Waves & Sound — JEE Main PYQs

Two loudspeakers ( $L_1$ and $L_2$ ) are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$, at equidistance to both loud speakers, is m …

In an open organ pipe $v_3$ and $v_6$ are $3^{\text{rd}}$ and $6^{\text{th}}$ harmonic frequencies, respectively. If $v_6-v_3=2200$ Hz then length of the pipe is $\_\_\_\_$ mm. (Take velocity of sound in air is $330$ m/s.)

The velocity of sound in air is doubled when the temperature is raised from $0^{\circ }\mathrm{C}$ to ${\alpha }^{\circ }\mathrm{C}$. The value of $\alpha$ is ______.

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x. The value of x is ____.

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

The speed of a longitudinal wave in a metallic bar is $400\mathrm{m}/\mathrm{s}$. If the density and Young's modulus of the bar material are increased by $0.5\%$ and $1\%$ respectively then the speed of the wave is changed approximately to ______ …

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s . When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s . If the original frequency of tuning fork B is 380 Hz , then the original frequency of tuning fork A is ______ Hz.

Two strings (A, B) having linear densities ${\mu }_{\mathrm{A}}=2\times 10^{-4}\mathrm{kg}/\mathrm{m}$ and ${\mu }_{\mathrm{B}}=4\times 10^{-4}\mathrm{kg}/\mathrm{m}$ and lengths ${\mathrm{L}}_{\mathrm{A}}=2.5\mathrm{m}$ and ${\mathrm{L}}_{\mathrm{B}}=1.5\mathrm{m}$ respectiv …

A transverse wave on a string is described by $y=3\sin (36t+0.018x+\pi /4)$. Where $x,y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is ______ cm.
(Nearest integer) ($\pi =3.14$)

The equation of a plane progressive wave is given by $y=5\cos \pi \left(200t-\frac{x}{150}\right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ____ $\mathrm{m}/\mathrm{s}$

A closed organ and an open organ tube filled by two different gases having same bulk modulus but different densities ${\rho }_1$ and ${\rho }_2$ respectively. The frequency of $9^{\text{th }}$ harmonic of closed tube is identical with $4^{\text{th }}$ harmonic of open tube. If th …

The equation of a transverse wave travelling along a string is $\mathrm{y}(\mathrm{x},\mathrm{t})=4.0\sin \left[20\times 10^{-3}\mathrm{x}+600\mathrm{t}\right]\mathrm{mm}$, where $x$ is in the mm and $t$ is in second. The velocity of the wave is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids.
In the light of the above statements, choose the co …

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at $x=0$ at $t=0$ sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave ?

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

Consider the sound wave travelling in ideal gases of $\mathrm{He}$, ${\mathrm{CH}}_4$, and ${\mathrm{CO}}_2$. All the gases have the same ratio $\frac{P}{\rho }$, where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases …

In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by

The equation of a wave travelling on a string is $y=\sin [20\pi x+10\pi t]$, where $x$ and $t$ are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

Two harmonic waves moving in the same direction superimpose to form a wave $x=a\cos (1.5t)\cos (50.5t)$ where $t$ is in seconds. Find the period with which they beat (close to nearest integer)

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is ${\mathrm{v}}_1$, …

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, ${\mathrm{y}}_1(\mathrm{x},\mathrm{t})=4\sin (\mathrm{kx}-\omega \mathrm{t})$ and $y_2(x,t)=2\sin \left(kx-\omega t+\frac{2\pi }{3}\right)$, are:
(Take the angular frequ …

A closed organ tube and an open organ tube are filled by two different gases having the same bulk modulus but different densities ρ₁ and ρ₂ respectively. The frequency of the 9th harmonic of the closed tube is identical with the 4th harmonic of the open tube. If the length of the …

Two open organ pipes of lengths 60 cm and 90 cm resonate at $6^{\text{th }}$ and $5^{\text{th }}$ harmonics respectively. The difference of frequency for the given modes is ______ Hz.

(Velocity of sound in air $=333\mathrm{m}/\mathrm{s}$ )

The equation of stationary wave is :
$y=2a\sin \left(\frac{2\pi nt}{\lambda }\right)\cos \left(\frac{2\pi x}{\lambda }\right)$
Which of the following is NOT correct

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension ______ cm.

