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

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 \( 60 \, \text{cm} \), the length of the closed pipe will be:

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

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

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

The speed of sound in oxygen at S.T.P. will be approximately:
(given, \( R = 8.3 \, \text{J} \, \text{K}^{-1} ,\; \gamma = 1.4 \))

In a closed organ pipe, the frequency of fundamental note is \( 30 \, \text{Hz} \). A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to \( 110 \, \text{Hz} \). If the organ pipe has a cross-sectional area of \( 2 \, \text{cm}^2 \), the amount of water poured in the organ tube is ______ \( \text{g} \). (Take speed of sound in air is \( 330 \, \text{m/s} \))

Two open organ pipes of lengths \( 60 \, \text{cm} \) and \( 90 \, \text{cm} \) resonate at \( 6^{\text{th}} \) and \( 5^{\text{th}} \) harmonics respectively. The difference of frequencies for the given modes is _______ \( \text{Hz} \).
(Velocity of sound in air \( = 333 \, \text{m/s} \))

A sonometer wire of resonating length \( 90 \, \text{cm} \) has a fundamental frequency of \( 400 \, \text{Hz} \) when kept under some tension. The resonating length of the wire with fundamental frequency of \( 600 \, \text{Hz} \) under same tension _____ \( \text{cm} \).

A point source is emitting sound waves of intensity \( 16 \times 10^{-8}\ \text{W}\ \text{m}^{-2} \) at the origin. The difference in intensity (magnitude only) at two points located at a distance of \( 2\,\text{m} \) and \( 4\,\text{m} \) from the origin respectively will be ______ \( \times 10^{-8}\ \text{W}\ \text{m}^{-2} \).

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JEE Main 2024 31st Jan Morning Shift

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 \( 60 \, \text{cm} \), the length of the closed pipe will be: