Waves & Sound — JEE Main PYQs

For a solid rod, the Young's modulus of elasticity is $3.2\times 10^{11}{\mathrm{Nm}}^{-2}$ and density is $8\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$. The velocity of longitudinal wave in the rod will be.

The displacement equations of two interfering waves are given by


respectively. The amplitude of the resultant wave is ____ cm.

Nearly $10\%$ of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is $a\times 10^{-2}\mathrm{W}/{\mathrm{m}}^2$. The value of 'a' will be

In the wave equation

the velocity of the wave will be :

The frequency of echo will be _____ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of $36$ km/h towards a hill from which an echo is heard by the train driver. Velocity of sound in air is $330$ m/s.

An observer is riding on a bicycle and moving towards a hill at $18{\mathrm{kmh}}^{-1}$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and vel …

A transverse wave is represented by $y=2\sin (\omega t-kx)$ cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be :

A wire of length 30 cm, stretched between rigid supports, has it's nᵗʰ and (n+1)ᵗʰ harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, it's linear mass density is ______ kg/m.

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of $n$ will be

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is ______ (deg …

A radio can tune to any station in 6 MHz to 10 MHz band. The value of corresponding wavelength bandwidth will be :

When a car is approaching the observer, the frequency of horn is 100 Hz . After passing the observer, it is 50 Hz . If the observer moves with the car, the frequency will be $\frac{\mathrm{X}}{3}\mathrm{Hz}$ where $\mathrm{x}=$ ____

A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ______ cm.
(Velocity of s …

If a wave gets refracted into a denser medium, then which of the following is true?

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be:

In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is $336{\mathrm{ms}}^{-1}$. The …

For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm.

The value of v is :

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is ______ Hz.

A longitudinal wave is represented by
$\mathrm{x}=10\sin 2\pi \left(\mathrm{nt}-\frac{\mathrm{x}}{\lambda }\right)\mathrm{cm}$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :

The equations of two waves are given by :


These waves are simultaneously passing through a string. The a …

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by
$y=\left(10\cos \pi x\sin \frac{2\pi t}{T}\right)\mathrm{cm}$
The amplitude of the particle at …

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is ______ cm.

A source and a detector move away from each other in absence of wind with a speed of $20\mathrm{m}/\mathrm{s}$ with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering spe …

Two travelling waves produces a standing wave represented by equation, $y=1.0\mathrm{mm}\cos \left(1.57{\mathrm{cm}}^{-1}\right)x\sin \left(78.5{\mathrm{s}}^{-1}\right)t$. The node closest to the origin in the region $x>0$ will be at $x=$____ cm.

Two waves are simultaneously passing through a string and their equations are: $y_1=A_1\sin k(x-vt),y_2=A_2\sin k\left(x-vt+x_0\right)$. Given amplitudes $A_1=12\mathrm{mm}$ and $A_2=5\mathrm{mm},x_0=$ 3.5 cm and wave number …

The amplitude of wave disturbance propagating in the positive $x$-direction is given by $\mathrm{y}=\frac{1}{1+(\mathrm{x}{)}^2}$ at time $\mathrm{t}=0$ and $\mathrm{y}=\frac{1}{1+(\mathrm{x}-2{)}^2}$ at $\mathrm{t}=1\mathrm{s}$, where x and y are in metres. The shape …

The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is $330\mathrm{m}/\mathrm{s}$. Then the speed of car is ____ $\mathrm{km}/\mathrm{h}$.

Which of the following equations represents a traveling wave?

Two cars are approaching each other at an equal speed of $7.2\mathrm{km}/\mathrm{hr}$. When they see each other, both blow horns of 676 Hz . The beat frequency heard by each driver will be ____ Hz . [Velocity of sound in air is $340\mathrm{m}/\mathrm{s}$ ]

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 Å is observed at 5896 Å ?

A tuning fork is vibrating at 250 Hz . The length of the shortest closed organ pipe that will resonate with the tuning fork will be ____ cm .
(Take speed of sound in air as $340{\mathrm{ms}}^{-1}$)

A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm . The Frequency of the tuning fork is 504 Hz . Speed of the sound at the given temperature is $336\mathrm{m}/\mathrm{s}$. The zero of the metre scale coincides with the top e …

The mass per unit length of a uniform wire is $0.135\mathrm{g}/\mathrm{cm}$. A transverse wave of the form $\mathrm{y}=-0.21\sin (x+30t)$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is …

Two cars X and Y are approaching each other with velocities $36\mathrm{km}/\mathrm{h}$ and $72\mathrm{km}/\mathrm{h}$ respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is 1320 Hz. If the velocity of sound in …

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

A wire having a linear mass density $9.0\times 10^{-4}kg/m$ is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at which the same wire resonates is 550 Hz. The length of the wire is __ …

Red light differs from blue light as they have:

A closed-organ pipe of length $L$ and an open pipe contain gases of densities ${\rho }_1$ and ${\rho }_2$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is …

A galaxy is moving away from the earth at a speed $286km/s$. The shift in wavelength of a redline at 630 nm is $x\times 10^{-10}\mathrm{m}$. The value of $x$, to the nearest integer, is ____
[Take the value of speed of light c, as …

A sound wave of frequency 245 Hz travels with the speed of $300{\mathrm{ms}}^{-1}$ along the positive x -axis. Each point of the wave moves to and for through a total distance of 6 cm . What will be the mathematical expression of this traveling wave?

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observers hears 2 beats/sec. The oscillation frequency of each tuning fork is …

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300\mathrm{m}/\mathrm{s}$, the frequency difference between the fundamental and second harmonic of this pipe is
____ Hz …

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is $2.06\times 10^4\mathrm{N}$. When the tension is changed to T, the velocity changed to $\mathrm{v}/2$. The value of T is close to:

A wire of length L and mass per unit length $6.0\times 10^{-3}\mathrm{kg}{\mathrm{m}}^{-1}$ is put under tension of 540 N. Two consecutive frequencies that it resonates at are: 420 Hz and 490 Hz . Then L in meters is

Three harmonic waves having equal frequency v and same intensity ${\mathrm{I}}_0$, have phase angles $0,\frac{\pi }{4}$ and $-\frac{\pi }{4}$ respectively. When they are superimposed the intensity of the resultant wave is close to:

Two coherent sources of sound, ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ produce source waves of the same wavelength, $\lambda =1\mathrm{m}$, in phase. ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are placed 1.5 m apart (see fig). A listener located at L , directly in front of $S_2$ find …

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 440 Hz to 480 Hz, when it gets reflected from the wall. If the speed of sound in air is $345\mathrm{m}/\mathrm{s}$, then the speed of the car is:

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave-train of wavelength 6 cm is produced at the lower and the rope. What is the wavelength of the wave train (in cm) wh …

In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm . If the velocity of sound in …