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of $a$ is ____.

A plane progressive wave is given by $y=2\cos 2\pi (330t-x)m$. The frequency of the wave is :

A closed organ pipe 150 cm long gives 7 beats per second with an open organ pipe of length 350 cm , both vibrating in fundamental mode. The velocity of sound is ____ $\mathrm{m}/\mathrm{s}$.

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is 60 cm, the length of the closed pipe will be:

A tuning fork resonates with a sonometer wire of length 1 m stretched with a tension of 6 N. When the tension in the wire is changed to 54 N, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ______ Hz.

In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross-sectional area of 2 cm², the amount of water poured in the organ t …

The speed of sound in oxygen at S.T.P. will be approximately:
(Given, $R=8.3$ JK${}^{-1}$, $\gamma =1.4$)

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz . The length of the string producing a fundamental frequency of 180 Hz will be ____\ cm.

The engine of a train moving with speed $10{\mathrm{ms}}^{-1}$ towards a platform sounds a whistle at frequency 400 Hz. The frequency heard by a passenger inside the train is (neglect air speed. Speed of sound in air $330{\mathrm{ms}}^{-1}$)

An organ pipe 40 cm long is open at both ends. The speed of sound in air is $360{\mathrm{ms}}^{-1}$. The frequency of the second harmonic is $\_\_\_\_$ Hz.

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

A transverse harmonic wave on a string is given by $y(x,t)=5\sin (6t+0.003x)$ where $x$ and $y$ are in cm and $t$ in sec. The wave velocity is $\_\_\_\_$ ${\mathrm{ms}}^{-1}$.

The equation of wave is given by
$\mathrm{Y}=10^{-2}\sin 2\pi \left(160\mathrm{t}-0.5\mathrm{x}+\frac{\pi }{4}\right)$
Where $x$ and $Y$ are in $m$ and $t$ is $s$. The speed of the wave is ____ $\mathrm{km}{\mathrm{h}}^{-1}$

For a certain organ pipe, the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is $324{\mathrm{ms}}^{-1}$ the length of the organ pipe is ____ m.

In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is $\_\_\_\_$ g.

The fundamental frequency of vibration of a string stretched between two rigid support is 50 Hz. The mass of the string is 18 g and its linear mass density is $20\mathrm{g}/\mathrm{m}$. The speed of the transverse waves so produced in the string is ______ ${\mathrm{ms}}^{-1}$.

A person driving car at a constant speed of $15\mathrm{m}/\mathrm{s}$ is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car's horn upon reflection from the wall. The frequency of horn is $\_\_\_\_$ Hz.
(Given : Speed of sound : …

A car P travelling at $20{\mathrm{ms}}^{-1}$ sounds its horn at a frequency of 400 Hz. Another car Q is travelling behind the first car in the same direction with a velocity $40{\mathrm{ms}}^{-1}$. The frequency heard by the passenger of the car Q is approximately [Take, velo …

A wire of density $8\times 10^3{kg/m}^3$ is stretched between two clamps 0.5 m apart. The extension developed in the wire is $3.2\times 10^{-4}\mathrm{m}$. If $Y=8\times 10^{10}{N/m}^2$, the fundamental frequency of vibration in the wire will be …

A steel wire with mass per unit length $7.0\times 10^{-3}\mathrm{kg}{\mathrm{m}}^{-1}$ is under tension of 70 N. The speed of transverse waves in the wire will be:

A travelling wave is described by the equation
$y(x,t)=[0.05\sin (8x-4t]m$
The velocity of the wave is : [all the quantities are in SI unit]

The distance between two consecutive points with phase difference of $60^{\circ }$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is traveling is ______ km/s

A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of $66\mathrm{m}/\mathrm{s}$. The frequency observed by the observer will be (given speed of sound $=330{\mathrm{ms}}^{-1}$) $\_\_\_\_$ Hz.

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $30\mathrm{m}/\mathrm{s}$. If both trains emit sounds with frequency 300 Hz, (Speed of sound : $330\mathrm{m}/\mathrm{s}$) approximate difference of frequenci …

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is ______ degree.