and $t$ is in second. Then
(A) First node occurs at $x=0.15 \mathrm{~m}$.
(B) First anti-node occurs at $x=0.3 \mathrm{~m}$.
(C) The speed of interfering waves is $5.0 \mathrm{~m} / \mathrm{s}$.
(D) The wavelength is 0.5 m .

Dheeraj Sharma

Numerade Educator

Problem 95

A train is moving with a constant speed along a circular track. The engine of the train emits a sound of frequency $f$. The frequency heard by the guard at rear end of the train
(A) is less than $f$.
(B) is greater than $f$.
(C) is equal to $f$.
(D) may be greater than, less than or equal tof depending on the factors like speed of train, length of train and radius of circular track.

Dheeraj Sharma

Numerade Educator

Problem 96

A massless rod $A B$ of length $L$ is hung from two identical wires of equal length. A block of mass $m$ is attached at point $O$ on the rod as shown in Fig. 9.28; the value of $A O$ so that a tuning fork excites the wire on the left in its fundamental tone and the wire on the right in its second harmonic is
(FIGURE CAN'T COPY)
Fig. 9.28
(A) $\frac{4 L}{5}$
(B) $\frac{L}{4}$
(C) $\frac{3 L}{4}$
(D) $\frac{L}{5}$

Dheeraj Sharma

Numerade Educator

Problem 97

The frequency of a sonometer wire is 100 Hz . When the weights producing the tensions are completely immersed in water, the frequency becomes 80 Hz and on immersing the weights in a certain liquid, the frequency becomes 60 Hz . The specific gravity of the liquid is
(A) 1.42
(B) 1.77
(C) 1.82
(D) 1.21

Dheeraj Sharma

Numerade Educator

Problem 98

A siren creates a sound level of 60 dB at a location of 500 m from the speaker. The siren is powered by a battery that delivers a total energy of 1 kJ . The efficiency of siren is $30 \%$. The total time for which the siren sound is
(A) 95 s
(B) 95.5 s
(C) 96 s
(D) 96.5 s

Dheeraj Sharma

Numerade Educator

Problem 99

A siren placed at a railway platform is emitting sound of frequency 5 kHz A passenger sitting in a moving train $A$ records a frequency of 5.5 kHz , while the train approaches the siren. During his return journey in a different train $B$, he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train $B$ to that train $A$ is
(A) $242 / 252$
(B) 2
(C) $5 / 6$
(D) $11 / 6$

Dheeraj Sharma

Numerade Educator

Problem 100

A stationary wave is set up on a string fixed at both ends. The distance between two consecutive nodes is 18 cm at a particular mode of vibration and for the next higher mode of vibration in the same string the distance between two consecutive nodes is 16 cm . The length of string is
(A) 144 cm
(B) 140 cm
(C) 36 cm
(D) 32 cm

Dheeraj Sharma

Numerade Educator

Problem 101

Two waves are represented as $y_1=2 a \sin (\alpha x+\pi / 6)$ and $y_2=-2 a \cos \left(\omega x-\frac{\pi}{6}\right)$. The phase difference between the two waves is
(A) $\frac{\pi}{3}$
(B) $\frac{4 \pi}{3}$
(C) $\frac{3 \pi}{3}$
(D) $\frac{5 \pi}{6}$

Dheeraj Sharma

Numerade Educator

Problem 102

Two cars are mowing towards each other with same speed, if frequency of hom blown by driver of one car and frequency appeared to another driver differ by $4 \%$ from the frequency of horn, then find out speed of cars (speed of sound $=300 \mathrm{~m} / \mathrm{s}$ )
(A) $12 \mathrm{~m} / \mathrm{s}$
(B) $6.6 \mathrm{~m} / \mathrm{s}$
(C) $4.2 \mathrm{~m} / \mathrm{s}$
(D) $5.9 \mathrm{~m} / \mathrm{s}$

Kumari Shilpi

Numerade Educator

Problem 103

If the velocity of sound in air is $320 \mathrm{~m} / \mathrm{s}$, then (maximum and minimum audible frequency are 20 Hz and 20000 Hz , respectively), the maximum and minimum lengths of a closed pipe that would produce a just audible sound are
(A) 2.6 m and $3.6 \times 10^{-3} \mathrm{~m}$
(B) 4 m and $4.2 \times 10^{-3} \mathrm{~m}$
(C) 3 m and $3 \times 10^{-3} \mathrm{~m}$
(D) 4 m and $4 \times 10^{-3} \mathrm{~m}$

Dheeraj Sharma

Numerade Educator

Problem 104

Four sources of sound each of sound level 10 dB are sounded together; the resultant intensity level will be $(\log 2=0.3)$
(A) 40 dB
(B) 26 dB
(C) 16 dB
(D) 13 dB

Dheeraj Sharma

Numerade Educator

Problem 105

The air in an open pipe of length 36 cm long is vibrating with 2 nodes and 2 antinodes. The temperature of the air inside the pipe is $51^{\circ} \mathrm{C}$. What is the wavelength of waves produced in air outside the tube where the temperature of air is $16^{\circ} \mathrm{C}$ ?
(A) 32.1 cm
(B) 68 cm
(C) 34 cm
(D) 10.2 cm

Dheeraj Sharma

Numerade Educator

Problem 106

A dog while barking delivers about 1 mW of power. If this power is uniformly over a hemispherical area, what is the sound level at a distance $\frac{5}{\sqrt{\pi}} \mathrm{~m}$ ?
(A) 73 dB
(B) 96 dB
(C) 32 dB
(D) 40 dB

Dheeraj Sharma

Numerade Educator

Problem 107

Two identical wires are stretched by the same tension of 100 N and each emits a note of frequency 200 Hz . If tension in one wire is increased by 1 N , the number of beats heard per second when the wires are plucked is
(A) 2
(B) 1
(C) 3
(D) 4

Dheeraj Sharma

Numerade Educator

Problem 108

An open organ pipe is vibrating in its fifth overtone. The distance between two consecutive points where pressure amplitude is $\frac{1}{\sqrt{2}}$ times pressure amplitude at pressure antinodes is 40 cm . Then the length of organ pipe is (Neglect end correction)
(A) 3 m
(B) 3.6 m
(C) 4.2 m
(D) 4.8 m

Yuva S

Numerade Educator

Problem 109

A particle is subjected to two SHM along $x$ and $y$ axis, according to $x=6 \sin 100 \pi t$ and $y=8 \cos$ $\left(100 \pi t-\frac{\pi}{2}\right)$, then motion of particle is
(A) Ellipse
(B) Circle
(C) Straight line
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 110

Two wave pulses are generated in a string. One of the pulses is given by equation $y_1=A \sin (c u r-k x)$. If average power transmitted by both the pulses along the string are same and is given by $P=\frac{T A^2 \omega^2}{2 v}$, where $T$ is the tension in the string, $A$ is amplitude of a pulse, $\omega$ is angular frequency of the source, and v is wave velocity, then which one of the following equations may represent the other wave pulse?
(A) $y_2=\frac{A}{\sqrt{2}} \sin (2 \omega k-k x)$
(B) $y_2=\frac{A}{\sqrt{2}} \sin (c \mathrm{or}-2 k x)$
(C) $y_2=2 A \sin \left(\frac{\omega t}{2}-k x\right)$
(D) $y_2=2 A \sin \left(\frac{k x}{2}-\frac{k x}{2}\right)$

Mohd Shahab

Numerade Educator

Problem 111

A knife edge divides a sonometer wire into two parts, which differ in length by 2 mm . The whole length of the wire is 1 metre. The two parts of the string when sounded together produce one beat per second, then the frequencies of the smaller and longer parts are
(A) 250.5 and 249.5
(B) 249.5 and 250.5
(C) 124.5 and 125.5
(D) 125.5 and 124.5

Dheeraj Sharma

Numerade Educator

Problem 112

Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of the velocity of sound in the mixture to that of oxygen is
(A) $\sqrt{\frac{1}{8}}$
(B) $\sqrt{\frac{32}{17}}$
(C) $\sqrt{\frac{17}{32}}$
(D) $\sqrt{8}$

Dheeraj Sharma

Numerade Educator

Problem 113

A whistle emitting a sound of frequency 440 Hz is tied to a string of 1.5 m length and rotated with an angular velocity of $20 \mathrm{rad} / \mathrm{sec}$ in the horizontal plane. Then the range of frequencies heard by an observer stationed at a large distance from the whistle will be $(v=330 \mathrm{~m} / \mathrm{s})$
(A) 400.0 Hz to 487.0 Hz
(B) 403.3 Hz to 480.0 Hz
(C) 400.0 Hz to 480.0 Hz
(D) 403.3 Hz to 484.0 Hz

Dheeraj Sharma

Numerade Educator

Problem 114

The frequency and wavelength of the wave shown in Fig. 9.29 are (wave speed $=320 \mathrm{~m} / \mathrm{s}$ )
(A) $8 \mathrm{~cm}, 400 \mathrm{~Hz}$
(B) $80 \mathrm{~cm}, 40 \mathrm{~Hz}$
(C) $8 \mathrm{~cm}, 4000 \mathrm{~Hz}$
(D) $40 \mathrm{~cm}, 8000 \mathrm{~Hz}$
(FIGURE CAN'T COPY)
Fig. 9.29

Dheeraj Sharma

Numerade Educator

Problem 115

Which frequency can be reflected from ionosphere?
(A) 5 MHz
(B) 6 GHz
(C) 5 KHz
(D) 500 MHz

Nishant Kumar

Numerade Educator

Problem 116

The range of frequencies allotted for FM radio is
(A) 88 to 108 kHz
(B) 88 to 108 MHz
(C) 47 to 230 kHz
(D) 47 to 230 MHz

Kyle Godbey

Numerade Educator

Problem 117

A stretched sonometer wire is in unison with a tuning fork. When the length of the wire is increased by $2 \%$, the number of beats heard per second is 5 . Then the frequency of the fork is
(A) 245 Hz
(B) 250 Hz
(C) 255 Hz
(D) 260 Hz

Dheeraj Sharma

Numerade Educator

Problem 118

A transverse wave is travelling along a string from left to right. Fig. 9.30 represents the shape of the string at a given instant. At this instant, among the following, choose the wrong statement
(A) Points $D, E, F$ have upwards positive velocity
(B) Points $A, B$, and $H$ have downwards negative velocity
(C) Point $C$ and $G$ have zero velocity
(D) Points $A$ and $E$ have minimum velocity
(FIGURE CAN'T COPY)
Fig. 9.310

Ajay Singhal

Numerade Educator

Problem 119

Let a disturbance $y$ be propagated as a plane wave along the $x$-axis. The wave profiles at the instants $t=t_1$ and $t=t_2$ are represented, respectively, as $y_1=f\left(x_1-v t_1\right)$ and $y_2=f\left(x_2-v t_2\right)$. The wave is propagating without change of shape.
(A) The velocity of the wave is $2 v$.
(B) The velocity of the wave is $v=\frac{x_2-x_1}{t_2}$.
(C) The particle velocity is $v_p=v$.
(D) None of these.

