Section 1
Round 1
Velocity of sound wave in air is $330 \mathrm{~m} / \mathrm{s}$ for a particular sound in air ; a path difference of $40 \mathrm{~cm}$ is equivalent to a phase difference of $1.6 \pi$. The frequency of this wave is(a) $165 \mathrm{~Hz}$(b) $150 \mathrm{~Hz}$(c) $660 \mathrm{~Hz}$(d) $330 \mathrm{~Hz}$
The equation of wave is represented by $Y=10^{-4} \sin \left[100 t-\frac{x}{10}\right] \mathrm{m}$, then the velocity of wave will be(a) $100 \mathrm{~ms}^{-1}$(b) $4 \mathrm{~ms}^{-1}$(c) $1000 \mathrm{~ms}^{-1}$(d) zero
A steel rod $100 \mathrm{~cm}$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53 \mathrm{kHz}$. What is the speed of sound in steel?(a) $5 \mathrm{~km} / \mathrm{s}$(b) $6 \mathrm{~km} / \mathrm{s}$(c) $7 \mathrm{~km} / \mathrm{s}$(d) $4 \mathrm{~km} / \mathrm{s}$
From a point source, if amplitude of waves at a distance $r$ is $A$, its amplitude at a distance $2 r$ will be(a) $A$(b) $2 A$(c) $A / 2$(d) $A / 4$
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) $54^{\circ}$(c) $36^{\circ}$(d) $72^{\circ}$
In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is $0.170 \mathrm{~s}$. The frequency of the wave is(a) $1.47 \mathrm{~Hz}$(b) $0.36 \mathrm{~Hz}$(c) $0.73 \mathrm{~Hz}$(d) $2.94 \mathrm{~Hz}$
$v_{1}$ and $v_{2}$ are the velocities of sound at the same temperature in two monoatomic gases of densities $\rho_{1}$ and $\rho_{2}$ respectively. If $\frac{\rho_{1}}{\rho_{2}}=\frac{1}{4}$, then the ratio of velocities $v_{1}$ and $v_{2}$ will be(a) $1: 2$(b) $4: 1$(c) $2: 1$(d) $1: 4$
A $1000 \mathrm{~Hz}$ sound wave in air strikes the surface of a lake and penetrates into water. If speed of sound in water is $1500 \mathrm{~ms}^{-1}$, the frequency and wavelength of waves in water are(a) $1500 \mathrm{~Hz}, 1 \mathrm{~m}$(b) $1000 \mathrm{~Hz}, 1.5 \mathrm{~m}$(c) $1000 \mathrm{~Hz}, 1 \mathrm{~m}$(d) $1500 \mathrm{~Hz}, 1.5 \mathrm{~m}$
The displacement $x$ (in metre) of a particle performing simple harmonic motion is related to time $t$ (in second) as $x=0.05 \cos \left(4 \pi t+\frac{\pi}{4}\right)$. The frequency of the motion will be(a) $0.5 \mathrm{~Hz}$(b) $1.0 \mathrm{~Hz}$(c) $1.5 \mathrm{~Hz}$(d) $2.0 \mathrm{~Hz}$
The temperature at which the speed of sound in air becomes double of its value at $0^{\circ} \mathrm{C}$ is(a) $273 \mathrm{~K}$(b) $546 \mathrm{~K}$(c) $1092 \mathrm{~K}$(d) $0 \mathrm{~K}$
A wave of frequency $500 \mathrm{~Hz}$ has a velocity $360 \mathrm{~ms}^{-1}$. The phase difference between two displacements at a certain point at time $10^{-3} \mathrm{~s}$ apart will be $\quad$ [NCERT](a) $\pi \mathrm{rad}$(b) $\pi / 2 \mathrm{rad}$(c) $\pi / 4 \mathrm{rad}$(d) $2 \pi \mathrm{rad}$
The phase difference between two points separated by $0.8 \mathrm{~m}$ in a wave of frequency $120 \mathrm{~Hz}$ is $0.5 \pi$. The wave velocity is(a) $144 \mathrm{~ms}^{-1}$(b) $384 \mathrm{~ms}^{-1}$(c) $256 \mathrm{~ms}^{-1}$(d) $720 \mathrm{~ms}^{-1}$
