Waves & Sound — JEE Main PYQs

A sound source S is moving along a straight track with speed v, and is emitting sound of frequency $v_0$ (see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by:
( …

For a transverse wave traveling along a straight line, the distance between two peaks (crests) is 5 m , while the distance between one crest and one trough is 1.5 m . The possible wavelengths (in m ) of the waves are:

The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is $330{\text{ ms}}^{-1}$:

A wire of length 2 L is made by joining two wires A and b of same lengths but different radii $r$ and $2r$ and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $A$ is $p$ and that in …

A string is clamed at both the ends and it is vibrating in its $4^{\text{th }}$ harmonic. The equation of the stationary wave is $\mathrm{Y}=0.3\sin (0.157\mathrm{x})\cos (200\pi \mathrm{t})$. The length of the string is: (all quantities are in SI units)

The pressure wave, $\mathrm{P}=0.01\sin [1000\mathrm{t}-3\mathrm{x}]{\mathrm{NM}}^{-2}$, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is $0^{\circ }\mathrm{C}$. On some other day when temperature is T , the speed of sound prod …

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N . The string is set into vibration using an external vibrator of frequency 100 Hz . The separation between successive nodes on the string is close to:

A train moves towards a stationary observer with speed $34\mathrm{m}/\mathrm{s}$. The train sounds a whistle and its frequency registered by the observer is ${\mathrm{f}}_1$. If the speed of the train is reduced to $17\mathrm{m}/\mathrm{s}$, the frequency registered is …

A progressive wave travelling along the positive $x$-direction is represented by $y(x,t)=A$ sin $(\mathrm{kx}-\omega \mathrm{t}+\varphi )$. Its snapshot at $\mathrm{t}=0$ is given in the figure:

For this wave, the phase $\varphi$ is :

A submarine (A) travelling at $18\mathrm{km}/\mathrm{hr}$ is being chased along the line of its velocity by another submarine (B) travelling at $27\mathrm{km}/\mathrm{hr}$. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency $v$. …

The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz,

A source of sound S is moving with the velocity of $50\mathrm{m}/\mathrm{s}$ towards a stationary observer. The observer measures the frequency of the sound as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing h …

Equation of travelling wave on a stretched string of linear density $5\mathrm{g}/\mathrm{m}$ is $y=0.03\sin (450\mathrm{t}-9\mathrm{x})$ where distance and time are measured in SI united. The tension in the string is:

A travelling harmonic wave is represented by the equation $y(x,t)=10^{-3}\sin (50t+2x)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave?

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle $60^{\circ }$ with ground level. But he finds the aeroplane right vertically above his position. If $v$ is the speed of sound, speed of the plane is:

A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound? [Given reference intensity of sound as $10^{-12}\mathrm{W}/{\mathrm{m}}^2$]

Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency 660 Hz . A listener is moving from source ${\mathrm{S}}_1$ towards ${\mathrm{S}}_2$ with a constant speed $\mathrm{um}/\mathrm{s}$ and he hears 10 beats $/\mathrm{s}$. The velo …

A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, ${\ell }_1=30\mathrm{cm}$ and ${\ell }_2=70\mathrm{cm}$. Then n is equal …

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tub …

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of $20{\mathrm{ms}}^{-1}$ with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency o …

A string 2.0 m long and fixed at its end is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is:

A musician using an open flute of length 50 cm produces second harmonic sound waves.
A person runs towards the musician from another end of a hall at a speed of $10\mathrm{km}/\mathrm{h}$. If the wave speed is $330\mathrm{m}/\mathrm{s}$, the frequency heard by the running …

A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in ${\mathrm{ms}}^{-1}$ (Given speed of sound $=300\mathrm{m}/\mathrm{s}$)

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7\times 10^3$ kg/m${}^3$ and its Young's modulus is $9.27\times 10^{10}$ Pa. What will be the fundamental frequency of the longitudinal vibrations?

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz . What is the frequency of the microwave measured by the observer ?
(speed of light $=3\times 10^8{\mathrm{ms}}^{-1}$)

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 : (take $g=10{\mathrm{ms}}^{-2}$)

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 :

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 $=320{\mathrm{ms}}^{-1}$) cl …

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 $340\mathrm{m}/\mathrm{s}$.

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of $1\%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7\times 10^3\mathrm{kg}/{\mathrm{m}}^3$ and …

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

The transverse displacement $y(x,t)$ of a wave on a string is given by $y(x,t)=e^{-(a{x}^2+b{t}^2+2\sqrt{ab}xt)}$. This represents a

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

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 sire. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\%$ …

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

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. …

The speed of sound in oxygen $\left({\mathrm{O}}_2\right)$ at a certain temperature is $460{\mathrm{ms}}^{-1}$. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

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

A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of

A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed $v{\text{ms}}^{-1}$. The velocity of sound in air is $300{\text{ms}}^{-1}$. If the person can hear frequencies upto a maximum of $10,000\text{Hz}$, the maximum value of v …

A string is stretched between fixed points separated by 75 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

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 th …

An observer moves towards a stationary source of sound, with a velocity one fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

The displacement $y$ of a particle in a medium can be expressed as $y=10^{-6}\sin (100t+20x+\pi /4)$ m, where $t$ is in seconds and $x$ in meter. The speed of the wave is