Mohd Shahab

Numerade Educator

Problem 120

A tuning fork of frequency 340 Hz is vibrated just above a cylindrical tube of length 120 cm . Water is slowly poured in the tube. If the speed of sound is 340 $\mathrm{m} / \mathrm{s}$, then the minimum height of water required for resonance is
(A) 25 cm
(B) 45 cm
(C) 75 cm
(D) 95 cm

Dheeraj Sharma

Numerade Educator

Problem 121

Two waves traveling in opposite directions produce a standing wave. The individual wave functions are given by $y_1=4 \sin (3 x-2 t) \mathrm{cm}$ and $y_2=4 \sin (3 x+2 t) \mathrm{cm}, x$ and $y$ are in cm . Now, select the correct statement:
(A) Nodes are formed at $x=0, \frac{\pi}{6}, \frac{\pi}{2}, \frac{5 \pi}{6}, \frac{7 \pi}{6} \ldots$
(B) Anti-nodesareformedat $x=0, \frac{\pi}{6}, \frac{\pi}{2}, \frac{5 \pi}{6}, \frac{7 \pi}{6} \ldots$.
(C) Nodes are formed at $x=0, \frac{\pi}{3}, \frac{2 \pi}{3}, \pi, \frac{4 \pi}{3} \ldots$
(D) Anti-nodes are formed at $x=\frac{\pi}{3}, \frac{2 \pi}{3}, \pi, \frac{4 \pi}{3} \ldots$

Dheeraj Sharma

Numerade Educator

Problem 122

The area of region covered by the TV broadcast by a TV tower of 100 m height will be (radius of the earth $=6.4 \times 10^6 \mathrm{~m}$ )
(A) $12.8 \pi \times 10^8 \mathrm{~km}^2$
(B) $1.28 \pi \times 10^3 \mathrm{~km}^2$
(C) $0.64 \pi \times 10^3 \mathrm{~km}^2$
(D) $1.28 \times 10^3 \mathrm{~km}^2$

Dheeraj Sharma

Numerade Educator

Problem 123

For a particular mode of vibration of string, the distance between two consecutive nodes is 18 cm . For the next higher mode, the distance becomes 16 cm . The length of the string is
(A) 18 cm
(B) 16 cm
(C) 144 cm
(D) 72 cm

Dheeraj Sharma

Numerade Educator

Problem 124

An organ pipe of length 33 cm closed at one end vibrates in its Sth overtone. If amplitude of a particle at anti-nodes is 6 mm , then amplitude of a particle which is at a distance 18 cm from closed end is
(A) 3 cm
(B) $3 \sqrt{2} \mathrm{~mm}$
(C) 2 mm
(D) Zero

Dheeraj Sharma

Numerade Educator

Problem 125

A stationary source of sound is emitting waves of frequency 30 Hz towards a stationary wall. There is an observer standing between the source and the wall. If the wind blows from the source to the wall with a speed $30 \mathrm{~m} / \mathrm{s}$ then the number of beats heard by the observer is (velocity of sound with respect to wind is $330 \mathrm{~m} / \mathrm{s}$ )
(A) 10
(B) 3
(C) 6
(D) Zero

Dheeraj Sharma

Numerade Educator

Problem 126

Two sources of sound are moving in opposite directions with velocities $v_1$ and $v_2\left(v_1>v_2\right)$. Both are mowing away from a stationary observer. The frequency of both the source is 1700 Hz . What is the value of $\left(v_1-v_2\right)$ so that the beat frequency observed by the observer is $10 \mathrm{~Hz} . v_{\text {eand }}=340 \mathrm{~m} / \mathrm{s}$ and assume that $v_1$ and $v_2$ both are very much less than $v_{\text {sened }}$.
(A) $1 \mathrm{~m} / \mathrm{s}$
(B) $2 \mathrm{~m} / \mathrm{s}$
(C) $3 \mathrm{~m} / \mathrm{s}$
(D) $4 \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 127

A 3.6 m long vertical pipe is filled completely with a liquid. A small hole is drilled at the base of the pipe due to which liquids starts leaking out. This pipe resonates with a tuning fork. The first two resonances occur when height of water column is 3.22 m and 2.34 m , respectively. The area of cross-section of pipe is
(A) $25 \pi \mathrm{~cm}^2$
(B) $100 \mathrm{mcm}^2$
(C) $200 \pi \mathrm{~cm}^2$
(D) $400 \pi \mathrm{~cm}^2$

Dheeraj Sharma

Numerade Educator

Problem 128

An organ pipe of length $3.9 \pi \mathrm{~m}$ open at both ends is driven to third harmonic standing wave pattern. If the maximum amplitude of pressure oscillations is $1 \%$ of mean atmospheric pressure ( $P_0=105 \mathrm{~N} / \mathrm{m}^2$ ), the maximum displacement of the particle from mean position will be (Velocity of sound $=200 \mathrm{~m} / \mathrm{s}$ and density of air $=1.3 \mathrm{~kg} / \mathrm{m}^3$ )
(A) 2.5 cm
(B) 5 cm
(C) 1 cm
(D) 2 cm

Dheeraj Sharma

Numerade Educator

Problem 129

Two trains ( $A$ and $B$ ) are moving towards each other on two parallel tracks at the same speed with respect to the ground. The whistle of train $A$ blows. In which of the following cases, the frequency of the sound heard by a passenger on the other train $B$ will be greatest?
(A) If the air is still.
(B) If a wind blows in the same direction and at the same speed as the other train $B$.
(C) If a wind blows in the opposite direction and at the same speed as the other train $B$.
(D) Frequency will be same in the above three cases.

Dheeraj Sharma

Numerade Educator

Problem 130

A tuning fork of known frequency is held at the open end of a long tube, which is dipped into water as shown in Fig. 9.31. The tuning fork of frequency 165 Hz resonates with air column, when air column is vibrating in 1st and 3 rd harmonic with air column lengths $l_1=(50 \pm 0.5) \mathrm{cm}$ and $l_2=(150 \pm 0.1) \mathrm{cm}$, respectively. The speed of sound in air column is
(A) $(320 \pm 1.98) \mathrm{m} / \mathrm{s}$
(B) $(330 \pm 1.98) \mathrm{m} / \mathrm{s}$
(C) $(320 \pm 0.99) \mathrm{m} / \mathrm{s}$
(D) $(330 \pm 0.99) \mathrm{m} / \mathrm{s}$
(FIGURE CAN'T COPY)
Fig. 9.31

Hunza Gilgit

Numerade Educator

Problem 131

A string of length $l$ is fixed at both ends. It is vibrating in its third overtone. Maximum amplitude of the particles on the string is $A$. The amplitude of the particle at a distance $1 / 3$ from one end is
(A) $A$
(B) 0
(C) $\frac{\sqrt{3 A}}{2}$
(D) $\frac{A}{2}$

Dheeraj Sharma

Numerade Educator

Problem 132

A closed organ pipe of length 99.4 cm is vibrating in its first overtone and in always resonance with a tuning fork having frequency $f=(300-2 t) \mathrm{Hz}$, where $t$ is time in second. The rate by which radius of organ pipe changes when its radius is 1 cm is (speed of sound in organ pipe $=320 \mathrm{~m} / \mathrm{s}$ )
(A) $\frac{1}{72} \mathrm{~m} / \mathrm{s}$
(B) $\frac{1}{36} \mathrm{~m} / \mathrm{s}$
(C) $\frac{1}{18} \mathrm{~m} / \mathrm{s}$
(D) $\frac{1}{9} \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 133

A closed organ pipe of length $L$ is vibrating in its first overtone. There is a point $Q$ inside the pipe at a distance $7 L / 9$ from the open end. The ratio of pressure amplitude at $Q$ to the maximum pressure amplitude in the pipe is
(A) $1: 2$
(B) $2: 1$
(C) $1: 1$
(D) $2: 3$

Ankur S

Numerade Educator

Problem 134

The general wave equation can be written as $y=m(x-v t), x \in\left[v t, v t+\frac{a}{2}\right] ;$ $y=-m[(x-v t)-a], x \in\left[v t+\frac{a}{2}, w+a\right]$

Sheh Lit Chang

University of Washington

Problem 135

Two identical sources $P$ and $Q$ emit waves in same phase and of same wavelength. Spacing between $P$ and $Q$ is $3 \lambda$. The maximum distance from $P$ along the $x$-axis at which a minimum intensity occurs is given by
(A) $6.58 \lambda$
(B) $2.25 \lambda$
(C) $8.75 \lambda$
(D) $0.55 \lambda$

Dheeraj Sharma

Numerade Educator

Problem 136

Two longitudinal waves propagating in the $X$ and $Y$ directions superimpose. The wave equations are as below $\psi_1=A \cos (\omega x-k x)$ and $\psi_2=A \cos (\omega t-k y)$. Trajectory of the motion of a particle lying on the line $y=x+\frac{(2 n+1) \lambda}{2}$ will be
(A) Straight line
(B) Circle
(C) Ellipse
(D) None of these

Dheeraj Sharma

Numerade Educator

Problem 137

Radio waves of wavelength $\lambda$ at an angle $\theta$ to vertical are received by a radar after reflecting from a nearby water surface and directly. If the radar records a maximum intensity, the height of antenna $h$ from water surface can be
(A) $\frac{\lambda}{2 \cos \theta}$
(B) $\frac{\lambda}{2 \sin \theta}$
(C) $\frac{\lambda}{4 \sin \theta}$
(D) $\frac{\lambda}{4 \cos \theta}$

Nidhi Singhi

Numerade Educator

Problem 138

Water waves produced by a motorboat sailing in water are
(A) neither longitudinal no transverse.
(B) both longitudinal and transverse.
(C) only longitudinal.
(D) only transverse.

Ankur S

Numerade Educator

Problem 139

Sound waves of wavelength $\lambda$ travelling in a medium with a speed of $v \mathrm{~m} / \mathrm{s}$ enter into another medium where its speed in $2 \mathrm{vm} / \mathrm{s}$. Wavelength of sound waves in the second medium is
(A) $\lambda$
(B) $\frac{\lambda}{2}$
(C) $2 \lambda$
(D) $4 \lambda$

Dheeraj Sharma

Numerade Educator

Problem 140

Speed of sound wave in air
(A) is independent of temperature.
(B) increases with pressure.
(C) increases with increase in humidity.
(D) decreases with increase in humidity.

Dheeraj Sharma

Numerade Educator

Problem 141

Change in temperature of the medium changes
(A) frequency of sound waves.
(B) amplitude of sound waves.
(C) wavelength of sound waves.
(D) loudness of sound waves.

Dheeraj Sharma

Numerade Educator

Problem 142

With propagation of longitudinal waves through a medium, the quantity transmitted is
(A) Matter
(B) Energy
(C) Energy and matter
(D) Energy, matter, and momentum

Dheeraj Sharma

Numerade Educator

Problem 143

Which of the following statements are true for wave motion?
(A) Mechanical transverse waves can propagate through all mediums.
(B) Longitudinal waves can propagate through solids only.
(C) Mechanical transverse waves can propagate through solids only.
(D) Longitudinal waves can propagate through vacuum.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 144

A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions,
(A) density remains constant.
(B) Boyle's law is obeyed.
(C) bulk modulus of air oscillates.
(D) there is no transfer of heat.

Hunza Gilgit

Numerade Educator

Problem 145

Equation of a plane progressive wave is given by $y=0.6 \sin 2 \pi\left(t-\frac{x}{2}\right)$. On reflection from a denser medium, its amplitude becomes $\frac{2}{3}$ of the amplitude of the incident wave. The equation of the reflected wave is (A) $y=0.6 \sin 2 \pi\left(t+\frac{x}{2}\right)$
(B) $y=-0.4 \sin 2 \pi\left(t+\frac{x}{2}\right)$
(C) $y=0.4 \sin 2 \pi\left(t+\frac{x}{2}\right)$
(D) $y=-0.4 \sin 2 \pi\left(t-\frac{x}{2}\right)$

Dheeraj Sharma

Numerade Educator

Problem 146

A string of mass 2.5 kg is under tension of 200 N . The length of the stretched string is 20.0 m . If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in
(A) 1 s
(B) 0.5 s
(C) 2 s
(D) Data given is insufficient

Hunza Gilgit

Numerade Educator

Problem 147

A train whistling at constant frequency is moving towards a station at a constant speed $v$. The train goes past a stationary observer on the station. The frequency $n$ of the sound as heard by the observer is plotted as a function of time $t$ (Fig.9.32). Identify the expected curve.
(FIGURE CAN'T COPY)

Nidhi Singhi

Numerade Educator

Problem 148

A particle moves on the $x$-axis as per the equation $x=x_0 \sin ^2 e r$. The motion is simple harmonic
(A) With amplitude $x_0$
(B) With amplitude $2 r_0$
(C) With time period $\frac{2 \pi}{\omega}$
(D) With time period $\frac{\pi}{\omega}$

Hunza Gilgit

Numerade Educator

Problem 149

A particle starts SHM at time $t=0$. Its amplitude is $A$ and angular frequency is $\omega$. At time $t=0$, its kinetic energy is $\frac{E}{4}$, where $E$ is total energy. Assuming potential energy to be zero at mean position, the displacement-time equation of the particle can be written as
(A) $x=A \cos \left(\omega t+\frac{\pi}{6}\right)$
(B) $x=A \sin \left(\omega x+\frac{\pi}{3}\right)$
(C) $x=A \sin \left(\omega r-\frac{2 \pi}{3}\right)$
(D) $x=A \cos \left(\cot -\frac{\pi}{6}\right)$

Hunza Gilgit

Numerade Educator

Problem 150

A particle moves along the $x$-axis as per the equation $x=4+3 \sin (2 \pi t)$. Here $x$ is in cm and $t$ in seconds. Select the correct alternative(s)
(A) The motion of the particle is simple harmonic with mean position at $x=0$.
(B) The motion of the particle is simple harmonic with mean position at $x=4 \mathrm{~cm}$.
(C) The motion of the particle is simple harmonic with mean position at $x=-4 \mathrm{~cm}$.
(D) Amplitude of oscillation is 3 cm .

