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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 \( 405\,\text{Hz} \) and the speed of sound in air is \( 324\,\text{m}\,\text{s}^{-1} \) the length of the organ pipe is _____ \( \text{m} \)

A guitar string of length \( 90 \, \text{cm} \) vibrates with a fundamental frequency of \( 120 \, \text{Hz} \). The length of the string producing a fundamental frequency of \( 180 \, \text{Hz} \) will be __________ \( \text{cm} \).

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

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

A car P travelling at \( 20 \, \text{m s}^{-1} \) sounds its horn at a frequency of \( 400 \, \text{Hz} \). Another car Q is travelling behind the first car in the same direction with a velocity \( 40 \, \text{m s}^{-1} \). The frequency heard by the passenger of the car Q is approximately. [Take: velocity of sound \( = 360 \, \text{m s}^{-1} \) ]

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

For a solid rod, the Youngs modulus of elasticity is \( 3.2 \times 10^{11} \, \text{N m}^{-2} \) and density is \( 8 \times 10^{3} \, \text{kg m}^{-3} \). The velocity of longitudinal wave in the rod will be:

In an experiment with sonometer when a mass of \( 180 \, \text{g} \) is attached to the string, it vibrates with fundamental frequency of \( 30 \, \text{Hz} \). When a mass \( m \) is attached, the string vibrates with fundamental frequency of \( 50 \, \text{Hz} \). The value of \( m \) is __________ \( \text{g} \).

The equation of wave is given by \( Y = 10^{-2} \sin 2\pi(160t - 0.5x + \pi/4) \) where \( x \) and \( Y \) are in \( \text{m} \) and \( t \) in \( \text{s} \). The speed of the wave is ______ \( \text{km h}^{-1} \).

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

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

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

A person driving car at a constant speed of \( 15 \, \text{m/s} \) is approaching a vertical wall. The person notices a change of \( 40 \, \text{Hz} \) in the frequency of his car's horn upon reflection from the wall. The frequency of horn is _________ \( \text{Hz} \). (Given: Speed of sound : \( 330 \, \text{m/s} \))

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JEE Main 2023 10th April Morning Shift

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