Waves

Statement-I : Velocity of sound in solids in more compared to that in gases.

Statement-II : Bulk modulus of gas is more than that of solids.

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 correct answer from the options given below.

[JEE Main 2025, 28 Jan (Shift 1)]

A closed organ and an open organ tube are 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 the length of the closed tube is 10 cm and the density ratio of the gases is \({\rho }_{1}:{\rho }_{2}=1:16\), then the length of the open tube is :

[JEE Main 2025, 22 Jan (Shift 1)]

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

[JEE Main 2025, 4 Apr (Shift 1)]

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 ?

[JEE Main 2025, 2 Apr (Shift 2)]

In an open organ pipe v₃ and v₆ are 3^rd and 6^th harmonic frequencies, respectively. If v₃ – v₆ = 2200 Hz then length of the pipe is_______mm.

(Take velocity of sound in air is 330 m/s.)

[JEE Main 2026, 22 Jan (Shift 2)]

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

[JEE Main 2025, 23 Jan (Shift 2)]

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 \(\frac{5}{x}\). The value of x is:

[JEE Main 2026, 24 Jan (Shift 2)]

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 correct answer from the options given below.

[JEE Main 2025, 28 Jan (Shift 1)]

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 be:

[JEE Main 2024, 1 Feb (Shift 2)]

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 \({\mathrm{y}}_{2}(\mathrm{x},\mathrm{t})=2\sin \left(\mathrm{kx}-\omega \mathrm{t}+\frac{2\pi }{3}\right)\), are :
(Take the angular frequency of initial waves same as \(\omega\))

[JEE Main 2025, 8 Apr (Shift 1)]

Statement-I : Velocity of sound in solids in more compared to that in gases.

Statement-II : Bulk modulus of gas is more than that of solids.

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 :

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

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:

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

[JEE Main 2025, 7 Apr (Shift 1)]

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

The speed of a longitudinal wave in a metallic bar is 400 m/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 ______ m/s.

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 \({v}_{1}\), and that in the other string having radius of cross section \(\frac{R}{2}\) is \({v}_{2}\). Then \(\frac{{v}_{2}}{{v}_{1}}=\)

[JEE Main 2025, 8 Apr (Shift 1)]

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

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 \({V}_{\mathrm{He}}:{\mathrm{V}}_{{\mathrm{CH}}_{4}}:{\mathrm{V}}_{{\mathrm{CO}}_{2}}\) is given by

A closed organ pipe of length \(10\text{ }\text{cm}\) is in the \({9}^{\text{th}}\) harmonic and resonates with the \({4}^{\text{th}}\) harmonic of an open organ pipe. Find the length of the open organ pipe.

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 _______ m / s.

[JEE Main 2026, 2 Apr (Shift 1)]

A closed organ pipe of length \(10\text{ }\text{cm}\) is in the \({9}^{\text{th}}\) harmonic and resonates with the \({4}^{\text{th}}\) harmonic of an open organ pipe. Find the length of the open organ pipe.

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

[JEE Main 2025, 7 Apr (Shift 2)]

The speed of a longitudinal wave in a metallic bar is 400 m/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 ______ m/s.

[JEE Main 2025, 22 Jan (Shift 2)]

Displacement of a wave is expressed as \(\mathrm{x}(\mathrm{t})=5\cos \left(628\mathrm{t}+\frac{\pi }{2}\right)\mathrm{m}\). The wavelength of the wave when its velocity is \(300\mathrm{m}/\mathrm{s}\) is :

[JEE Main 2025, 4 Apr (Shift 2)]

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 correct answer from the options given below.

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:

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

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

[JEE Main 2025, 23 Jan (Shift 2)]

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:

[JEE Main 2024, 27 Jan (Shift 1)]

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 correct answer from the options given below.

A closed organ and an open organ tube are 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 the length of the closed tube is 10 cm and the density ratio of the gases is \({\rho }_{1}:{\rho }_{2}=1:16\), then the length of the open tube is :

[JEE Main 2025, 22 Jan (Shift 1)]

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

In an open organ pipe v₃ and v₆ are 3^rd and 6^th harmonic frequencies, respectively. If v₃ – v₆ = 2200 Hz then length of the pipe is_______mm.

(Take velocity of sound in air is 330 m/s.)

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

Two coherent light sources having intensity in the ratio \(\ 2 x\) produce an interference pattern. The ratio \(\ \frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}\) will be:

[JEE Main 2021, 25 Feb (Shift 1)]

Three harmonic waves having equal frequency and same intensity \( \mathrm{l}_{0} \), 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:

[JEE Main 2019, 10 Jan (Shift 2)]

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]

A uniform thin rope of length \( 12 \mathrm{~m} \) and mass \( 6 \mathrm{~kg} \) hangs vertically from a rigid support and a block of mass \( 2 \mathrm{~kg} \) is attached to its free end. A transverse short wavetrain of wavelength \( 6 \mathrm{~cm} \) is produced at the lower end of the rope. What is the wavelength of the wavetrain (in \( \mathrm{cm} \) ) when it reaches the top of the rope?

[JEE Main 2020, 3 Sep (Shift 1)]

A car \(P\) travelling at \(20 \mathrm{~ms}^{-1}\) sounds its horn at a frequency of \(400 \mathrm{~Hz}\). 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, velocity of sound \(=360 \mathrm{~ms}^{-1}\) ]

[JEE Main 2023, 11 Apr (Shift 2)]

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 student is performing the experiment of resonance column. The diameter of the column tube is \(\ 6 \mathrm{~cm}\). The frequency of the tuning fork is \(\ 504 \mathrm{~Hz}\). Speed of the sound at the given temperature is \(\ 336 \mathrm{~m} / \mathrm{s}\). The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:

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

[JEE Main 2023, 1 Feb (Shift 1)]

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 \(A\) ?

[JEE Main 2021, 26 Feb (Shift 2)]

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

[JEE Main 2020, 8 Jan (Shift 2)]

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]

[JEE Main 2023, 24 Jan (Shift 1)]

In a resonance tube experiment when the tube is filled with water up to a height of \( 17.0 \mathrm{~cm} \) 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 \( 24.5 \mathrm{~cm} \). If the velocity of sound in air is \( 330 \mathrm{~m} / \mathrm{s} \), the tuning fork frequency is

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:

[JEE Main 2023, 31 Jan (Shift 2)]

A wire of density \( 9 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3} \) is stretched between two clamps \( 1 \mathrm{~m} \) apart and is subjected to an extension of \( 4.9 \times 10^{-4} \mathrm{~m} \). What will be the lowest frequency (in Hz) of transverse vibration in the wire? \( \left(Y=9 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}\right) \)

[JEE Main 2020, 2 Sep (Shift 2)]