Two sitar strings $A$ and $B$ playing the note 'Ga' are slightly out of tune and produce beats of frequency $6 \mathrm{~Hz}$. The tension in the string $A$ is slightly reduced and the beat frequency is found to reduce to $3 \mathrm{~Hz}$. If the original frequency of $A$ is $324 \mathrm{~Hz}$, what is the frequency of $B$ ?(a) $218 \mathrm{~Hz}$(b) $518 \mathrm{~Hz}$(c) $418 \mathrm{~Hz}$(d) $318 \mathrm{~Hz}$
A stone dropped from the top of a tower of height 300 $\mathrm{m}$ high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is $340 \mathrm{~m} / \mathrm{s} ?$ $\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right) \quad\mathrm{}$(a) $8.7 \mathrm{~s}$(b) $9.7 \mathrm{~s}$(c) $6.7 \mathrm{~s}$(d) $10 \mathrm{~s}$
Speed of sound in mercury at a certain temperatur is $1450 \mathrm{~m} / \mathrm{s}$. Given the density of mercury a $13.6 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, the bulk modulus for mercury is(a) $2.86 \times 10^{10} \mathrm{~N} / \mathrm{m}^{3}$(b) $3.86 \times 10^{10} \mathrm{~N} / \mathrm{m}^{3}$(c) $4.86 \times 10^{10} \mathrm{~N} / \mathrm{m}^{3}$(d) $5.86 \times 10^{10} \mathrm{~N} / \mathrm{m}^{3}$
Speed of sound in mercury at a certain temperature is $1450 \mathrm{~m} / \mathrm{s}$. Given the density of mercury as $13.6 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, the bulk modulus for mercury is(a) $2.86 \times 10^{10} \mathrm{~N} / \mathrm{m}^{3}$(b) $3.86 \times 10^{10} \mathrm{~N} / \mathrm{m}^{3}$(c) $4.86 \times 10^{10} \mathrm{~N} / \mathrm{m}^{3}$(d) $5.86 \times 10^{10} \mathrm{~N} / \mathrm{m}^{3}$
The path difference between 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) $\frac{2 \pi}{\lambda}(\phi)$
Which of the following equations represents a wave?(a) $y=A \sin \omega t$(b) $y=A \cos k x$(c) $y=A \sin (a t-b x+c)$(d) $y=A(\omega t-k x)$
Ultrasonic waves are produced by(a) Piezoelectric effect(b) Pettiro's effect(c) Doppler's effect(d) Coulomb's law
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) $\lambda=\pi y_{0} / 4$(b) $\lambda=2 \pi y_{0}$(c) $\lambda=\pi / y_{0}$(d) $\lambda=\pi y_{0} / 2$
The wavelength of infrasonics in air is of the order of(a) $10^{0} \mathrm{~m}$(b) $10^{1} \mathrm{~m}$(c) $10^{-1} \mathrm{~m}$(d) $10^{-2} \mathrm{~m}$
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.
The speed of sound in a mixture of 1 mole of helium and 2 moles of oxygen at $27^{\circ} \mathrm{C}$ is(a) $800 \mathrm{~ms}^{-1}$(b) $400.8 \mathrm{~ms}^{-1}$(c) $600 \mathrm{~ms}^{-1}$(d) $1200 \mathrm{~ms}^{-1}$
A wave is represented by the equation $y=0.5 \sin (10 t+x) \mathrm{m}$ It is a travelling wave propagating along $+X$ direction with velocity(a) $40 \mathrm{~ms}^{-1}$(b) $20 \mathrm{~ms}^{-1}$(c) $5 \mathrm{~ms}^{-1}$(d) None of these
Under identical conditions of pressure and density, the speed of sound is highest in a(a) monoatomic gas(b) diatomic gas(c) triatomic gas(d) polyatomic gas
A sound absorber attenuates the sound level by $20 \mathrm{~dB}$. The intensity decreases by a factor of(a) 100(b) 1000(c) 10000(d) 10
The velocity of sound in air is $330 \mathrm{~ms}^{-1}$ and the velocity of light in air is $3 \times 10^{8} \mathrm{~ms}^{-1}$. What frequency, in Hz does a BBC station which transmits at $1500 \mathrm{~m}$ broadcast?(a) $2 \times 10^{5} \mathrm{~Hz}$(b) $595 \times 10^{3} \mathrm{~Hz}$(c) $0.22 \mathrm{~Hz}$(d) $5 \times 10^{-6} \mathrm{~Hz}$
Walls of auditorium should be(a) good absorber(b) reflector(c) amplifier(d) modifier
The velocity of sound in air is $330 \mathrm{~ms}^{-1}$. The $\mathrm{rms}$ velocity of air molecules $(\gamma=1.4)$ is approximately equal to(a) $400 \mathrm{~ms}^{-1}$(b) $471.4 \mathrm{~ms}^{-1}$(c) $231 \mathrm{~ms}^{-1}$(d) $462 \mathrm{~ms}^{-1}$
The ratio of intensities between two coherent sound sources is $4: 1$. The difference of loudness in decibels (dB) between maximum and minimum intensities, on their interference in space is(a) $20 \log 2$(b) $10 \log 2$(c) $20 \log 3$(d) $10 \log 3$
A sine wave has an amplitude $A$ and a wavelength $\lambda$. Let $v$ be the wave velocity, and $V$ be maximum velocity of a particle in the medium.(a) $V$ cannot be equal to $v$(b) $V=v$, if $A=\lambda / 2 \pi$(c) $V=v$, if $A=2 \pi \lambda$(d) $V=v$, if $\lambda=A / \pi$
Two identical sounds $A$ and $B$ reach a point in the same phase. The resultant sound is $C$. The loudness of $C$ is $n \mathrm{~dB}$ higher than the loudness of $A$.(a) 2(b) 3(c) 4(d) 6
The velocity of sound hydrogen is $1224 \mathrm{~ms}^{-1}$. Its velocity in mixture of hydrogen and oxygen containing 4 parts by volume of hydrogen and 1 part oxygen is(a) $1224 \mathrm{~ms}^{-1}$(b) $612 \mathrm{~ms}^{-1}$(c) $2448 \mathrm{~ms}^{-1}$(d) $306 \mathrm{~ms}^{-1}$
A wave represented by the given equation $y=a \cos (k x-\omega t)$ is superposed with another wave to form a stationary wave such that the point $x=0$ is a node. The equation for the other wave is(a) $y=a \sin (k x+\omega t)$(b) $y=-a \cos (k x+\omega t)$(c) $y=-a \cos (k x-\omega t)$(d) $y=-a \sin (k x-\omega t)$
A string of mass $2.5 \mathrm{~kg}$ is under a tension of $200 \mathrm{~N}$. The length of the stretched string is $20.0 \mathrm{~m}$. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in(a) $1 \mathrm{~s}$(b) $0.5 \mathrm{~s}$(c) $2 \mathrm{~s}$(d) data is insufficient
A wave of wavelength $2 \mathrm{~m}$ is reflected from a surface if a node is formed at $3 \mathrm{~m}$ from the surface, then at what distance from the surface another node will be formed?(a) $3 \mathrm{~m}$(b) $2 \mathrm{~m}$(c) $3 \mathrm{~m}$(d) $4 \mathrm{~m}$
Two wires made up of same material are of equal lengths but their radii are in the ratio $1: 2 .$ On stretching each of these two strings by the same tension, the ratio between the fundamental frequencies is(a) $1: 2$(b) $2: 1$(c) $1: 4$(d) $4: 1$
$n$ waves are produced on a string in one second. When the radius of the string is doubled and the tension is maintained the same, the number of waves produced in one second for the same harmonic will be(a) $\frac{n}{2}$(b) $\frac{n}{3}$(c) $2 n$(d) $\frac{n}{\sqrt{2}}$
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
A string in a musical instrument is $50 \mathrm{~cm}$ long and its fundamental frequency is $800 \mathrm{~Hz}$. If a frequency of $1000 \mathrm{~Hz}$ is to be produced, then required length of string is(a) $62.5 \mathrm{~cm}$(b) $50 \mathrm{~cm}$(c) $40 \mathrm{~cm}$(d) $37.5 \mathrm{~cm}$
