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

In the resonance experiment, two air columns (closed at one end) of \( 100 \, \text{cm} \) and \( 120 \, \text{cm} \) 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:

A body of mass \( m \) is suspended by two strings making angles \( \theta_{1} \) and \( \theta_{2} \) with the horizontal ceiling with tensions \( T_{1} \) and \( T_{2} \) simultaneously. \( T_{1} \) and \( T_{2} \) are related by \( T_{1} = \sqrt{3}\, T_{2} \), the angles \( \theta_{1} \) and \( \theta_{2} \) are:

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 \( R/2 \) is \( v_2 \). Then \( \frac{v_2}{v_1} = \)

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

Displacement of a wave is expressed as \( x(t) = 5 \cos\!\left(628 t + \frac{\pi}{2}\right) \, \text{m} \). The wavelength of the wave when its velocity is \( 300 \, \text{m/s} \) is: \( (\pi = 3.14) \)

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, \( y_1(x, t) = 4\sin(kx - \omega t) \) and \( y_2(x, t) = 2\sin(kx - \omega t + \frac{2\pi}{3}) \), are:

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 \( x = a \cos(1.5\, t)\cos(50.5\, t) \) where \( t \) is in seconds. Find the period with which they beat. (close to nearest integer):

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

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 \( 10 \, \text{cm} \) and the density ratio of the gases is \( \rho_1 : \rho_2 = 1 : 16 \), then the length of the open tube is:

If \( \vec{L} \) and \( \vec{P} \) represent the angular momentum and linear momentum respectively of a particle of mass ‘\( m \)’ having position vector as \( \vec{r} = a \left( \hat{i} \cos \omega t + \hat{j} \sin \omega t \right) \). The direction of force is:

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JEE Main 2025 23rd Jan Evening Shift

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