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Genius Physics (Class 11) - For IIT-JEE and CBSE

Pradeep Kshetrapal

Chapter 12

Wave Motion - all with Video Answers

Educators

RZ

Chapter Questions

01:00

Problem 1

The speed of a wave in a certain medium is $960 \mathrm{~m} / \mathrm{sec}$. If 3600 waves pass over a certain point of the medium in 1 minute, the wavelength is
(a) 2 meters
(b) 4 meters
(c) 8 meters
(d) 16 meters

RZ
Rubeena Zulfiqar
Numerade Educator
03:36

Problem 2

A simple harmonic progressive wave is represented by the equation $y=8 \sin 2 \pi(0.1 x-2 t)$ where $x$ and $y$ are in $\mathrm{cm}$ and $t$ is in seconds. At any instant the Phase difference between two particles separated by $2.0$ $\mathrm{cm}$ in the $x$-direction is
(a) $18^{\circ}$
(b) $36^{\circ}$
(c) $54^{\circ}$
(d) $72^{\circ}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:28

Problem 3

The frequency of sound wave is $\mathrm{n}$ and its velocity is $\mathrm{v}$ if the frequency is increased to $4 n$ the velocity of the wave will be
(a) $v$
(b) $2 v$
(c) $4 v$
(d) $v / 4$

RZ
Rubeena Zulfiqar
Numerade Educator
01:54

Problem 4

The displacement of a particle is given by $\mathrm{x}=3 \sin (5 \pi t)+4 \cos (5 \pi t)$ The amplitude of particle is [MP PMT 1999]
(a) 3
(b) 4
(c) 5
(d) 7

RZ
Rubeena Zulfiqar
Numerade Educator
02:10

Problem 5

The equation of a transverse wave travelling on a rope is given by $y=10 \sin \pi(0.01 x-2.00 t)$ where $y$ and $x$ are in $\mathrm{cm}$ and $t$ in seconds. The maximum transverse speed of a particle in the rope is about [MP PET 1999]
(a) $63 \mathrm{~cm} / \mathrm{sec}$
(b) $75 \mathrm{~cm} / \mathrm{s}$
(c) $100 \mathrm{~cm} / \mathrm{sec}$
(d) $121 \mathrm{~cm} / \mathrm{sec}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:34

Problem 6

In a wave motion $y=a \sin (k x-\omega t), y$ can represents
(a) Electric Field
(b) magnetic field
(c) Displacement
(d) Pressure

RZ
Rubeena Zulfiqar
Numerade Educator
02:04

Problem 7

Find the ratio of the speed of sound in nitrogen gas to that of helium gas, at $300 k$ is
(a) $\frac{1}{2}$
(b) $\frac{2}{3}$
(c) $\sqrt{\frac{3}{5}}$
(d) $\frac{4}{5}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:29

Problem 8

The displacement $x$ (in metres) of a particle performing simple harmonic motion is related to time $t$ (in seconds) as $x=0.05 \cos \left(4 \pi t+\frac{\pi}{4}\right)$. The frequency of the motion will be [MP PMT / PET 1998]
(a) $\mathrm{O} .5 \mathrm{~Hz}$
(b) $1.0 \mathrm{~Hz}$
(c) $1.5 \mathrm{~Hz}$
(d) $2.0 \mathrm{~Hz}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:31

Problem 9

A wave is represented by the equation $Y=7 \sin \left(7 \pi t-0.04 \pi x+\frac{\pi}{3}\right) \quad x$ is in meters and $t$ is in seconds. The speed of the wave is
(a) $175 \mathrm{~m} / \mathrm{sec}$
(b) $49 \pi \mathrm{m} / \mathrm{s}$
(c) $\frac{49}{\pi} \mathrm{m} / \mathrm{s}$
(d) $0.28 \mathrm{\pim} / \mathrm{s}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:14

Problem 10

A wave is represented by the equation $\mathrm{y}=0.5 \sin (10 \mathrm{t}+\mathrm{x}) \mathrm{m}$. It is a travelling wave propagating along the $x$ direction with velocity. [Roorkee 1995]
(a) $10 \mathrm{~m} / \mathrm{s}$
(b) $20 \mathrm{~m} / \mathrm{s}$
(c) $5 \mathrm{~m} / \mathrm{s}$
(d) None of these