Hunza Gilgit

Numerade Educator

Problem 151

If $y, u$, and $a$ represent displacement, velocity, and acceleration at any instant for a particle executing SHM, which of the following statements are true?
(A) vand $y$ may have same direction.
(B) $v$ and $a$ have same direction twice in each cycle.
(C) $a$ and $y$ may have same direction.
(D) $a$ and $v$ never have same direction.

Hunza Gilgit

Numerade Educator

Problem 152

A book with many printing errors contains four different expressions for the displacement $y$ of a particle executing SHM. Which of the following expressions are wrong?
(A) $y=A \sin \left(\frac{2 \pi t}{T}\right)$
(B) $y=A \sin v t$
(C) $y=\frac{A}{T} \sin \left(\frac{t}{A}\right)$
(D) $y=\frac{A}{\sqrt{2}}(\sin \varphi x+\cos \varphi x)$

Hunza Gilgit

Numerade Educator

Problem 153

If force $(F)$ versus displacement $(x)$ and displacement $(x)$ versus time graph of a particle performing SHM is shown in Fig. 9.33. Then choose correct statement.
(FIGURE CAN'T COPY)
Fig. 9.33
(A) Mass of the particle $\frac{160}{\pi^2} \mathrm{~kg}$.
(B) Mass of the particle $160 \pi^2 \mathrm{~kg}$.
(C) Maximum kinetic energy of particle is 80 J .
(D) Maximum kinetic energy of particle is 40 J .

Hunza Gilgit

Numerade Educator

Problem 154

Two SHMs are represented by the equations:

$$
\begin{aligned}
& Y_1=10 \sin [3 \pi+\pi / 4] \\
& Y_2=5[\sin 3 \pi+\sqrt{3} \cos 3 \pi]
\end{aligned}
$$

(A) The amplitude ratio of the two SHM is $1: 1$.
(B) The amplitude ratio of the two SHM is $2: 1$.
(C) Time periods of both the SHMs are equal.
(D) Time periods of two SHMs are different.

Hunza Gilgit

Numerade Educator

Problem 155

In Fig. 9.34, the block of mass $m$ is in equilibrium initially. Now the block is pushed down by a slight distance and released (springs are identical and massless having spring constant $k$ ). Then
(A) Initial elongation of the spring is $\frac{m g}{2 k \cos \theta}$.
(B) Initial elongation of the spring is $\frac{m g}{2 k \cos ^2 \theta}$.
(C) Time period of oscillation of the block is

$$
2 \pi \sqrt{\frac{m}{2 k \cos ^2 \theta}}
$$
(D) Time period of oscillation of the block is $2 \pi \sqrt{\frac{m}{2 k}}$.
(FIGURE CAN'T COPY)
Fig. 9.34

Hunza Gilgit

Numerade Educator

Problem 156

Two pendulums of same amplitude but time period 3 s and 7 s start oscillating simultaneously from two opposite extreme positions. After how much time they will be in phase
(A) $\frac{21}{8} \mathrm{~s}$
(B) $\frac{21}{4} \mathrm{~s}$
(C) $\frac{21}{2} \mathrm{~s}$
(D) $\frac{21}{10} \mathrm{~s}$

Hunza Gilgit

Numerade Educator

Problem 157

A particle of mass $m$ is moving in a field where the potential energy is given by $U(x)=U_0(1-\cos a x)$, where $U_0$ and a are constants and $x$ is the displacement from mean position. Then (for small oscillations)
(A) The time period is $T=2 \pi \sqrt{\frac{m}{a U_0}}$.
(B) The speed of particle is maximum at $x=0$.
(C) The amplitude of oscillations is $\frac{\pi}{a}$.
(D) The time period is $T=2 \pi \sqrt{\frac{m}{a^2 U_0}}$.

Hunza Gilgit

Numerade Educator

Problem 158

Two SHMs are represented by the equations:

$$
\begin{aligned}
& Y_1=10 \sin [3 \pi r+\pi / 4] \\
& Y_2=5 \cos \pi
\end{aligned}
$$

(A) The amplitude ratio of the two SHM is $1: 1$.
(B) The amplitude ratio of the two SHM is $2: 1$.
(C) Time periods of both the SHMs are equal.
(D) Time periods of two SHMs are different.

Hunza Gilgit

Numerade Educator

Problem 159

A particle of mass $m$ moves in a straight line. If $v$ is the velocity at a distance $x$ from a fixed point on the line and $v^2=a-b x^2$, where $a$ and $b$ are constant, then
(A) The motion continues along the positive $x$-direction only.
(B) The motion is simple harmonic.
(C) The particle oscillates with a frequency equal to $\frac{\sqrt{b}}{2 \pi}$.
(D) The total energy of the particle is ma.

Dheeraj Sharma

Numerade Educator

Problem 160

A particle of mass $m$ is attached to three identical springs $A, B$, and $C$ each of force constant $k$ as shown in Fig. 9.35. If the particle of mass $m$ is pushed slightly against the spring $A$ and released, then the time period of oscillation
(A) Extension in springs are same
(B) $2 \pi \sqrt{\frac{m}{2 k}}$
(C) Extension in A is different from B and C
(D) $2 \pi \sqrt{\frac{m}{3 k}}$
(FIGURE CAN'T COPY)
Fig. 9.35

Hunza Gilgit

Numerade Educator

Problem 161

A particle vibrates in SHM along a straight line. Its greatest acceleration is $5 \pi^2 \mathrm{~cm} \mathrm{~s}^{-2}$ and its distance from the equilibrium position is 4 cm , the velocity of the particle is $3 \pi \mathrm{cms}^{-1}$, then
(A) The amplitude is 10 cm
(B) The period of oscillation 2 s
(C) The amplitude is 5 cm
(D) The period of oscillation 4 s

Hunza Gilgit

Numerade Educator

Problem 162

A block $A$ of mass $m$ connected with a spring of force constant $k$ is executing SHM. The position $(x)$ and time ( $t$ ) equation of the block is $x=x_0+a \sin \omega t$. An identical block $B$ moving towards negative $x$-axis with velocity $v_0$ collides elastically with block $A$ at time $t=0$. Then
(A) Displacement time equation of $A$ after collision will be $x=x_0-v_0 \sqrt{\frac{m}{k}} \sin \omega r$.
(B) Displacement time equation of $A$ after collision will be $x=x_0+v_0 \sqrt{\frac{m}{k}} \sin \alpha N$.
(C) Velocity of $B$ just after collision will be $a \omega$ towards positive $x$-direction.
(D) Velocity of $B$ just after collision will be $v_0$ towards positive $x$-direction.

Hunza Gilgit

Numerade Educator

Problem 163

Two particles undergo SHM along the same line with the same time period ( $T$ ) and equal amplitudes $(A)$. At a particular instant, one particle is at $x=-A$ and the other is at $x=0$. They move in the same direction. They will cross each other at time $t$ and at position $x$ then
(A) $t=\frac{4 T}{3}$
(B) $t=\frac{3 T}{8}$
(C) $x=\frac{A}{2}$
(D) $x=\frac{A}{\sqrt{2}}$

Hunza Gilgit

Numerade Educator

Problem 164

A block $A$ of mass $m$ connected with a spring of force constant $k$ is executing SHM. The position ( $x$ ) and time ( $t$ ) equation of the block is $x=x_0+a \sin \omega t$. An identical block $B$ moving towards negative $x$-axis with velocity $v_0$ collides elastically with block $A$ at time $t=0$. Then
(A) Displacement time equation of $A$ after collision will be $x=x_0-v_0 \sqrt{\frac{m}{k}} \sin \varphi x$.
(B) Displacement time equation of $A$ after collision will be $x=x_0+v_0 \sqrt{\frac{m}{k}} \sin \omega x$.
(C) Velocity of $B$ just after collision will be $a \omega$ towards positive $x$-direction.
(D) Velocity of $B$ just after collision will be $v_0$ towards positive $x$-direction.

Hunza Gilgit

Numerade Educator

Problem 165

Velocity of sound in air is $320 \mathrm{~m} / \mathrm{s}$. A pipe closed at one end has a length of 1 m . Neglecting end corrections, the air column in the pipe can resonate for sound at frequency
(A) 80 Hz
(B) 240 Hz
(C) 320 Hz
(D) 400 Hz

Hunza Gilgit

Numerade Educator

Problem 166

A sound wave of frequency $v$ travels horizontally to the right. It is reflected from a large vertical plane surface moving to the left with a speed $V$. The speed of sound in the medium is $c$.
(A) The number of wave pulse striking the surface per second is $\frac{V(c+V)}{c}$
(B) The wavelength of the reflected wave is $\frac{c(c-V)}{V(c+V)}$
(C) The frequency of the reflected wave is $\frac{V(c+V)}{(c-V)}$
(D) The number of beats heard by a stationary listener to the left of the reflecting surface is $\frac{v V}{c-V}$

Hunza Gilgit

Numerade Educator

Problem 167

A traveling wave pulse is given by $y=\frac{6}{2+(x+3)^2}$, where symbols have their usual meanings, $x, y$ are in metre and $t$ is in second. Then
(A) The pulse is traveling along $+\mathrm{ve} x$-axis with velocity $3 \mathrm{~m} / \mathrm{s}$.
(B) The pulse is traveling along -ve $x$-axis with velocity $3 \mathrm{~m} / \mathrm{s}$.
(C) The amplitude of the wave pulse is 3 m .
(D) The pulse is a symmetric pulse.

Hunza Gilgit

Numerade Educator

Problem 168

$Y(x, t)=\frac{0.8}{\left[(4 x+5 t)^2+5\right]}$ represents a moving pulse, where $x$ and $y$ are in metres and $t$ in second. Then
(A) Pulse is moving in positive $x$-direction
(B) In 2 s it will travel a distance of 2.5 m
(C) It maximum displacement is 0.16 m
(D) It is a symmetric pulse at $t=0$

Hunza Gilgit

Numerade Educator

Problem 169

Two monochromatic coherent point sources $S_i$ and $S_2$ are separated by a distance $L$. Each source emits light of wavelength $\lambda$, where $L \gg \lambda$. The line $S_1 S_2$ when extended meets a screen perpendicular to it at a point $A$.
(A) The interference fringes on the screen are circular in shape.
(B) The interference fringes on the screen are straight lines perpendicular to the line $S_1 S_2 A$.
(C) The point $A$ is an intensity maxima if $L=n \lambda$.
(D) The point $A$ is always an intensity maxima for any separation $L$.

Ankur S

Numerade Educator

Problem 170

For a certain stretched string, three consecutive resonance frequencies are observed as $105,175,245 \mathrm{~Hz}$, respectively. Then select the correct alternatives
(A) The string is fixed at both ends.
(B) The string is fixed at one end only.
(C) The fundamental frequency is 35 Hz
(D) The fundamental frequency is 52.5 Hz .