The tension in a wire is decreased by $19 \%$. The percentage decrease in frequency will be(a) $19 \%$(b) $10 \%$(c) $0.19 \%$(d) None of these
An echo repeats two syllables. If the velocity of sound is $330 \mathrm{~ms}^{-1}$, then the distance of the reflecting surface is(a) $66.0 \mathrm{~m}$(b) $33.0 \mathrm{~m}$(c) $99.0 \mathrm{~m}$(d) $16.5 \mathrm{~m}$
A tuning fork of frequency $512 \mathrm{~Hz}$ is used to produce vibrations in a sonometer wire of natural frequency $256 \mathrm{~Hz}$. The wire will vibrate in(a) one segment(b) two segments(c) four segments(d) three segments
The following equations represent progressive transverse waves $Z_{1}=A \cos (\omega t-k X), \quad Z_{2}=A \cos (\omega t+k X)$$Z_{3}=A \cos (\omega t-k Y), \quad 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 $Z_{4}$
The equation of a stationary wave along a stretched string is given by $y=4 \sin \frac{2 \pi x}{2} \cos 40 \pi t$where $x$ and $y$ are in $\mathrm{cms}$ and $t$ is in sec. The separation between two adjacent nodes is(a) $3 \mathrm{~cm}$(b) $1.5 \mathrm{~cm}$(c) $6 \mathrm{~cm}$(d) $4 \mathrm{~cm}$
The length of a sonometer wire $A B$ is $110 \mathrm{~cm}$. 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
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) $\frac{1}{n}=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\frac{1}{n_{3}}$(b) $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_{1}}}+\frac{1}{\sqrt{n_{2}}}+\frac{1}{\sqrt{n_{3}}}$(c) $\sqrt{n}=\sqrt{n_{1}}+\sqrt{n_{2}}+\sqrt{n_{3}}$(d) $n=n_{1}+n_{2}+n_{3}$
An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is(a) $3: 8$(b) $8: 3$(c) $1: 2$(d) $4: 1$
In Melde's experiment, three loops are formed by putting a weight of $8 \mathrm{~g}$ in a massless pan. The weight required to form two loops is(a) $18 \mathrm{~g}$(b) $8 \mathrm{~g}$(c) $36 \mathrm{~g}$(d) $24 \mathrm{~g}$
A stretched string of length $l$ fixed at both ends can sustain stationary waves of wavelength $\lambda$ given by(a) $\lambda=2 \ln$(b) $\lambda=2 l / n$(c) $\lambda=l^{2} / 2 n$(d) $\lambda=n^{2} / 2 l$
In Melde's experiment, the string vibrates in 4 loops when a $50 \mathrm{~kg}$-wt weight is placed in the pan of weight 15 kg-wt. To made the string vibrate in 6 loops, the weight that has to be removed from the pan is approximately(a) $7 \mathrm{~kg}$-wt(b) $36 \mathrm{~kg}-\mathrm{wt}$(c) $21 \mathrm{~kg}-\mathrm{wt}$(d) $29 \mathrm{~kg}-\mathrm{wt}$
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 $2 / 3$ 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) $y=-0.4 \sin 2 \pi\left(t-\frac{x}{2}\right)$
A wave of frequency $100 \mathrm{~Hz}$ is sent along a string towards a fixed end. When this wave travels back, after reflection, a node is formed at a distance of $10 \mathrm{~cm}$ from the fixed end of the string. The speeds of incident (and reflected) waves are(a) $5 \mathrm{~ms}^{-1}$(b) $10 \mathrm{~ms}^{-1}$(c) $20 \mathrm{~ms}^{-1}$(d) $40 \mathrm{~ms}^{-1}$
An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher at $100 \mathrm{~Hz}$. The fundamental frequency of the open pipe is(a) $200 \mathrm{~Hz}$(b) $480 \mathrm{~Hz}$(c) $240 \mathrm{~Hz}$(d) $300 \mathrm{~Hz}$