RZ
Rubeena Zulfiqar
Numerade Educator
01:56

Problem 11

A transverse progressive wave on a stretched string has a velocity of $10 \mathrm{~ms}^{-1}$ and a frequency of $100 \mathrm{~Hz}$. The phase difference between two particles of the string which are $2.5 \mathrm{~cm}$ apart will be
(a) $\pi / 8$
(b) $\pi / 4$
(c) $3 \pi / 8$
(d) $\pi / 2$

RZ
Rubeena Zulfiqar
Numerade Educator
00:52

Problem 12

In a stationary wave, all particles are
(a) At rest at the same time twice in every period of oscillation
(b) At rest at the same time only once in every period of oscillation
(c) Never at rest at the same time
(d) Never at rest at all

RZ
Rubeena Zulfiqar
Numerade Educator
01:48

Problem 13

The path difference between the two waves $y_{1}=a_{1} \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right)$ and $y_{2}=a_{2} \cos \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)$ is
(a) $\frac{\lambda}{2 \pi} \phi$
(b) $\frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)$
(c) $\frac{2 \pi}{\lambda}\left(\phi-\frac{\pi}{2}\right)$
(d) $\frac{2 \pi}{\lambda}(\phi)$

Yuva S
Yuva S
Numerade Educator
01:39

Problem 14

A plane wave is described by the equation $y=3 \cos \left(\frac{x}{4}-10 t-\frac{\pi}{2}\right) .$ The maximum velocity of the particles of the medium due to this wave is
(a) 30
(b) $3 \pi / 2$
(c) $3 / 4$
(d) 40

RZ
Rubeena Zulfiqar
Numerade Educator
02:44

Problem 15

A wave represented by the given equation $y=A \sin \left(10 \pi x+15 \pi t+\frac{\pi}{3}\right)$ where $x$ is in meter and $t$ is in second. The expression represents
(a) A wave travelling in the positive $x$-direction with a velocity of $1.5 \mathrm{~m} / \mathrm{sec}$
(b) A wave travelling in the negative $x$-direction with a velocity of $1.5 \mathrm{~m} / \mathrm{sec}$
(c) A wave travelling in the negative $x$-direction with a wavelength of o.2 $m$
(d) A wave travelling in the positive $x$-direction with a wavelength of $0.2 \mathrm{~m}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:05

Problem 16

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 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) $\lambda=2 \pi y_{0}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:51

Problem 17

The equation of a wave travelling in a string can be written as $y=3 \cos \pi(100 t-x)$ Its wavelength is [MP PMT 1991, 94, 97; MNR 1985]
(a) $100 \mathrm{~cm}$
(b) $2 \mathrm{~cm}$
(c) $5 \mathrm{~cm}$
(d) None of these

RZ
Rubeena Zulfiqar
Numerade Educator
02:12

Problem 18

A plane wave is represented by $x=1.2 \sin (314 \mathrm{t}+12.56 \mathrm{y})$ where $x$ and $y$ are distances measured along in $x$ and $y$ direction in meter and $t$ is time in seconds. This wave has
(a) A wave length of $0.25 \mathrm{~m}$ and travels $\mathrm{m}+\mathrm{ve} x$-direction
(b) A wavelength of $0.25 \mathrm{~m}$ and travels in $+v e y$-direction
(c) A wavelength of o.5 $m$ and travels in - ve $y$-direction
(d) A wavelength of o.5 $m$ and travels in $-$ ve $x$-direction

RZ
Rubeena Zulfiqar
Numerade Educator
00:43

Problem 19

A wave is reflected from a rigid support. The change in phase on reflection will be
(a) $\pi / 4$
(b) $\pi / 2$
(c) $\pi$
(d) $2 \pi$

RZ
Rubeena Zulfiqar
Numerade Educator
01:37

Problem 20

The equation of displacement of two waves are given as $y_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right) ; \quad y_{2}=5$ $[\sin 3 \pi t+\sqrt{3} \cos 3 \pi]$
Then what is the ratio of their amplitudes
(a) $1: 2$
(b) $2: 1$
(c) $1: 1$
(d) None of these