Akshaya Rs

Numerade Educator

Problem 171

A source of sound moves along a circle of radius 2 m with constant angular velocity $40 \mathrm{rad} / \mathrm{s}$. Frequency of the source is 300 Hz . A detector is kept at some distance from the circle in the same plane of the circle (as shown in Fig. 9.36). Which of the following is not the possible value of frequency registered by the detector? (Speed of sound $=320 \mathrm{~m} / \mathrm{s}$ )
(FIGURE CAN'T COPY)
Fig. 9.36
(A) 250 Hz
(B) 360 Hz
(C) 410 Hz
(D) 220 Hz

MM

Mahammadabrar Liyakatbhai Mamon

Numerade Educator

Problem 172

A wave disturbance in a medium is described by $y(x, t)=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)$.
where $x$ and $y$ are in meter and $t$ is in second. Then
(A) First node occurs at $x=0.15 \mathrm{~m}$
(B) First anti-node occurs at $x=0.3 \mathrm{~m}$
(C) The speed of interfering waves is $5.0 \mathrm{~m} / \mathrm{s}$
(D) The wavelength is 0.2 m

Hunza Gilgit

Numerade Educator

Problem 173

A 10 m long horizontal stainless steel wire AB of mass 1 kg , whose end A is fixed, is connected to a massless string BC passing over a smooth pulley. String BC is connected to a container of mass 2 kg at end C. Water (density $=1 \times 103 \mathrm{~kg} / \mathrm{m}^3$ ) is poured in the container at a constant rate of 2.25 litre/sec at $t=$ 0 . Also at $t=0$, a pulse is generated at end $A$.
(A) Time taken by the pulse to reach point $B$ is 0.612 s
(B) Time taken by the pulse to reach point $B$ is 0.212 s
(C) Tension in the string at this moment is 33.77 N
(D) Tension in the string at this moment is 24.77 N

Hunza Gilgit

Numerade Educator

Problem 174

The $(x, y)$ co-ordinates of the corners of a square plate are $(0,0),(L, 0),(L, L)$, and $(0, L)$. The edges of the plate are clamped and transverse standing waves are set up in it. If $u(x, y)$ denotes the displacement of the plate at the point $(x, y)$ at some instant of time, the possible expression(s) for $u$ is (are) ( $a=$ positive constant)
(A) $a \cos (\pi x / 2 L) \cos (\pi y / 2 L)$
(B) $a \sin (\pi x / L) \sin (\pi y / L)$
(C) $a \sin (\pi x / L) \sin (2 \pi y / L)$
(D) $a \cos (2 \pi x / L) \sin (\pi y / L)$

Hunza Gilgit

Numerade Educator

Problem 175

When more than one force (say two forces) acts on a system, it might produce more than one SHM. The combination may form another SHM depending on the direction of such SHM, the amplitude will vary. The phase difference between the two also has a role to play in deciding the resultant amplitude. However, when the superimposed SHMs are in perpendicular direction, the pattern may change not only with phase but also with frequencies. When different oscillating systems are connected, there can be an influence of one on another.
When two SHMs in the same direction with amplitude $A_1$ and $A_2$ are superimposed, the resultant amplitude will be
(A) $\left|A_1+A_2\right|$ always
(B) $\left|A_1+A_2\right|$ for $\delta=\pi$
(C) $\left|A_1-A_2\right|$ for $\delta=0$
(D) between $\left|A_1-A_2\right|$ and $\left(A_1+A_2\right)$ if $0 \leq \delta \leq \pi$

Ankur S

Numerade Educator

Problem 176

When more than one force (say two forces) acts on a system, it might produce more than one SHM. The combination may form another SHM depending on the direction of such SHM, the amplitude will vary. The phase difference between the two also has a role to play in deciding the resultant amplitude. However, when the superimposed SHMs are in perpendicular direction, the pattern may change not only with phase but also with frequencies. When different oscillating systems are connected, there can be an influence of one on another.
The track followed for two perpendicular SHMs is a perfect ellipse when ( $\delta$-phase difference, $A_1, A_2$ amplitudes)
(A) $\delta=\frac{\pi}{4}, A_1 \neq A_2$
(B) $\delta=\frac{3 \pi}{4}, A_1 \neq A_2$
(C) $\delta=\frac{\pi}{2}, A_1 \neq A_2$
(D) $\delta=\pi, A_1=A_2$

Ankur S

Numerade Educator

Problem 177

When more than one force (say two forces) acts on a system, it might produce more than one SHM. The combination may form another SHM depending on the direction of such SHM, the amplitude will vary. The phase difference between the two also has a role to play in deciding the resultant amplitude. However, when the superimposed SHMs are in perpendicular direction, the pattern may change not only with phase but also with frequencies. When different oscillating systems are connected, there can be an influence of one on another.
If $Y_1=5 \sin (\omega t)$ and $Y_2=5[\sqrt{3} \sin \omega t+\cos \omega t]$ are two SHMs, the ratio of their amplitude is
(A) $1: \sqrt{3}$
(B) $1: 3$
(C) $1: 2$.
(D) $1: \cos \left(\frac{\pi}{6}\right)$

Ankur S

Numerade Educator

Problem 178

A particle of mass $m$ is attached to one end of the light inextensible string and other end of the string is fixed in vertical plane as shown in Fig. 9.37. Particle is given the horizontal velocity $u=\sqrt{\frac{5}{2} g l}$.
(FIGURE CAN'T COPY)
Fig. 9.37
The maximum angle made by the particle with downward vertical is
(A) $\cos ^{-1}\left(\frac{1}{4}\right)$
(B) $\sin ^{-1}\left(\frac{1}{4}\right)$
(C) $\frac{\pi}{2}+\cos ^{-1}\left(\frac{1}{4}\right)$
(D) $\pi-\cos ^{-1}\left(\frac{1}{4}\right)$

Prabhu Ramji

Numerade Educator

Problem 179

A particle of mass $m$ is attached to one end of the light inextensible string and other end of the string is fixed in vertical plane as shown in Fig. 9.37. Particle is given the horizontal velocity $u=\sqrt{\frac{5}{2} g l}$.
(FIGURE CAN'T COPY)
Fig. 9.37
The tension in string at an instant when acceleration of the particle is horizontal is
(A) mg
(B) 2 mg
(C) 4 mg
(D) 6 mg

Hunza Gilgit

Numerade Educator

Problem 180

A particle of mass $m$ is attached to one end of the light inextensible string and other end of the string is fixed in vertical plane as shown in Fig. 9.37. Particle is given the horizontal velocity $u=\sqrt{\frac{5}{2} g l}$.
(FIGURE CAN'T COPY)
Fig. 9.37
The string makes an angle $\theta$ with downward vertical when acceleration of the particle is horizontal, where $\theta$ is
(A) $30^{\circ}$
(B) $60^{\circ}$
(C) $120^{\circ}$
(D) $\pi-\cos ^{-1}\left(\frac{1}{4}\right)$

Prabhu Ramji

Numerade Educator

Problem 181

A particle of mass $m$ is attached to one end of the light inextensible string and other end of the string is fixed in vertical plane as shown in Fig. 9.37. Particle is given the horizontal velocity $u=\sqrt{\frac{5}{2} g l}$.
(FIGURE CAN'T COPY)
Fig. 9.37
The particle will
(A) Oscillate about mean position.
(B) Leave the vertical circle at some point.
(C) Complete the vertical circle.
(D) None of these.

Prem Bijarniya

Numerade Educator

Problem 182

A body of mass $m$ fell from a height $h$ at $t=0$ onto the pan of a spring balance. The masses of the pan and the spring are negligible. The spring constant of the spring is $k=\frac{3 \mathrm{mg}}{2 h}$. Having stuck to the pan, the body starts performing harmonic oscillations in vertical direction.
Find the time period of oscillations.
(A) $2 \pi \sqrt{\frac{2 h}{3 g}}$
(B) $\frac{1}{2 \pi} \sqrt{\frac{3 g}{2 h}}$
(C) $\pi \sqrt{\frac{2 h}{3 g}}$
(D) $\frac{1}{\pi} \sqrt{\frac{3 g}{2 h}}$

Ajay Singhal

Numerade Educator

Problem 183

A body of mass $m$ fell from a height $h$ at $t=0$ onto the pan of a spring balance. The masses of the pan and the spring are negligible. The spring constant of the spring is $k=\frac{3 \mathrm{mg}}{2 h}$. Having stuck to the pan, the body starts performing harmonic oscillations in vertical direction.
Speed of the block when acceleration of the block is zero is
(A) $\sqrt{2 g h}$
(B) $\sqrt{\frac{8}{3} g h}$
(C) $2 \sqrt{g h}$
(D) $\frac{8}{3}$

Ajay Singhal

Numerade Educator

Problem 184

A body of mass $m$ fell from a height $h$ at $t=0$ onto the pan of a spring balance. The masses of the pan and the spring are negligible. The spring constant of the spring is $k=\frac{3 \mathrm{mg}}{2 h}$. Having stuck to the pan, the body starts performing harmonic oscillations in vertical direction.
Amplitude of SHM is
(A) $h$
(B) $\frac{4}{3} h$
(C) $\frac{3 / h}{4}$
(D) $2 h$

Ajay Singhal

Numerade Educator

Problem 185

A body of mass $m$ fell from a height $h$ at $t=0$ onto the pan of a spring balance. The masses of the pan and the spring are negligible. The spring constant of the spring is $k=\frac{3 \mathrm{mg}}{2 h}$. Having stuck to the pan, the body starts performing harmonic oscillations in vertical direction.
Time after block reaches its extreme position for first time is (when block performing SHM)
(A) $\sqrt{2 g h}$
(B) $\sqrt{2 g h}+\frac{7}{6} \pi \sqrt{\frac{2 h}{3 g}}$
(C) $\sqrt{2 g h}+\frac{6}{7} \sqrt{\frac{3 g}{2 h}}$
(D) $\sqrt{2 g h}+\pi \sqrt{\frac{3 g}{2 h}}$

Ajay Singhal

Numerade Educator

Problem 186

A pendulum inside a stationary elevator has a time period $T$ where acceleration due to gravity is g . When elevator moves up by acceleration a, its time period is measured as $T_1$, and when it moves down by same acceleration its time period is $T_2$.

Now instead of time period, experiment is done to find out acceleration due to gravity in stationary elevator. Suppose while doing the experiment, a student made a timy error $d T$ in measuring time period. Then corresponding error in $g$ is found to be $d g$.

Again the pendulum is in stationary elevator but due to temperature change, its length changes from $l$ to $l+a$ ( $a \ll l$ ) and due to change in place, acceleration due to gravity changes from $g$ to $g-b(b<g)$. Due to this, its percentage change in time period is found to be $\eta$. Now to restore its original time period, its length is decreased by $l_1$.
Relation between $T_1, T_2$, and $T$ is
(A) $T=\left(\frac{T_2 \sqrt{T_1 T_2}}{T_1^2+T_2^2}\right)$
(B) $T=\frac{\sqrt{2}\left(T_1 T_2\right)}{\sqrt{T_1^2+T_2^2}}$
(C) $T=\frac{\sqrt{5}\left(T_1 T_2\right)}{2 \sqrt{T_1^2+T_2^2}}$
(D) $T=\frac{T_1^2 T_2^2}{\left(T_1^2+T_2^2\right)^{3 / 2}}$

Supratim Pal

Numerade Educator

Problem 187

A pendulum inside a stationary elevator has a time period $T$ where acceleration due to gravity is g . When elevator moves up by acceleration a, its time period is measured as $T_1$, and when it moves down by same acceleration its time period is $T_2$.

Now instead of time period, experiment is done to find out acceleration due to gravity in stationary elevator. Suppose while doing the experiment, a student made a timy error $d T$ in measuring time period. Then corresponding error in $g$ is found to be $d g$.

Again the pendulum is in stationary elevator but due to temperature change, its length changes from $l$ to $l+a$ ( $a \ll l$ ) and due to change in place, acceleration due to gravity changes from $g$ to $g-b(b<g)$. Due to this, its percentage change in time period is found to be $\eta$. Now to restore its original time period, its length is decreased by $l_1$.
Error $d g$ is
(A) $\frac{-g d T}{\pi \sqrt{g l}}$
(B) $\frac{-g \sqrt{g} d T}{\pi \sqrt{l}}$
(C) $\frac{-g^{3 / 2} d T}{\pi l}$
(D) $\frac{-4 g \sqrt{g}}{\pi \sqrt{l}} d T$

Mirza Aslam Beig

Mirza Aslam Beig

Numerade Educator

Problem 188

A pendulum inside a stationary elevator has a time period $T$ where acceleration due to gravity is g . When elevator moves up by acceleration a, its time period is measured as $T_1$, and when it moves down by same acceleration its time period is $T_2$.