The vibrating of four air columns are represented in the figure. The ratio of frequencies $n_{p}: n_{q}: n_{r}: n_{s}$ is(a) $12: 6: 3: 5$(b) $1: 2: 4: 3$(c) $4: 2: 3: 1$(d) $6: 2: 3: 4$
In a resonance column first and second resonance are obtained at depths $22.7 \mathrm{~cm}$ and $70.2 \mathrm{~cm}$. The third resonance will be obtained at a depth of(a) $117.7 \mathrm{~cm}$(b) $92.9 \mathrm{~cm}$(c) $115.5 \mathrm{~cm}$(d) $113.5 \mathrm{~cm}$
A cylindrical tube open at both ends, has a fundamental frequency $f_{0}$ in air. The tube is dipped vertically into water such that half of its length inside water. The fundamental frequency of the air column now is(a) $3 f_{0} / 4$(b) $f_{0}$(c) $f_{0} / 2$(d) $2 f_{0}$
A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tunning fork of frequency 340 $\mathrm{Hz}$ ) when the tube length is $25.5 \mathrm{~cm}$ or $79.3 \mathrm{~cm}$. Estimate the speed of sound in air at the temperature of the experiment. The edge effect may be neglected. (a) $336 \mathrm{~m} / \mathrm{s}$(b) $331 \mathrm{~m} / \mathrm{s}$(c) $356 \mathrm{~m} / \mathrm{s}$(d) $366 \mathrm{~m} / \mathrm{s}$
If $\lambda_{1}, \lambda_{2}, \lambda_{3}$ 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 $\lambda_{1}, \lambda_{2}, \lambda_{3}$ is(a) $1: 3: 5$(b) $1: 2: 3$(c) $5: 3: 1$(d) $1: \frac{1}{3}: \frac{1}{5}$
In a resonance tube, the first resonance with a tuning fork occurs at $16 \mathrm{~cm}$ and second at $49 \mathrm{~cm}$. If the velocity of sound is $330 \mathrm{~m} / \mathrm{s}$, the frequency of tunning fork is(a) 500(b) 300(c) 330(d) 165
An open organ pipe has fundamental frequency $100 \mathrm{~Hz}$. What frequency will be produced if its one end is closed?(a) $100,200,300 \ldots$(b) $50,150,250 \ldots$(c) $50,100,200,300 \ldots$(d) $50,100,150,200 \ldots$
An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by $100 \mathrm{~Hz}$. Then the fundamental frequency of open pipe is(a) $480 \mathrm{~Hz}$(b) $300 \mathrm{~Hz}$(c) $240 \mathrm{~Hz}$(d) $200 \mathrm{~Hz}$
A column of air of length $50 \mathrm{~cm}$ resonates with a stretched string of length $40 \mathrm{~cm}$. The length of the same air column which will resonate with $60 \mathrm{~cm}$ of the same string at the same tension is(a) $100 \mathrm{~cm}$(b) $75 \mathrm{~cm}$(c) $50 \mathrm{~cm}$(d) $25 \mathrm{~cm}$
In a resonance tube, using a tuning fork of frequency $325 \mathrm{~Hz}$, two successive resonance length are observed as $25.4 \mathrm{~cm}$ and $77.4 \mathrm{~cm}$ respectively. The velocity of sound in air is(a) $338 \mathrm{~ms}^{-1}$(b) $328 \mathrm{~ms}^{-1}$(c) $330 \mathrm{~ms}^{-1}$(d) $320 \mathrm{~ms}^{-1}$
An organ pipe $P_{1}$ closed at one end vibrating in its first harmonic and another pipe $P_{2}$ open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of $P_{1}$ to that of $P_{2}$ is(a) $1 / 3$(b) $1 / 6$(c) $3 / 8$(d) $8 / 3$
The tones that are separated by three octaves have a frequency ratio of(a) 3(b) 4(c) 8(d) 16
