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Question

An air column in a pipe closed at one end is made to vibrate in its second overtone by a tuning fork of frequency 440 Hz. The speed of sound wave in air is 330 m/s. End corrections may be neglected. Let P0 denote the mean pressure at any point in the pipe and ΔP0 be the maximum amplitude of pressure variation. Then


A
length of the pipe is 1516 m
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B
length of the pipe is 916 m
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C
the maximum pressure at the open end is P0
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D
the minimum pressure at the open end is P0
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Solution

The correct options are
A length of the pipe is 1516 m
C the maximum pressure at the open end is P0
D the minimum pressure at the open end is P0
The frequency of vibration of air column in second overtone:

f=5.v4l

l=5v4f=1516 m

The open end is position of node of pressure. Hence, there is no pressure variation at open end. Hence, minimum and maximum pressure at open end will be P0

Physics

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