Now instead of time period, experiment is done to find out acceleration due to gravity in stationary elevator. Suppose while doing the experiment, a student made a timy error $d T$ in measuring time period. Then corresponding error in $g$ is found to be $d g$.

Again the pendulum is in stationary elevator but due to temperature change, its length changes from $l$ to $l+a$ ( $a \ll l$ ) and due to change in place, acceleration due to gravity changes from $g$ to $g-b(b<g)$. Due to this, its percentage change in time period is found to be $\eta$. Now to restore its original time period, its length is decreased by $l_1$.
Value of $l_1$ is
(A) $a^2+\frac{l b^2}{g}$
(B) $a+\frac{l b}{g}$
(C) $a-\frac{l^2 b}{g}$
(D) $\frac{a l}{g}-b$

Mirza Aslam Beig

Mirza Aslam Beig

Numerade Educator

Problem 189

An incident wave $y=A \sin \left(a x+b t+\frac{\pi}{2}\right)$ is reflected by a rigid obstacle at $x=0$, which reduces intensity of reflected wave by $36 \%$. Due to superposition, the resulting wave consists of a standing wave and a traveling wave, which is given by $Y=-d A \sin a x \cdot \sin b t+c A \cos (b t+a x)$, where $A$, $a, b, c$ are positive constants.
Amplitude of reflected wave is
(A) 0.6 A
(B) 0.8 A
(C) 0.4 A
(D) 0.2 A

Ankur S

Numerade Educator

Problem 190

An incident wave $y=A \sin \left(a x+b t+\frac{\pi}{2}\right)$ is reflected by a rigid obstacle at $x=0$, which reduces intensity of reflected wave by $36 \%$. Due to superposition, the resulting wave consists of a standing wave and a traveling wave, which is given by $Y=-d A \sin a x \cdot \sin b t+c A \cos (b t+a x)$, where $A$, $a, b, c$ are positive constants.
Value of $c$ is
(A) 0.2 .
(B) 0.4
(C) 0.6 .
(D) 0.3

Ankur S

Numerade Educator

Problem 191

An incident wave $y=A \sin \left(a x+b t+\frac{\pi}{2}\right)$ is reflected by a rigid obstacle at $x=0$, which reduces intensity of reflected wave by $36 \%$. Due to superposition, the resulting wave consists of a standing wave and a traveling wave, which is given by $Y=-d A \sin a x \cdot \sin b t+c A \cos (b t+a x)$, where $A$, $a, b, c$ are positive constants.
Maximum displacement of a medium particle is
(A) A
(B) 0.2 A
(C) 0.8 A
(D) 1.8 A

Mishal Gul

Numerade Educator

Problem 192

An oscillator of frequency 680 Hz drives two speakers. The speakers are fixed on a vertical pole at a distance 3 m from each other as shown in Fig. 9.38. A person whose height is almost the same as that of the lower speaker walks towards the lower speaker in a direction perpendicular to the pole. Assuming that there is no reflection of sound from the ground and speed of sound is $v=340 \mathrm{~m} / \mathrm{s}$, answer the following questions.
(FIGURE CAN'T COPY)
Fig. 9.34
As the person walks towards the pole, his minimum distance from the pole when he first hears a minimum in sound intensity is nearly
(A) 14.6 m
(B) 17.9 m
(C) 10.1 m
(D) 22.4 m

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 193

An oscillator of frequency 680 Hz drives two speakers. The speakers are fixed on a vertical pole at a distance 3 m from each other as shown in Fig. 9.38. A person whose height is almost the same as that of the lower speaker walks towards the lower speaker in a direction perpendicular to the pole. Assuming that there is no reflection of sound from the ground and speed of sound is $v=340 \mathrm{~m} / \mathrm{s}$, answer the following questions.
(FIGURE CAN'T COPY)
Fig. 9.34
As the person walks toward the pole, the total number of times that the person hears a minimum in sound intensity will be
(A) 2
(B) 8
(C) 4
(D) 6

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 194

An oscillator of frequency 680 Hz drives two speakers. The speakers are fixed on a vertical pole at a distance 3 m from each other as shown in Fig. 9.38. A person whose height is almost the same as that of the lower speaker walks towards the lower speaker in a direction perpendicular to the pole. Assuming that there is no reflection of sound from the ground and speed of sound is $v=340 \mathrm{~m} / \mathrm{s}$, answer the following questions.
(FIGURE CAN'T COPY)
Fig. 9.34
At some instant, when the person is at a distance 4 m from the pole, the wave function (at the person's location) that describes the waves coming from the lower speaker is $y=A \cos (k x-\omega x)$ (where A is the ampli-tude, $\omega=2 \pi v$ with $v=680 \mathrm{~Hz}$ (given) and $k=\frac{2 \pi}{\lambda}$ ) Then wave function (at the person's location) that describes waves coming from the upper speaker can be expressed as
(A) $y=A \cos (k x-\omega k+2 \pi)$
(B) $y=A \cos (k x-\omega t+\pi)$
(C) $y=A \cos (k x-\omega t+4 \pi)$
(D) $y=A \cos \left(k x-\omega \mathrm{t}+\frac{3 \pi}{2}\right)$

Hunza Gilgit

Numerade Educator

Problem 195

An oscillator of frequency 680 Hz drives two speakers. The speakers are fixed on a vertical pole at a distance 3 m from each other as shown in Fig. 9.38. A person whose height is almost the same as that of the lower speaker walks towards the lower speaker in a direction perpendicular to the pole. Assuming that there is no reflection of sound from the ground and speed of sound is $v=340 \mathrm{~m} / \mathrm{s}$, answer the following questions.
(FIGURE CAN'T COPY)
Fig. 9.34
Suppose at one instant of time, the person is at certain position and the frequency of upper speaker is changed (by connecting it with some other oscillator) without change in its intensity. Then the net intensity of sound heard by the person at $P$ will
(A) increase.
(B) decrease.
(C) remains same.
(D) may increase of decrease depending upon the position of the person.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 196

The equations of two plane progressive sound waves are given as $y_1=A \cos (0.5 \pi x-100 \pi t)$ and $y_2=A \cos (0.46 \pi x-92 \pi r)$. Answer the following questions based on above equations
How many times the value of $y_1+y_2$ becomes zero at $x=0$ in 1 second?
(A) 46
(B) 42
(C) 100
(D) 184

Akshaya Rs

Numerade Educator

Problem 197

The equations of two plane progressive sound waves are given as $y_1=A \cos (0.5 \pi x-100 \pi t)$ and $y_2=A \cos (0.46 \pi x-92 \pi r)$. Answer the following questions based on above equations
Wave speed of the louder wave is
(A) $192 \mathrm{~m} / \mathrm{s}$
(B) $200 \mathrm{~m} / \mathrm{s}$
(C) $100 \mathrm{~m} / \mathrm{s}$
(D) $184 \mathrm{~m} / \mathrm{s}$

Kumari Shilpi

Numerade Educator

Problem 198

The equations of two plane progressive sound waves are given as $y_1=A \cos (0.5 \pi x-100 \pi t)$ and $y_2=A \cos (0.46 \pi x-92 \pi r)$. Answer the following questions based on above equations
When the given waves superimpose the number of times the intensity of sound becomes maximum in 1 second is
(A) 4
(B) 6
(C) 8
(D) 12

Akshaya Rs

Numerade Educator

Problem 199

A sound source $S$ of frequency 600 Hz is performing SHM with amplitude 300 cm between $A A^{\prime}$ along $x$-axis, about mean position as origin $O$. There is a detector with another stationary sound source $S^{\prime}$ of sound of same frequency lying near to point $A^{\prime}$, i.e., at point $B$ as shown in Fig. 9.39. If the maximum number of beats detected by the detector is 60 at time $T / 2$, where $T$ is the time period of SHM of source $S$. (velocity of sound is $330 \mathrm{~m} / \mathrm{s}$ )
(FIGURE CAN'T COPY)
The maximum velocity of the source is
(A) $20 \mathrm{~m} / \mathrm{s}$
(B) $30 \mathrm{~m} / \mathrm{s}$
(C) $40 \mathrm{~m} / \mathrm{s}$
(D) $60 \mathrm{~m} / \mathrm{s}$

Mishal Gul

Numerade Educator

Problem 200

A sound source $S$ of frequency 600 Hz is performing SHM with amplitude 300 cm between $A A^{\prime}$ along $x$-axis, about mean position as origin $O$. There is a detector with another stationary sound source $S^{\prime}$ of sound of same frequency lying near to point $A^{\prime}$, i.e., at point $B$ as shown in Fig. 9.39. If the maximum number of beats detected by the detector is 60 at time $T / 2$, where $T$ is the time period of SHM of source $S$. (velocity of sound is $330 \mathrm{~m} / \mathrm{s}$ )
(FIGURE CAN'T COPY)
The equation of SHM of the source $S$ is
(A) $300 \sin 20 t$
(B) $300 \sin (10 t+\pi)$
(C) $300 \cos (10 t+\pi)$
(D) $300 \cos 20 t$

Hunza Gilgit

Numerade Educator

Problem 201

A sound source $S$ of frequency 600 Hz is performing SHM with amplitude 300 cm between $A A^{\prime}$ along $x$-axis, about mean position as origin $O$. There is a detector with another stationary sound source $S^{\prime}$ of sound of same frequency lying near to point $A^{\prime}$, i.e., at point $B$ as shown in Fig. 9.39. If the maximum number of beats detected by the detector is 60 at time $T / 2$, where $T$ is the time period of SHM of source $S$. (velocity of sound is $330 \mathrm{~m} / \mathrm{s}$ )
(FIGURE CAN'T COPY)
The minimum number of beats detected by the detector is
(A) Zero
(B) 45
(C) 50
(D) 55

Dheeraj Sharma

Numerade Educator

Problem 202

The vibration of a string of length 60 cm fixed at both ends are represented by the equation

$$
y=4 \sin \left[\frac{\pi x}{15}\right] \cos (96 \pi t)
$$

where $x$ and $y$ are in cm and $t$ in second.
Answer the following questions based on the above statement.
The maximum displacement at $x=5 \mathrm{~cm}$ is
(A) $2 \sqrt{3} \mathrm{~cm}$
(B) $3 \sqrt{2} \mathrm{~cm}$
(C) Zero
(D) $2 \sqrt{3} \mathrm{~m}$

Saman Zulfiqar

Numerade Educator

Problem 203

The vibration of a string of length 60 cm fixed at both ends are represented by the equation

$$
y=4 \sin \left[\frac{\pi x}{15}\right] \cos (96 \pi t)
$$

where $x$ and $y$ are in cm and $t$ in second.
Answer the following questions based on the above statement.
Where are the nodes located along the string?
(A) $0,15 \mathrm{~cm}, 30 \mathrm{~cm}, 45 \mathrm{~cm}, 60 \mathrm{~cm}$
(B) $7.5 \mathrm{~cm}, 22.5 \mathrm{~cm}, 37.5 \mathrm{~cm}, 52.5 \mathrm{~cm}$
(C) Both (A) and (B)
(D) None

Saman Zulfiqar

Numerade Educator

Problem 204

The vibration of a string of length 60 cm fixed at both ends are represented by the equation

$$
y=4 \sin \left[\frac{\pi x}{15}\right] \cos (96 \pi t)
$$

where $x$ and $y$ are in cm and $t$ in second.
Answer the following questions based on the above statement.
The equation of components wave whose superposition gives the above wave are
(A) $2 \sin \left(96 \pi t+\frac{\pi x}{15}\right) \mathrm{cm} ; 2 \cos \left(96 \pi t+\frac{\pi x}{15}\right) \mathrm{cm}$
(B) $2 \cos \left(96 \pi t+\frac{\pi x}{15}\right) \mathrm{cm} ; 2 \cos \left(96 \pi t-\frac{\pi x}{15}\right) \mathrm{cm}$
(C) $2 \sin \left(96 \pi t+\frac{\pi x}{15}\right) \mathrm{cm} ; 2 \sin \left(96 \pi t-\frac{\pi x}{15}\right) \mathrm{cm}$
(D) None of these