Air is blown at the mouth of a tube of length $25 \mathrm{~cm}$ and diameter equal to $2 \mathrm{~cm}$ open at both ends. If velocity of sound in air is $330 \mathrm{~ms}^{-1}$, the sound emitted will have all the frequencies in the group(a) $330,990,1690 \mathrm{~Hz}$(b) $302,664,1320 \mathrm{~Hz}$(c) $660,1320,1980 \mathrm{~Hz}$(d) $660,100,3300 \mathrm{~Hz}$
A pipe closed at one end and open at the other end, resonates with sound waves of frequency $135 \mathrm{~Hz}$ and also $165 \mathrm{~Hz}$, but not with any wave of frequency intermediate between these two. Then the frequency of the fundamental note is(a) $30 \mathrm{~Hz}$(b) $15 \mathrm{~Hz}$(c) $60 \mathrm{~Hz}$(d) $7.5 \mathrm{~Hz}$
In two similar wires of tensions $16 \mathrm{~N}$ and $\mathrm{T}, 3$ beats are heard, then $T=$(a) $49 \mathrm{~N}$(b) $25 \mathrm{~N}$(c) $64 \mathrm{~N}$(d) None of these
When 2 tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats $\mathrm{s}^{-1}$ are heard. Now, some tape is attached on the prong of fork $2 .$ When the tuning forks are sounded again, 6 beats $\mathrm{s}^{-1}$ are heard if the frequency of fork 1 is $200 \mathrm{~Hz}$, then what was the original frequency of fork 2 ?(a) $196 \mathrm{~Hz}$(b) $200 \mathrm{~Hz}$(c) $202 \mathrm{~Hz}$(d) $204 \mathrm{~Hz}$
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45 \mathrm{~Hz}$. The mass of the wire is $3.5 \times 10^{-2} \mathrm{~kg}$ and its linear mass density is $4.0 \times 10^{-2} \mathrm{~kg} / \mathrm{m}$. What is (i) the speed of a transverse wave on the string and (ii) the tension in the string?(a) (i) $80 \mathrm{~m} / \mathrm{s}$ (ii) $250 \mathrm{~N}$(b) (i) $88 \mathrm{~m} / \mathrm{s}$ (ii) $208 \mathrm{~N}$(c) (i) $90 \mathrm{~m} / \mathrm{s}$ (ii) $249 \mathrm{~N}$(d) (i) $78.75 \mathrm{~m} / \mathrm{s}$ (ii) $248 \mathrm{~N}$
Ten tuning forks are arranged in increasing order of frequency in such a way that any two nearest tuning forks produce 4 beats $\mathrm{s}^{-1} .$ The highest frequency is twice that of the lowest. Possible highest and lowest frequencies are(a) 80 and 40(b) 100 and 50(c) 44 and 32(d) 72 and 36
A source of frequency $n$ given 5 beats $\mathrm{s}^{-1}$, when sounded with a source of frequency $200 \mathrm{~s}^{-1}$. The second harmonic $(2 n)$ gives 10 beats $\mathrm{s}^{-1}$, when sounded with a source of frequency $420 \mathrm{~s}^{-1}, n$ is equal to(a) $200 \mathrm{~s}^{-1}$(b) $205 \mathrm{~s}^{-1}$(c) $195 \mathrm{~s}^{-1}$(d) $210 \mathrm{~s}^{-1}$
Two forks $A$ and $B$ when sounded together produce four beats $\mathrm{s}^{-1}$. The fork $A$ is in unison with $30 \mathrm{~cm}$ length of a sonometer wire and $B$ is in unison with $25 \mathrm{~cm}$ length of the same wire at the same tension. The frequencies of the forks are(a) $24 \mathrm{~Hz}, 28 \mathrm{~Hz}$(b) $20 \mathrm{~Hz}, 24 \mathrm{~Hz}$(c) $16 \mathrm{~Hz}, 20 \mathrm{~Hz}$(d) $26 \mathrm{~Hz}, 30 \mathrm{~Hz}$
Beats are produced by two travelling waves each of loudness $I$ and nearly equal frequencies $n_{1}$ and $n_{2}$. The beat frequency will be ... and maximum loudness hard will be(a) $\left(n_{1}-n_{2}\right), 21$(b) $\left.\left(n_{1}-n_{2}\right), 4\right]$(c) $\left(n_{1}-n_{2}\right), 3 l$(d) $\left(n_{1}-n_{2}\right), \quad l$