RZ
Rubeena Zulfiqar
Numerade Educator
01:44

Problem 21

The equation of a wave travelling on a string is $\mathrm{y}=4 \sin \frac{\pi}{2}\left(8 t-\frac{x}{8}\right)$ if $x$ and $y$ are in $\mathrm{cm}$, then velocity of wave is
(a) $64 \mathrm{~cm} / \mathrm{sec}$ in $-x$ direction
(b) $32 \mathrm{~cm} / \mathrm{sec}$ in $-x$ direction
(c) $32 \mathrm{~cm} /$ sec in $+\mathrm{x}$ direction
(d) $64 \mathrm{~cm} / \mathrm{sec}$ in $+x$ direction

RZ
Rubeena Zulfiqar
Numerade Educator
02:31

Problem 22

The equation of wave is $y=2 \sin \pi(0.5 x-200 t)$ where $x$ and $y$ are expressed in $\mathrm{cm}$ and $t$ in $\mathrm{sec}$. The wave velocity is
(a) $100 \mathrm{~cm} / \mathrm{sec}$
(b) $200 \mathrm{~cm} / \mathrm{sec}$
(c) $300 \mathrm{~cm} / \mathrm{sec}$
(d) $400 \mathrm{~cm} / \mathrm{sec}$

RZ
Rubeena Zulfiqar
Numerade Educator
03:09

Problem 23

The stationary wave produced on a string is represented by the equation $y=5 \cos \left(\frac{\pi x}{3}\right) \sin (40 \pi t)$ where $x$ and $y$ are in $\mathrm{cm}$ and $t$ is in seconds. The distance between consecutive nodes is
(a) $5 \mathrm{~cm}$
(b) $\pi \mathrm{cm}$
(c) $3 \mathrm{~cm}$
(d) $40 \mathrm{~cm}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:14

Problem 24

On sounding tuning fork $A$ with another tuning fork B of frequency $384 \mathrm{~Hz}, 6$ beats are produced per second. After loading the prongs of $A$ with wax and then sounding it again with $B, 4$ Beats are produced per second what is the frequency of the tuning fork $A$.
(a) $388 \mathrm{~Hz}$
(b) $8 \mathrm{o} \mathrm{Hz}$
(c) $378 \mathrm{~Hz}$
(d) $390 \mathrm{~Hz}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:07

Problem 25

Two sound waves of slightly different frequencies propagating in the same direction produces beats due to [MP PET 2000]
(a) Interference
(b) Diffraction
(c) Polarization
(d) Refraction

RZ
Rubeena Zulfiqar
Numerade Educator
01:50

Problem 26

Beats are produced with the help of two sound waves on amplitude 3 and 5 units. The ratio of maximum to minimum intensity in the beats is
(a) $2: 1$
(b) $5: 3$
(c) $4: 1$
(d) $16: 1$

RZ
Rubeena Zulfiqar
Numerade Educator
01:33

Problem 27

Two tuning forks have frequencies 380 and 384 hertz respectively. When they are sounded together, they produce 4 beats. After hearing the maximum sound, how long will it take to hear the minimum sound [MP PMT/PET 1998]
(a) $1 / 2 \mathrm{sec}$
(b) $1 / 4 \mathrm{sec}$
(c) $1 / 8 \mathrm{sec}$
(d) $1 / 16 \mathrm{sec}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:10

Problem 28

Two tuning fork $A$ and $B$ give 4 beats per second when sounded together. The frequency of $A$ is $320 \mathrm{~Hz}$. When some wax is added to $B$ and it is sounded with $A, 4$ beats per second are again heard. The frequency of $B$ is
(a) $312 \mathrm{~Hz}$
(b) $316 \mathrm{~Hz}$
(c) $324 \mathrm{~Hz}$
(d) $328 \mathrm{~Hz}$

RZ
Rubeena Zulfiqar
Numerade Educator
03:10

Problem 29

41 forks are so arranged that each produces 5 beat/sec when sounded with its near fork. If the frequency of last fork is double the frequency of first fork, then the frequencies of the first and last fork respectively
[MP PMT 1997]
(a) 200,400
(b) 205,410
(c) 195,390
(d) 100,200

RZ
Rubeena Zulfiqar
Numerade Educator
01:25

Problem 30

In stationary waves, antinodes are the points where there is
(a) Minimum displacement and minimum pressure change
(b) Minimum displacement and maximum pressure change
(c) Maximum displacement and maximum pressure change
(d) Maximum displacement and minimum pressure change