Hunza Gilgit

Numerade Educator

Problem 205

In the two block springs, force constant of spring is $K=6 \mathrm{~N} / \mathrm{m}$. Spring is stretched by 12 cm and then left.
(TABLE CAN'T COPY)

Khushbu Rani

Numerade Educator

Problem 206

In Fig. 9.40 , a block of mass $M=1 \mathrm{~kg}$ is attached to one end of masalesa apring of apring conatant $k=100 \mathrm{~N} / \mathrm{m}$ and other end of spring is fixed. Initially, spring in its natural length. A horizontal force $F=10 \mathrm{~N}$ at $t=0$ is applied on the block.
(TABLE CAN'T COPY)

Ze-Han Lee

Numerade Educator

Problem 207

The speed ( $v$ ) of a particle of mass 1 kg moving along a straight line, when it is at a distance ( $x$ ) from a fixed point on the line is given by $v^2=144-9 x^2$.
(TABLE CAN'T COPY)

Dheeraj Sharma

Numerade Educator

Problem 208

A particle of mass 4 kg is tied with a spring of spring constant ' 64 ' $\mathrm{N} / \mathrm{m}$. The system is kept on a horizontal frictionless surface and performing SHM of amplitude $A=25 \mathrm{~cm}$.
(TABLE CAN'T COPY)

Shoukat Ali

Other Schools

Problem 209

A uniform ring of mass $M=1 \mathrm{~kg}$ has massless spokes. A spring of stiffness constant $K=1 \mathrm{~N} / \mathrm{m}$ is attached to the centre of the ring at one end and the other end is fixed to the wall as shown in Fig. 9.41. The ring is given an angular velocity $\omega$ and released from point $A$. As it reaches point $B$, its velocity of centre of mass becomes $V=1 \mathrm{~m} / \mathrm{s}$, where $V=R \omega$. The surface to the left of point $B$ is perfectly rough, so that no slipping takes place. There is a point $O$ on the rough part which corresponds to zero deformation of spring.
(TABLE CAN'T COPY)

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 210

From a single source, two wave trains sent in two different strings of same length. String-2 is four times heavy than string-1. The two wave equations are (area of cross-section and tension of both strings is same).

$$
y_1=A \sin \left(\omega_1 t-k_1 x\right) \text { and } y_2=2 A \sin \left(\omega_2 t-k_2 x\right)
$$

Suppose $u=$ energy density, $P=$ power transmitted, and $I=$ intensity of wave, $v=$ velocity of wave, then match the following:$$
\begin{array}{ll}
\hline \text { Column-I } & \text { Column-II } \\
\hline \text { (A) } \frac{u_1}{u_2}= & 1 \cdot \frac{1}{8} \\
\text { (B) } \frac{P_1}{P_2}= & 2 . \frac{1}{16} \\
\text { (C) } \frac{v_1}{v_2}= & 3.2 \\
\text { (D) } \frac{k_1}{k_2}= & \text { 4. } \frac{1}{2} \\
& \text { 5. } 5 \\
\hline
\end{array}
$$

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 211

A closed organ pipe of length $L$ vibrating in second overtone, then match the following
$$
\begin{array}{ll}
\hline \text { Column-I } & \text { Column-II } \\
\hline \text { (A) Displacement node } & \text { 1. Closed end } \\
\text { (B) Displacement anti-node } & \text { 2. Open end }
\end{array}
$$
(C) Pressure node
3. $4 L / 5$ from closed end
(D) Pressure anti-node
4. $L / 5$ from closed end

Nikhil Choudhary

Nikhil Choudhary

Numerade Educator

Problem 212

Match the information given in Column-I with that given in Column-II
(TABLE CAN'T COPY)

Deepanshu Kumar

Deepanshu Kumar

Numerade Educator

Problem 213

$$
\begin{array}{cc}
\hline \text { Column-I } & \text { Column-II } \\
\hline
\end{array}
$$
$$
\begin{array}{ll}
\hline \text { (A) Beats } & \text { 1. Redistribution of energy } \\
\text { (B) Standing waves } & \text { 2. Multiple reflection } \\
\text { (C) Interference } & \text { 3. Varying amplitude } \\
\text { (D) Echo } & \text { 4. Reflection from a rigid } \\
& \\
& \text { support }
\end{array}
$$

Prem Bijarniya

Numerade Educator

Problem 214

A long wire $A B C$ is made by joining two wires $A B$ and $B C$ of equal area of cross-section. $A B$ has length 4.8 m and mass 0.12 kg while $B C$ has length 2.56 m and mass 0.4 kg . The wire is under a tension of 160 N . A wave $Y($ in cm$)=3.5 \sin (k x-w t)$ is sent along $A B C$ from end $A$. No power is dissipated during propagation of wave.
$$
\begin{array}{cc}
\hline \text { Column-I } & \text { Column-II } \\
\hline
\end{array}
$$
(A) Amplitude of reflected wave
1. 2.0
(B) Amplitude of transmitted wave
2. 1.5
(C) Maximum displacement of
3. 5 antinodes in the wire $A B$
(D) Percentage fraction of power
4. 82 transmitted in the wire $B C$
5. 92

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 215

Assertion: Average speed of a particle performing SHM (of amplitude $A$ with time period $T$ ) in one time period is $\frac{4 A}{T}$.
Reason: In case of SHM, displacement of particle in one time period is zero.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 216

Assertion: Speed of a particle and magnitude of its acceleration in its SHM (time period $2 \pi$ second) are equal when its displacement from mean position is $\frac{A}{\sqrt{2}}$, where $A$ is amplitude of SHM.
Reason: Speed of particle is maximum when acceleration of particle is zero.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 217

Assertion: In SHM, total mechanical energy is always equal to sum of kinetic energy and potential energy.
Reason: At the mean position, the particle has only kinetic energy.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 218

Assertion: The scalar product of the displacement and the acceleration in SHM is never greater than zero.
Reason: Acceleration is linearly proportional to and opposite to displacement.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 219

Assertion: Tension in the string remains same irrespective of the position of bob in oscillation.
Reason: Tension is maximum at mean position.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 220

Assertion: A heavy mass is hanging from a string in equilibrium without breaking it. When this same mass is set into oscillation, then string can break.
Reason: In above assertion, tension in string can never be greater than weight of hanging mass.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 221

Assertion: Maximum speed of a particle performing SHM is $2 \mathrm{~m} / \mathrm{s}$, then average speed of particle during it move from one extreme to other extreme position is $\frac{4}{\pi} \mathrm{~m} / \mathrm{s}$.
Reason: $<v>=\frac{\int v d t}{\int d t}$ (A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 222

Assertion: Two SHMs are given by $y_1=10 \sin \left(3 \pi t+\frac{\pi}{4}\right)$ and $y_2=5 \sin (3 \pi t)+\sqrt{3} \cos$ (3kt).
Reason: $y_2$ represents two SHMs each of amplitude 5 and so total amplitude is 10 , same as that of $y_{\text {I- }}$.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 223

Assertion: The function $Y=\cos ^2 \alpha t+\sin \alpha x$ does not represent a SHM.
Reason: Sum of two harmonic functions may not be a harmonic motion.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 224

Assertion: Time period of a simple pendulum having a hollow sphere, filled with water, as bob then its time period increases continuously as water drains out.
Reason: Effective length of above mentioned pendulum changes until all the water drains out.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 225

Assertion: For two identical sources, the maximum intensity in interference pattern is four times the intensity due to each wave.
Reason: The intensity is directly proportional to the square of amplitude.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 226

Assertion: A closed organ pipe is vibrating in its first overtone with frequency 340 Hz . Speed of sound in organ pipe is $340 \mathrm{~m} / \mathrm{s}$. Length of organ pipe is less than 75 cm .
Reason: In case of standing wave in closed organ pipe, pressure amplitude is maximum at closed end.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 227

Assertion: In Young's double slit experiment, the two slits are at distance $d$ apart. Interference pattern is observed on a screen at distance $D$ from the slits. At a point on the screen when it is directly opposite to one of the slits, a dark fringe is observed. Then the wavelength of wave proportional to square of distance between the two slits.
Reason: For a dark fringe, intensity is zero.
(A) A
(B) B
(C) C
(D) D

Saman Zulfiqar

Numerade Educator

Problem 228

Assertion: When two vibrating tuning forks having frequencies 300 Hz and 246 Hz are placed near each other, beats cannot be heard by normal human ear.
Reason: The principle of superposition is valid only if the frequencies of the oscillators are nearly equal.
(A) A
(B) B
(C) C
(D) D

Yuva S

Numerade Educator

Problem 229

Assertion: $Y=2 A \sin k x \cos \omega \mathrm{r}$ refers to a standing wave.
Reason: When a continuous traveling wave interacts with its reflected wave from a rigid support, it may form a standing wave.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 230

Assertion: If two transverse pulses are generated in the same string given by $y=A \sin (k x-\omega k+\varphi)$ and $y=2 A \sin (2 k x-\omega t+\varphi)$, then the ratio of average power for the pulses will be $1 / 8$.
Reason: Average power for transverse wave is $\frac{T \omega K A^2}{2}$.
(A) A
(B) B
(C) C
(D) D

Mohd Shahab

Numerade Educator

Problem 231

Assertion: A sound wave can be studsed as any of the three waves, namely, pressure wave, displacement wave, and density wave.
Reason: In a sound wave pressure, displacement and density change simultaneously to a maximum or minimum.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 232

Assertion: There are two sound waves propagating in same medium having amplitudes and frequencies $2 A$, $f$ and $A, 2 f$, respectively. The intensity of first wave is four times that of the other.
Reason: Intensity of a wave $I=\frac{1}{2} \rho v \omega^2 A^2$
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 233

Assertion: No interference pattern is detected when two sources are infinitely close to each other
Reason: The fringe width is inversely proportional to the distance between the fwo slits.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 234

Assertion: When two vibrating tuning forks having frequencies 256 Hz and 512 Hz are held near each other, beats cannot be heard.
Reason: The principle of superposition is valid only if the frequencies of the oscillations are nearly equal.
(A) A
(B) B
(C) C
(D) D

Ankur S

Numerade Educator

Problem 235

Find the time period of the motion of the particle shown in Fig. 9.42. (Neglect the small effect of the bend near the bottom)

Supratim Pal

Numerade Educator

Problem 236

A simple pendulum is suspended from the ceiling of an empty box falling in air near earth surface. The total mass of system is $M$. The box experiences air resistance $\vec{R}=-k \vec{v}$, where $v$ is the velocity of box and $k$ is a positive constant. After some time, it is found that period of oscillation of pendulum becomes double the value when it would have suspended from a point on earth. The velocity of box at that moment $v=\frac{M g}{n k}$, then the value of n is. (Take g in air same as on earth's surface.)

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 237

In Fig. 9.43, string, spring, and pulleys are massless. Block $A$, performing SHM of amplitude 1 m and time period $\pi / 2 \mathrm{~s}$. If block $B$ remains at rest, then minimum value of co-efficient of friction between block $B$ and surface will be $\frac{13}{5 n}$, then the value of $n$ is. $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

Ankur S

Numerade Educator

Problem 238

A particle of mass $M$ is attached to four springs as shown in Fig.9.44. Initial tensicen in each spring is $F_0$ and length of each spring is $l$, if the period of small oscillations of the particle along a line perpendicular to the plane containing the springs is $T=2 \pi \sqrt{\frac{M l}{n F_0}}$, then the value of $n$ is (Neglect effect of gravity and assume that the force developed in springs due to displacement is much smaller than the original tension $F_0$ ), then
(FIGURE CAN'T COPY)

Jonathan Ibarra

Jonathan Ibarra

Numerade Educator

Problem 239

Two blocks $A$ and $B$, each of mass $m$ are connected by means of a pulley-spring system on a smooth inclined plane of inclination $\theta$ as shown in Fig 9.45. All the pulleys and spring are ideal. Now, $B$ is slightly displaced from its equilibrium position. It starts to oscillate. Time period of oscillation of $B$ will be $T=2 \pi \sqrt{\frac{5 m}{n k}}$, then the value of $n$ is.