A tuning fork of frequency $200 \mathrm{~Hz}$ is in unison with a sonometer wire. The number of beats heard per second when the tension is increased by $1 \%$ is(a) 1(2) 2(c) 4(d) $1 / 2$
Two organ pipes both closed at on end have length $l$ and $(l+\Delta l) .$ Neglect end correction. If velocity of sound in air is $v$, the number of beats $\mathrm{s}^{-1}$ is(a) $v / 4 I$(b) $v / 2 l$(c) $\frac{v}{4 l^{2}}(\Delta l)$(d) $\frac{v}{2 l^{2}}(\Delta l)$
A fork of unknown frequency gives four beats $\mathrm{s}^{-1}$ when sounded with another of frequency 256 . The fork is now loaded with a piece of wax and again four beats $\mathrm{s}^{-1}$ are heard. Then the frequency of the unknown fork is(a) $256 \mathrm{~Hz}$(b) $252 \mathrm{~Hz}$(c) $264 \mathrm{~Hz}$(d) $260 \mathrm{~Hz}$
When two waves of almost equal frequencies $n_{1}$ and $n_{2}$ are produced simultaneously, then the time interval between successive maxima is(a) $\frac{1}{n_{1}-n_{2}}$(b) $\frac{1}{n_{1}}-\frac{1}{n_{2}}$(c) $\frac{1}{n_{1}}+\frac{1}{n_{2}}$(d) $\frac{1}{n_{1}+n_{2}}$
A tuning fork of frequency $480 \mathrm{~Hz}$ produces 10 beats ${ }^{-1}$ when sounded with a vibrating sonometer string. What must have been the frequency of string if slight increase in tension produces fewer beats $\mathrm{s}^{-1}$ than before?(a) $490 \mathrm{~Hz}$(b) $470 \mathrm{~Hz}$(c) $460 \mathrm{~Hz}$(d) $480 \mathrm{~Hz}$
Two organ pipes, each closed at one end, give 5 beats $\mathrm{s}^{-1}$ when emitting their fundamental notes. If their lengths are in the ratio $50: 51$, their fundamental frequencies are(a) 250,255(b) 255,260(c) 260,265(d) 265,270
A source of sound gives 5 beats $\mathrm{s}^{-1}$ when sounded with another source of frequency $100 \mathrm{~Hz}$. The second harmonic of the source together with a source of frequency $205 \mathrm{~Hz}$ gives 5 beats $\mathrm{s}^{-1}$. What is the frequency of the source?(a) $105 \mathrm{~Hz}$(b) $205 \mathrm{~Hz}$(c) $95 \mathrm{~Hz}$(d) $100 \mathrm{~Hz}$
Two uniform wires are vibrating simultaneously in their fundamental notes. The tension, lengths diameters and the densities of the two wires are in the ratio $8: 1,36: 35,4: 1$ and $1: 2$ respectively. If the note of the higher pitch has a frequency $360 \mathrm{~Hz}$, the number of beats produced per second is(a) 5(b) 15(c) 10(d) 20
Two sound sources emitting sound each of wavelength $\lambda$ are fixed at a given distance apart. A listener moves with a velocity $u$ along the line joining the two sources. The number of beats heard by him per second is(a) $2 \mathrm{u} / \lambda$(b) $u / \lambda$(c) $\frac{u}{3 \lambda}$(d) $\frac{2 \lambda}{u}$
A bus is moving with a velocity of $5 \mathrm{~ms}^{-1}$ towards a huge wall. The driver sounds a horn of frequency $165 \mathrm{~Hz}$. If the speed of sound in air is $335 \mathrm{~ms}^{-1}$, the number of beats heard per second by the passengers in the bus will be(a) 3(b) 4(c) 5(d) 6
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 $n^{\prime}$ of the sound as heard by the observer is plotted as a function of time $t$ (figure.). Identify the expected curve.
