(B) For an open organ pipe,the frequency of the first harmonic (fundamental frequency) is given by:$f = \frac{v}{2L} = 480 \, Hz$For a pipe closed at

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(B) For an open organ pipe,the frequency of the first harmonic (fundamental frequency) is given by:$f = \frac{v}{2L} = 480 \, Hz$For a pipe closed at one end,the frequency of the first harmonic (fundamental frequency) is given by:$f' = \frac{v}{4L'} = 480 \, Hz$Since the tuning fork is the same,$f = f'$,therefore:$\frac{v}{2L} = \frac{v}{4L'}$By simplifying the equation:$4L' = 2L$$L' = \frac{2L}{4} = \frac{L}{2}$Thus,the length of the pipe closed at one end should be $\frac{L}{2}$.

Class 11 Physics Waves and Sound Longitudinal Stationary Waves (Organ Pipes) and Resonance Tube

Medium

An organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of $480 \, Hz$. What should be the length of a pipe closed at one end,so that it also vibrates in its first harmonic with the same tuning fork?

A
$\frac{L}{4}$
B
$\frac{L}{2}$
C
$L$
D
$2L$

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Waves and Sound

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Longitudinal Stationary Waves (Organ Pipes) and Resonance Tube

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Medium

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$A$ pipe open at both ends and a pipe closed at one end have the same length and both are vibrating in their fundamental mode. If the air column vibrating in the open pipe has a resonance frequency $n_1$ and the air column vibrating in the closed pipe has a resonance frequency $n_2$,then:

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An organ pipe of length $L$ open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of $480 \, Hz$. What should be the length of a pipe closed at one end,so that it also vibrates in its first harmonic with the same tuning fork?

Similar Questions

$A$ tuning fork of frequency '$n$' is held near the open end of a tube which is dipped in water and length of the tube is adjusted until resonance occurs. If the two shortest lengths that produce resonance are $l_1$ and $l_2$, the speed of sound in air is (neglect end correction)

The number of possible natural oscillations of an air column in a pipe closed at one end of length $85 \, cm$ whose frequencies lie below $1250 \, Hz$ are (Velocity of sound $= 340 \, m s^{-1}$)

The first overtone frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. Further,the $n^{th}$ harmonic of the closed organ pipe is also equal to the $m^{th}$ harmonic of the open pipe,where $n$ and $m$ are:

$A$ pipe $20 \; cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a $430 \; Hz$ source? Will the same source be in resonance with the pipe if both ends are open? (Speed of sound in air is $340 \; m/s$).

$A$ pipe open at both ends and a pipe closed at one end have the same length and both are vibrating in their fundamental mode. If the air column vibrating in the open pipe has a resonance frequency $n_1$ and the air column vibrating in the closed pipe has a resonance frequency $n_2$,then:

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