Mahendra Kumar

Numerade Educator

Problem 240

The equation of a particle executing SHM is given by $x=3 \cos \left(\frac{\pi}{2}\right) t \mathrm{~cm}$, where $t$ is in second. The distance travelled by the particle in the first 8.5 s is $\left(24+\frac{n}{\sqrt{2}}\right)$ then the value of $n$ is.

Ankur S

Numerade Educator

Problem 241

An open organ pipe has a fundamental frequency of $240 \mathrm{vib} / \mathrm{s}$. The first overtone of a closed organ pipe has the same frequency as the first overtone of the open pipe. How long is each pipe? Velocity of sound at the room temperature is 350 ms .

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 242

A wire of length 1.5 m under tension emits a fundamental note of frequency 120 Hz .
(A) What would be its fundamental frequency if the length is increased by half under the same tension?
(B) By how much should the length be shortened so that the frequency is increased three-fold?

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 243

A bus is moving towards a huge wall with a velocity of $5 \mathrm{~m} / \mathrm{s}$. The driver sounds a born of frequency 200 Hz . What is the frequency of beats heard by a passenger of the bus, if the speed of sound in air is $330 \mathrm{~m} / \mathrm{s}$.

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 244

A U-tube having uniform cross-section but unequal arm lengths $I_1$ and $l_2\left(<l_1\right)$ has same liquid of density $\rho_1$ filled in it upto a height $h$ as shown in Fig. 9.46. Another liquid of density $\rho_2=\left(\rho_1 / 2\right)$ is poured in arm $A$. Both liquids are immiscible. What length of the second liquid should be poured in A so that first overtone of A is in unison with fundamental tone of $B$. (Take $l_S=5 \mathrm{~m}, l_2=1 \mathrm{~m}$ and $h=0.5 \mathrm{~m}$ )

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 245

A pipe of length $L$ closed at one end is located along $x$-axis with closed end at origin and open end at ( $l$, 0 ). The pipe resonates in its $n^{\text {th }}$ overtone with maximum amplitude of air molecules to be equal to $a_0$. Calculate the $x$-co-ordinates of those points, where maximum pressure change ( $\Delta P_n$ ) occurs and calculate $\left(\Delta P_n\right)$. Density of air is equal to $\rho$ and velocity of sound in air is $v$.

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 246

A rope, under tension of 200 N and fixed at both ends, oscillates in a second harmonic standing wave pattem. The displacement of the rope is given by $y=(0.10 \mathrm{~m}) \sin \left(\frac{\pi x}{2}\right) \sin (12 \pi)$, where $x=0$ at one end of the rope, $x$ is in metres, and $t$ is in seconds. Find
(A) the length of the rope
(B) the speed of waves on the rope
(C) the mass of the rope
(D) if the rope oscillates in a third harmonic standing wave pattern, what will be the period of oscillation?

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 247

A bus $B$ is moving with a velocity $v_B$ in the positive $x$-direction along a road as shown in Fig. 9.47. A shooter $S$ is at a distance $l$ from the road. He has a detector which can detect signals only of frequency 1500 Hz . The bus blows horn of frequency 1000 Hz . When the detector detects a signal, the shooter immediately shoots towards the road along $S C$ and the bullet hits the bus. Find the velocity of the bullet if velocity of sound in air is $v=340 \mathrm{~m} / \mathrm{s}$ and $\frac{v_E}{v}=\frac{2}{3 \sqrt{3}}$.
(FIGURE CAN'T COPY)
Fig. 9.97

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 248

Sound waves of frequency 16 kHz are emitted by two coherent point sources of sound placed 2 m apart at the centre of a circular train track of large radius. A person riding the train observes 2 maxima per second when the train is running at a speed of $36 \mathrm{~km} / \mathrm{h}$. Calculate the radius of the track. [Velocity of sound in air is $320 \mathrm{~m} / \mathrm{s}$.]

Lisa Tarman

Numerade Educator

Problem 249

A sound source $S$ emitting a sound of frequency 500 Hz and receiver $R$ of mass $m$ are at the same point. $R$ is performing SHM with the help of a spring of force constant $k$. At a time $t=0, R$ is at mean position and mowing towards right extreme position as shown in Fig. 9.48. At the same time, source starts moving away from the $R$ with an acceleration $18.75 \mathrm{~m} / \mathrm{s}^2$.
Find the frequency (in Hz ) registered by receiver at a time $t=10 \mathrm{~s}$. Given that $\frac{m}{k}=\frac{100}{\pi^2}$, amplitude of oscillation of $R=\frac{150}{\pi} \mathrm{~m}, v_{\text {weund }}=300 \mathrm{~m} / \mathrm{s}$.

Keshav Singh

Numerade Educator

Problem 250

A column of air at $16^{\circ} \mathrm{C}$ and a tuning fork produces 1 beat per second when sounded together. When temperature is raised to $51^{\circ} \mathrm{C}$ the two produces 4 beats per second. Find the frequency of tuning fork?

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 251

In a simple harmonic oscillator, at the mean position
[2002]
(A) kinetic energy is minimum, potential energy is maximum.
(B) both kinetic and potential energies are maximum.
(C) kinetic energy is maximum, potential energy is minimum.
(D) both kinetic and potential energies are minimum.

Dheeraj Sharma

Numerade Educator

Problem 252

If a spring has time period $T$, and is cut into n equal parts, then the time period of each part will be
[2002]
(A) $T \sqrt{n}$
(B) $T / \sqrt{n}$
(C) $n T$
(D) T

Dheeraj Sharma

Numerade Educator

Problem 253

A child swinging on a swing in sitting position, stands up, then the time period of the swing will
[2002]
(A) increase.
(B) decrease.
(C) remains same.
(D) increase of the child is long and decreases if the child is short.

Dheeraj Sharma

Numerade Educator

Problem 254

A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period $T$. If the mass is increased by $m$, the time period becomes $\frac{5 T}{3}$. Then the radio of $\frac{m}{M}$ is
[2003]
(A) $\frac{3}{5}$
(B) $\frac{25}{9}$
(C) $\frac{16}{9}$
(D) $\frac{5}{3}$

Dheeraj Sharma

Numerade Educator

Problem 255

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constant $k_1$ and $k_2$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is
[2003]
(A) $\sqrt{\frac{k_1}{k_2}}$
(B) $\frac{k_2}{k_1}$
(C) $\sqrt{\frac{k_2}{k_1}}$
(D) $\frac{k_1}{k_2}$

Dheeraj Sharma

Numerade Educator

Problem 256

The length of a simple pendulum executing simple harmonic motion is increased by $21 \%$. The percentage increase in the time period of the pendulum of increased length is
[2003]
(A) $11 \%$
(B) $21 \%$
(C) $42 \%$
(D) $10 \%$

Dheeraj Sharma

Numerade Educator

Problem 257

The displacement of a particle varies according to the relation. $x=4(\cos \pi t+\sin \pi t)$ The amplitude of the particle is
[2003]
(A) -4
(B) 4
(C) $4 \sqrt{2}$
(D) 8

Dheeraj Sharma

Numerade Educator

Problem 258

A body executes simple harmonic motion. The potential energy (PE), the kinetic energy (KE) and total energy (TE) are measured as a function of displacement $x$. Which of the following statements is true?
(A) KE is maximum when $x=0$.
(B) TE is zero when $x=0$
(C) KE is maximum when $x$ is maximum
(D) PE is maximum when $x=0$

Dheeraj Sharma

Numerade Educator

Problem 259

The total energy of a particle, executing simple harmonic motion is
[2004]
(A) independent of $x$
(B) $\propto x^2$
(C) $\propto x$
(D) $\propto x^{1 / 2}$
where $x$ is the displacement from the mean position.

Dheeraj Sharma

Numerade Educator

Problem 260

A particle of mass $m$ is attached to a spring (of spring constant $k$ ) and has a natural angular frequency $\omega_0$. An external force $F(t)$ proportional to $\cos \omega r\left(\omega \neq \omega_0\right)$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
[2004]
(A) $\frac{1}{m\left(\omega_0^2+\omega^2\right)}$
(B) $\frac{1}{m\left(\omega_0^2-\omega^2\right)}$
(C) $\frac{m}{\omega_0^2-\omega^2}$
(D) $\frac{m}{\left(\omega_0^2+\omega^2\right)}$

Dheeraj Sharma

Numerade Educator

Problem 261

In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_1$ of the force while the energy is maximum for a frequency $\omega_2$ of the force; then
[2004]
(A) $\omega_1<\omega_2$ when damping is small and $\omega_1>\omega_2$ when damping is large
(B) $\omega_1>\omega_2$
(C) $\omega_1=\omega_2$
(D) $\omega_1<\omega_2$

Dheeraj Sharma

Numerade Educator

Problem 262

Two simple harmonic motions are represented by the equations $y_1=0.1 \sin \left(100 \pi t+\frac{\pi}{3}\right)$ and $y_2=0.1 \cos \pi t$. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is
[2005]
(A) $\frac{\pi}{3}$
(B) $\frac{-\pi}{6}$
(C) $\frac{\pi}{6}$
(D) $\frac{-\pi}{3}$

Dheeraj Sharma

Numerade Educator

Problem 263

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
[2005]
(A) first decrease and then increase to the original value.
(B) first increase and then decrease to the original value.
(C) increase towards a saturation value.
(D) remain unchanged.

Dheeraj Sharma

Numerade Educator

Problem 264

If a simple harmonic motion is represented by $\frac{d^2 x}{d t^2}+\alpha x=0$, its time period is
[2005]
(A) $\frac{2 \pi}{\sqrt{\alpha}}$
(B) $\frac{2 \pi}{\alpha}$
(C) $2 \pi \sqrt{\alpha}$
(D) $2 \pi \alpha$

Dheeraj Sharma

Numerade Educator

Problem 265

The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm , is $4.4 \mathrm{~m} / \mathrm{s}$. The period of oscillation is
[2006]
(A) 0.01 s
(B) 10 s
(C) 0.1 s
(D) 100 s

Dheeraj Sharma

Numerade Educator

Problem 266

Starting from the origin a body oscillates simple harmonically with a period of 2 s . After what time will its kinetic energy be $75 \%$ of the total energy?
(A) $\frac{1}{6} \mathrm{~s}$
(B) $\frac{1}{4} \mathrm{~s}$
(C) $\frac{1}{3} \mathrm{~s}$
(D) $\frac{1}{12} \mathrm{~s}$

Dheeraj Sharma

Numerade Educator

Problem 267

Two springs, of force constants $k_1$ and $k_2$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f$. If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes
[2007]
(A) $2 f$
(B) $\frac{f}{2}$
(C) $\frac{f}{4}$
(D) $4 f$

Dheeraj Sharma

Numerade Educator

Problem 268

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x=2 \times 10^{-2}$ meter. The time at which the maximum speed first occurs is
[2007]
(A) 0.25 s
(B) 0.5 s
(C) 0.75 s
(D) 0.125 s

Dheeraj Sharma

Numerade Educator

Problem 269

While measuring the speed of sound by performing a resonance column experiment, a student gets the first reconance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be $x \mathrm{~cm}$ for the second resonance. Then
[2008]
(A) $18>x$
(B) $x>54$
(C) $54>x>36$
(D) $36>x>18$

Dheeraj Sharma

Numerade Educator

Problem 270

A wave travelling along the $x$-axis is described by the equation $y(x, t)=0.005 \cos (\alpha x-\beta t)$. If the wavelength and the time period of the wave are 0.08 m and 2.0 s , respectively, then $\alpha$ and $\beta$ in appropriate units are
[2008]
(A) $\alpha=25.00 \pi, \beta=\pi$
(B) $\alpha=\frac{0.08}{\pi}, \beta=\frac{2.0}{\pi}$
(C) $\alpha=\frac{0.04}{\pi}, \beta=\frac{1.0}{\pi}$
(D) $\alpha=12.50 \pi, \beta=\frac{\pi}{2.0}$