A rocket is receding away from earth with velocity $=0.2 c .$ The rocket emits signal or frequency $4 \times 10^{7} \mathrm{~Hz}$. The apparent frequency of the signal produced by the rocket observed by the observer on earth will be(a) $3 \times 10^{6} \mathrm{~Hz}$(b) $4 \times 10^{6} \mathrm{~Hz}$(c) $2.4 \times 10^{7} \mathrm{~Hz}$(d) $5 \times 10^{7} \mathrm{~Hz}$
A source of sound of frequency $256 \mathrm{~Hz}$ is moving towards a wall with a velocity of $5 \mathrm{~ms}^{-1}$. Velocity of sound is $330 \mathrm{~ms}^{-1} .$ The number of beats $\mathrm{s}^{-1}$ heard by an observer standing between the source and the wall is nearly(a) $\frac{256 \times 330}{325}-\frac{256 \times 330}{325}$(b) $256-\frac{256 \times 330}{325}$(c) $\frac{256 \times 330}{325}-\frac{256 \times 330}{325}$(d) $\frac{256 \times 330}{325}-256$
A bat flies at a steady speed of $4 \mathrm{~m} / \mathrm{s}$ emitting a sound of $f=90 \times 10^{3} \mathrm{~Hz}$. It is flying horizontally towards a vertical wall. The frequency of the reflected sound as detected by the bat will be (Take velocity of sound in air as $330 \mathrm{~m} / \mathrm{s}$ )(a) $88.1 \times 10^{3} \mathrm{~Hz}$(b) $87.1 \times 10^{3} \mathrm{~Hz}$(c) $92.1 \times 10^{3} \mathrm{~Hz}$(d) $89.1 \times 10^{3} \mathrm{~Hz}$
A source of sound emitting a tone of frequency $200 \mathrm{~Hz}$ moves towards an observer with a velocity $v$ equal to the velocity of sound. If the observer also moves away from the source with the same velocity $v$, the apparent frequency heard by the observer is(a) $50 \mathrm{~Hz}$(b) $100 \mathrm{~Hz}$(c) $150 \mathrm{~Hz}$(d) $200 \mathrm{~Hz}$
A source and an observer move away from each other with a velocity of $10 \mathrm{~m} / \mathrm{s}$ with respect to ground. If the observer finds the frequency of sound coming from the source as $1950 \mathrm{~Hz}$, then actual frequency of the source is (velocity of sound in air $=340 \mathrm{~m} / \mathrm{s}$ )(a) $1950 \mathrm{~Hz}$(b) $2068 \mathrm{~Hz}$(c) $2132 \mathrm{~Hz}$(d) $2486 \mathrm{~Hz}$
A sound wave of frequency $n$ travels horizontally to the right. It is reflected from a large vertical plane surface moving to the left with speed $v$. The speed of the sound in the medium is $c$. Then,(a) the frequency of the reflected wave is $\left[\frac{c+v}{c-v}\right]$(b) the wavelength of the reflected wave is $\left[\frac{c}{n}\right]\left[\frac{c+v}{c-v}\right]$(c) the number of waves striking the surface per second is $\left[\frac{\mathrm{c}+\mathrm{v}}{\mathrm{c}}\right]$(d) the number of beats heard by a stationary listener to the left to the reflecting surface is $\frac{n v}{c-v}$
A whistle giving out $450 \mathrm{~Hz}$ approaches a stationary observer at a speed of $33 \mathrm{~ms}^{-1}$. The frequency heard by the observer in $\mathrm{Hz}$ is [velocity of sound in air $=333 \mathrm{~ms}^{-1}$ ](a) 409(b) 429(c) 517(d) 500
A train moves towards a stationary observer with speed $34 \mathrm{~ms}^{-1}$. The train sounds a whistle and its frequency registered by the observer is $f_{1}$. If the train's speed is reduced to $17 \mathrm{~ms}^{-1}$, the frequency registered is $f_{2}$. If the speed of sound is $340 \mathrm{~ms}^{-1}$, then the ratio $f_{1} / f_{2}$ is(a) $18 / 19$(b) $1 / 2$(c) 2(d) $19 / 18$
A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v=$ the velocity of sound, the velocity of the car is(a) $v / \sqrt{2}$(b) $v / 2$(c) $\mathrm{v} / 3$(d) $v / 4$
A source of sound $S$ is moving with a velocity of $50 \mathrm{~ms}^{-1}$ 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 the sound in medium is $350 \mathrm{~ms}^{-1}$(a) $750 \mathrm{~Hz}$(b) $857 \mathrm{~Hz}$(c) $1143 \mathrm{~Hz}$(d) $1333 \mathrm{~Hz}$
A source of sound of frequency $500 \mathrm{~Hz}$ is moving towards an observer with velocity $30 \mathrm{~ms}^{-1}$. The speed of sound is $330 \mathrm{~ms}^{-1}$. The frequency heard by the observer will be(a) $545 \mathrm{~Hz}$(b) $580 \mathrm{~Hz}$(c) $558.3 \mathrm{~Hz}$(d) $550 \mathrm{~Hz}$