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The velocity of sound in a gas, in which two wavelengths \( 4.08 \, \text{m} \) and \( 4.16 \, \text{m} \) produce \( 40 \) beats in \( 12 \, \text{s} \), will be:

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 \( 20 \, \text{cm} \). The length of the open organ pipe is _______ \( \text{cm} \).

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

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of \( 20.0 \, \text{cm} \) for a tuning fork of frequency \( 400 \, \text{Hz} \) is used. The velocity of the sound at room temperature is \( 336 \, \text{m s}^{-1} \). The third resonance is observed when the air column has a length of _______ \( \text{cm} \).

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

An observer is riding on a bicycle and moving towards a hill at \( 18 \, \text{km h}^{-1} \). 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 \( 640 \, \text{Hz} \) and velocity of the sound in air is \( 320 \, \text{m /s} \) the beat frequency between the two sounds heard by observer will be _________ \( \text{Hz} \).

The frequency of echo will be _______ \( \text{Hz} \) if the train blowing a whistle of frequency \( 320 \, \text{Hz} \) is moving with a velocity of \( 36 \, \text{km/h} \) towards a hill from which an echo is heard by the train driver. Velocity of sound in air is \( 330 \, \text{m/s} \).

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:

In the wave equation
\( y = 0.5 \sin \dfrac{2\pi}{\lambda}(400t-x) \, \mathrm{m} \)
The velocity of the wave will be:

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

The speed of a transverse wave passing through a string of length \( 50\,\text{cm} \) and mass \( 10\,\text{g} \) is \( 60\,\text{m s}^{-1} \). The area of cross-section of the wire is \( 2.0\,\text{mm}^2 \) and its Young’s modulus is \( 1.2\times10^{11}\,\text{N m}^{-2} \). The extension of the wire over its natural length due to its tension will be \( x\times10^{-5}\,\text{m} \). The value of \( x \) 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 _______ \( \text{Hz} \).

In young’s double slit experiment performed using a monochromatic light of wavelength \( \lambda \), when a glass plate \( ( \mu = 1.5 ) \) of thickness \( x \lambda \) is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of \( x \) will be

The equations of two waves are given by: \( y_{1} = 5 \sin 2\pi(x - vt) \, \text{cm} \) ; \( y_{2} = 3 \sin 2\pi(x - vt + 1.5) \, \text{cm} \) These waves are simultaneously passing through a string. The amplitude of the resulting wave is:

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JEE Main 2022 29th June Morning Shift

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