Ajay Singhal
Ajay Singhal
Numerade Educator
03:16

Problem 31

The equation $y=0.15 \sin 5 x \cos 300 t$, describes a stationary wave. The wavelength of the stationary wave is
[MP PMT 1995]
(a) Zero meter
(b) $1.256$ meter
(c) $2.512$ meter
(d) $0.628$ meter

RZ
Rubeena Zulfiqar
Numerade Educator
02:03

Problem 32

The equation of a stationary wave is $y=0.8 \cos \left(\frac{\pi x}{20}\right) \sin 200 \pi t$ where $x$ is in $c m .$ and $t$ is in $\mathrm{sec}$. The separation between consecutive nodes will be
(a) $20 \mathrm{~cm}$
(b) $10 \mathrm{~cm}$
(c) $40 \mathrm{~cm}$
(d) $30 \mathrm{~cm}$

RZ
Rubeena Zulfiqar
Numerade Educator
00:58

Problem 33

Which of the property makes difference between progressive and stationary waves
(a) Amplitude
(b) Frequency
(d) Phase of the wave
(c) Propagation of energy

RZ
Rubeena Zulfiqar
Numerade Educator
02:13

Problem 34

If amplitude of waves at distance $\mathrm{r}$ from a point source is $A$, the amplitude at a distance $2 r$ will be [MP PMT $\left.198_{5}\right]$
(a) $2 A$
(b) $A$
(c) $A / 2$
(d) $A / 4$

RZ
Rubeena Zulfiqar
Numerade Educator
01:37

Problem 35

If two waves of same frequency and same amplitude respectively on superimposition produced a resultant disturbance of the same amplitude the wave differ in phase by
(a) $\pi$
(b) $2 \pi / 3$
(c) $\pi / 2$
(d) zero

RZ
Rubeena Zulfiqar
Numerade Educator
01:51

Problem 36

The superposition takes place between two waves of frequency $\mathrm{f}$ and amplitude $a$. The total intensity is directly proportional to [MP PMT 1986]
(a) $a$
(b) $2 a$
(c) $2 a^{2}$
(d) $4 a^{2}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:50

Problem 37

The following equation represent progressive transverse waves
$$
\begin{aligned}
&z_{1}=A \cos (\omega t-k x) \\
&Z_{2}=A \cos (\omega t+k x)
\end{aligned}
$$
$z_{3}=A \cos (\omega t+k y)$
$z_{4}=A \cos (2 \omega t-2 k y)$
A stationary wave will be formed by superposing
(a) $z_{1}$ and $z_{2}$
(b) $z_{1}$ and $z_{4}$
(c) $z_{2}$ and $z_{3}$
(d) $z_{3}$ and $z_{4}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:02

Problem 38

When two sound waves with a phase difference of $\pi / 2$ and each having amplitude $A$ and frequency $\omega$ are superimposed on each other, then the maximum amplitude and frequency of resultant wave is $\quad$ [MP PMT 1989]
(a) $\frac{A}{\sqrt{2}} ; \omega / 2$
(b) $\frac{A}{\sqrt{2}} ; \omega$
(c) $\sqrt{2} A ; \frac{\omega}{2}$
(d) $\sqrt{2} A ; \omega$

RZ
Rubeena Zulfiqar
Numerade Educator
01:10

Problem 39

There is a destructive interference between the two waves of wavelength $\lambda$ coming from two different paths at a point. To get maximum sound or constructive interference at that point, the path of one wave is to be increased by [MP PET 198 5 ]
(a) $\lambda / 4$
(b) $\lambda / 2$
(c) $\frac{3 \lambda}{4}$
(d) $\lambda$

RZ
Rubeena Zulfiqar
Numerade Educator
04:44

Problem 40

The tuning fork and sonometer wire were sounded together and produce 4 beats/second when the length of sonometer wire is $95 \mathrm{~cm}$ or $100 \mathrm{~cm} .$ The frequency of tuning fork is [MP PMT 1990]
(a) $156 \mathrm{~Hz}$
(b) $152 \mathrm{~Hz}$
(c) $148 \mathrm{~Hz}$
(d) $160 \mathrm{~Hz}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:19