Dheeraj Sharma

Numerade Educator

Problem 271

Three sound waves of equal amplitudes have frequencies $(v-1), v,(v+1)$. They superpose to give beats. The number of beats produced per second will be
[2009]
(A) 3
(B) 2
(C) 1
(D) 4

Dheeraj Sharma

Numerade Educator

Problem 272

A motor cycle starts from rest and accelerates along a straight path at $2 \mathrm{~m} / \mathrm{s}^2$. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the direiver hears the frequency of the siren at $94 \%$ of its value when the motor cycle was at rest?
[2009]
(Speed of sound $=330 \mathrm{~ms}^{-1}$ )
(A) 98 m
(B) 147 m
(C) 196 m
(D) 49 m

Dheeraj Sharma

Numerade Educator

Problem 273

The equation of a wave on a string of linear mass density $0.04 \mathrm{~kg} \mathrm{~m}^{-1}$ is given by

$$
y=0.02(m) \sin \left[2 \pi\left(\frac{t}{0.04(s)}-\frac{x}{0.50(m)}\right)\right]
$$

The tension in the string is
[2010]
(A) 4.0 N
(B) 12.5 N
(C) 0.5 N
(D) 6.25 N

Dheeraj Sharma

Numerade Educator

Problem 274

A cylindrical tube, open at both ends has a fundamental frequency, $f$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now
[2012]
(A) $f$
(B) $f / 2$
(B) 3.84
(D) $2 f$

Dheeraj Sharma

Numerade Educator

Problem 275

If a simple pendulum has significant amplitude (up to a factor $1 /$ e of original) only in the period between $t=0 s$ to $t=\mathrm{Ts}$, then $\tau$ may be called the average lift of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with $b$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:
[2012]
(A) $\frac{0.693}{b}$
(B) $b$
(C) $\frac{1}{b}$
(D) $\frac{2}{b}$

Dheeraj Sharma

Numerade Educator

Problem 276

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5 s . In another 10 s it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals
[2013]
(A) 0.81
(B) 0.729
(C) 0.6
(D) 0.7

Dheeraj Sharma

Numerade Educator

Problem 276

A particle moves with simple harmonic motion in a straight line. In first rs , after starting from rest it travels a distance $a$, and in next $\tau s$ it travels $2 a$, in same direction, then
[2014]
(A) amplitude of motion is $3 a$.
(B) time period of oscillation is $8 \pi$.
(C) amplitude of motion is $4 a$.
(D) time period of oscillation is 6 r .

Sandeep Kumar Dhania

Sandeep Kumar Dhania

Numerade Educator

Problem 278

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm . What will be length of the air column above mercury in the tube now?
[2014]
(Atmospheric pressure $=76 \mathrm{~cm}$ of Hg )
(A) 16 cm
(B) 22 cm
(C) 38 cm
(D) 6 cm

Dheeraj Sharma

Numerade Educator

Problem 279

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz . The velocity of sound in air is $340 \mathrm{~m} / \mathrm{s}$
[2014]
(A) 12
(B) 8
(C) 6
(D) 4

Dheeraj Sharma

Numerade Educator

Problem 280

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz . The frequencies of the resulting signal is/are
[2015]
(A) 2005 kHz , and 1995 kHz
(B) $2005 \mathrm{kHz}, 2000 \mathrm{kHz}$ and 1995 kHz
(C) 2000 kHz and 1995 kHz
(D) 2 MHz only

Dheeraj Sharma

Numerade Educator

Problem 281

For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against displacement $d$. Which one of the following represents these correctly?
(graphs are schematic and not drawn to scale) [2015]
(A)
(B)
(C)
(D)
(FIGURE CAN'T COPY)

Dheeraj Sharma

Numerade Educator

Problem 282

A train is moving on a straight track with speed $20 \mathrm{~ms}^{-1}$. It is blowing its whistle at the frequency of 1000 Hz . The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $=320 \mathrm{~ms}^{-1}$ ) close to
[2015]
(A) $12 \%$
(B) $18 \%$
(C) $24 \%$
(D) $6 \%$

Dheeraj Sharma

Numerade Educator

Problem 283

Length of a string tied to two rigid supports is 40 cm . Maximum length (wavelength in cm ) of a stationary wave produced on it is
[2002]
(A) 20
(B) 80
(C) 40
(D) 120

Dheeraj Sharma

Numerade Educator

Problem 284

Tube A has both ends open while tube B has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube A and B is
[2002]
(A) $1: 2$
(B) 1:4
(C) $2: 1$
(D) $4: 1$

Dheeraj Sharma

Numerade Educator

Problem 285

A tuning fork arrangement (pair) produces 4 beats/s with one fork of frequency 288 cps . A little wax is placed on the unknown fork and it then produces 2 beats/sec. The frequency of the unknown fork is
[2002]
(A) 286 cps
(B) 292 cps
(C) 294 cps
(D) 288 cps

Dheeraj Sharma

Numerade Educator

Problem 286

When temperature increase, the frequency of a tuning fork
[2002]
(A) increase.
(B) decrease.
(C) remains same.
(D) increase or decreases depending on the material.

Dheeraj Sharma

Numerade Educator

Problem 287

The displacement $y$ of a wave travelling in the $x$-direction isgivenby $y=10^{-4} \sin \left(600 t-2 x+\frac{\pi}{3}\right)$ metres wherex is expressed in meters and $t$ in seconds, The speed of the wave-motion, $\mathrm{ms}^{-1} \mathrm{in}$, is
[2003]
(A) 300
(B) 600
(C) 1200
(D) 200

Dheeraj Sharma

Numerade Educator

Problem 288

A metal wire of linear mass density of $9.8 \mathrm{~g} / \mathrm{m}$ is stretched with a tension of 10 kg -wt between two rigid supports 1 meter apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is
[2003]
(A) 50 Hz
(B) 100 Hz
(C) 200 Hz
(D) 25 Hz

Dheeraj Sharma

Numerade Educator

Problem 289

A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
[2003]
(A) $256+2 \mathrm{~Hz}$
(B) $256-2 \mathrm{~Hz}$
(C) $256-5 \mathrm{~Hz}$
(D) $256+5 \mathrm{~Hz}$

Dheeraj Sharma

Numerade Educator

Problem 290

The displacement $y$ of a particle in a medium can be expressed as, $y=10^{-6} \sin \left(100 t+20 x+\frac{\pi}{4}\right) m$ where $t$ is in second and $x$ in meter. The speed of the wave is
[2004]
(A) $20 \mathrm{~m} / \mathrm{s}$
(B) $5 \mathrm{~m} / \mathrm{s}$
(C) $2000 \mathrm{~m} / \mathrm{s}$
(D) $5 \pi \mathrm{~m} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 291

When two tuning forks (fork 1 and fork 2 ) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2 . When the tuning forks are sounded again, 6 beats per second are heard. If the frequency of fork 1 is 200 Hz , then what was the original frequency of fork 2?
[2005]
(A) 202 Hz
(B) 200 Hz
(C) 204 Hz
(D) 196 Hz

MM

Mahammadabrar Liyakatbhai Mamon

Numerade Educator

Problem 292

An observer moves towards a stationary source of sound, with velocity one-fifth of the velocity of sound. What is the percentage increases in the in the apparent frequency?
[2006]
(A) $0.5 \%$
(B) Zero
(C) $20 \%$
(D) $5 \%$

Kumari Shilpi

Numerade Educator

Problem 293

A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed $v \mathrm{~ms}^{-1}$. The velocity of sound in air is $300 \mathrm{~ms}^{-1}$. If the person can hear frequencies upto a maximum of $10,000 \mathrm{~Hz}$, the maximum value of v upto which he can bear whistle is
[2006]
(A) $15 \sqrt{2} \mathrm{~ms}^{-1}$
(B) $\frac{15}{\sqrt{2}} \mathrm{~ms}^{-1}$
(C) $15 \mathrm{~ms}^{-1}$
(D) $30 \mathrm{~ms}^{-1}$

Dheeraj Sharma

Numerade Educator

Problem 294

A sound absorber attenuates the sound level by 20 dB . The intensity decreases by a factor of
[2007]
(A) 100
(B) 1000
(C) 10000
(D) 10

Dheeraj Sharma

Numerade Educator

Problem 295

A wave travelling along the $x$-axis is described by the equation $y(x, t)=0.005 \cos (\alpha x-\beta t)$. If the wavelength and the time period of the wave are 0.08 m and 2.0 s , respectively, then $\alpha$ and $\beta$ in appropriate units are
[2008]
(A) $\alpha=25.00 \pi, \beta=\pi$
(B) $\alpha=\frac{0.08}{\pi}, \beta=\frac{2.0}{\pi}$
(C) $\alpha=\frac{0.04}{\pi}, \beta=\frac{1.0}{\pi}$
(D) $\alpha=12.50 \pi, \beta=\frac{\pi}{2.0}$

Dheeraj Sharma

Numerade Educator

Problem 296

A motor cycle starts from rest and accelerates along a straight path at $2 \mathrm{~m} / \mathrm{s}^2$. At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $94 \%$ of its value when the motor cycle was at rest? (Speed of sound $=330 \mathrm{~ms}^{-1}$ ).
(A) 98 m
(B) 147 m
(C) 196 m
(D) 49 m

Dheeraj Sharma

Numerade Educator

Problem 297

The equation of a wave on a string of linear mass density $0.04 \mathrm{~kg} \mathrm{~m}^{-1}$ is given by $y=0.02(m) \sin \left[2 \pi\left(\frac{t}{0.04(s)}-\frac{x}{0.50(m)}\right)\right]$. The tension in the string is
[2010]
(A) 4.0 N
(B) 12.5 N
(C) 0.5 N
(D) 6.25 N

Dheeraj Sharma

Numerade Educator

Problem 298

A cylindrical tube, open at both ends has a fundamental frequency, $f$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now
(A) $f$
(B) $\frac{f}{2}$
(C) $\frac{3 f}{4}$
[2012]
(D) $2 f$

Dheeraj Sharma

Numerade Educator

Problem 299

An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm . What will be length of the air column above mercury in the tube now?
[2014]
(Atmospheric pressure $=76 \mathrm{~cm}$ of Hg )
(A) 16 cm
(B) 22 cm
(C) 38 cm
(D) 6 cm

Dheeraj Sharma

Numerade Educator

Problem 300

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz . The velocity of sound in air is $340 \mathrm{~m} / \mathrm{s}$
[2014]
(A) 12
(B) 8
(C) 6
(D) 4

Dheeraj Sharma

Numerade Educator

Problem 301

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz . The frequencies of the resulting signal is/are
(A) 2005 kHz , and 1995 kHz
(B) $2005 \mathrm{kHz}, 2000 \mathrm{kHz}$ and 1995 kHz
(C) 2000 kHz and 1995 kHz
(D) 2 MHz only

Dheeraj Sharma

Numerade Educator

Problem 302

A train is moving on a straight track with speed $20 \mathrm{~ms}^{-1}$. It is blowing its whistle at the frequency of 1000 Hz . The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $=320 \mathrm{~ms}^{-1}$ ) close to
[2015]
(A) $12 \%$
(B) $18 \%$
(C) $24 \%$
(D) $6 \%$

Dheeraj Sharma

Numerade Educator

Problem 303

A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is
[2016]
(A) 2 s
(B) $2 \sqrt{2} \mathrm{~s}$
(C) $\sqrt{2} \mathrm{~s}$
(D) $2 \pi \sqrt{2} \mathrm{~s}$

Dheeraj Sharma

Numerade Educator

Problem 304

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now
|2016]
(A) $\frac{3 f}{4}$
(B) $2 f$
(C) $f$
(D) $\frac{f}{2}$

Dheeraj Sharma

Numerade Educator

Problem 305

A particle performs simple harmonic motion with amplitude $A$. Its speed is trebled at the instant that it is at a distance $\frac{2 A}{3}$ from equilibrium position. The new amplitude of the motion is
[2016]
(A) $3 A$
(B) $A \sqrt{3}$
(C) $\frac{7 A}{3}$
(D) $\frac{A}{3} \sqrt{41}$

Dheeraj Sharma

Numerade Educator