Problem 41

A tuning fork $F_{1}$ has a frequency of $256 \mathrm{~Hz}$ and it is observed to produce 6 beats/second with another tuning fork $F_{2}$. When $F_{2}$ is loaded with wax. It still produces 6 beats/second with $F_{1}$. The frequency of $F_{2}$ before loading was
(a) $253 \mathrm{~Hz}$
(b) $262 \mathrm{~Hz}$
(c) $250 \mathrm{~Hz}$
(d) $259 \mathrm{~Hz}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:03

Problem 42

A source of sound of frequency 90 vibration/sec is approaching a stationary observer with a speed equal to $1 / 10$ the speed of sound. What will be the frequency heard by the observer $\quad$ [MP PMT 2000]
(a) $8 \mathrm{o}$ vibration $/ \mathrm{sec}$
(b) 90 vibration/sec
(c) 100 vibration $/ \mathrm{sec}$
(d) 120 vibration/sec

RZ
Rubeena Zulfiqar
Numerade Educator
01:10

Problem 43

A source of sound of frequency $500 \mathrm{~Hz}$ is moving towards an observer with velocity $30 \mathrm{~m} / \mathrm{s}$. The speed of the sound is $330 \mathrm{~m} / \mathrm{s}$. The frequency heard by the observer will be [MP PET 2000]
(a) $550 \mathrm{~Hz}$
(b) $458.3 \mathrm{~Hz}$
(c) $530 \mathrm{~Hz}$
(d) $545.5 \mathrm{~Hz}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:34

Problem 44

A motor car blowing a horn of frequency 124 vibration/sec moves with a velocity $72 \mathrm{~km} / \mathrm{hr}$ towards a tall wall. The frequency of the reflected sound heard by the driver will be (velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$ ) [MP PET 1997]
(a) 109 vibration $/ \mathrm{sec}$
(b) 132 vibration $/ \mathrm{sec}$
(c) 140 vibration $/ \mathrm{sec}$
(d) 248 vibration $/ \mathrm{sec}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:19

Problem 45

The driver of car travelling with a speed 30 meter/sec. towards a hill sounds a horn of frequency $600 \mathrm{~Hz}$. If the velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$ the frequency of reflected sound as heard by the driver is [MP PMT $\mathbf{1 9}$
(a) $720 \mathrm{~Hz}$
(b) $555.5 \mathrm{~Hz}$
(c) $550 \mathrm{~Hz}$
(d) $500 \mathrm{~Hz}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:41

Problem 46

The source of sound $\mathrm{s}$ is moving with a velocity $50 \mathrm{~m} / \mathrm{s}$ towards a stationary observer. The observer measures the frequency of the source as $1000 \mathrm{~Hz}$. What will be the apparent frequency of the source when it is moving away from the observer after crossing him ? The velocity of sound in the medium is $350 \mathrm{~m} / \mathrm{s}$ [MP PM
(a) $750 \mathrm{~Hz}$
(b) $857 \mathrm{~Hz}$
(c) $1143 \mathrm{~Hz}$
(d) $1333 \mathrm{~Hz}$

RZ
Rubeena Zulfiqar
Numerade Educator
01:37

Problem 47

A source and listener are both moving towards each other with speed $v / 10$ where $v$ is the speed of sound. If the frequency of the note emitted by the source is $f$, the frequency heard by the listener would be nearly [MP PMT 1994]
(a) $1.11 f$
(b) $1.22 f$
(c) $f$
(d) $1.27 f$

RZ
Rubeena Zulfiqar
Numerade Educator
04:47

Problem 48

A man is watching two trains, one leaving and the other coming in with equal speed of $4 \mathrm{~m} / \mathrm{s}$. If they sound their whistles, each of frequency $240 \mathrm{~Hz}$, the number of beats heard by the man (velocity of sound in air = $320 \mathrm{~m} / \mathrm{s}$ ) will be equal to
(a) 6
(b) 3
(c) 0
(d) 12

RZ
Rubeena Zulfiqar
Numerade Educator
02:14

Problem 49

At what speed should a source of sound move so that observer finds the apparent frequency equal to half of the original frequency [RPMT 1996]
(a) $v / 2$
(b) $2 v$
(c) $v / 4$
(d) $v$

RZ
Rubeena Zulfiqar
Numerade Educator