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Question

Velocity of sound in air is 320 m/s. A pipe closed at one end has a length of 1 m, neglecting end corrections. Find the frequency(s) for which the air column in the pipe can resonate.


A
80 Hz
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B
240 Hz
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C
500 Hz
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D
400 Hz
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Solution

The correct options are
A 80 Hz
B 240 Hz
D 400 Hz
Given ,
Length of pipe, l=1 m
Speed of sound in air v=320 m/s

Modes of vibration of air column in closed organ pipe are given by
fn=(2n1)v4l    where  n=1,2,3,4....

[For a closed organ pipe, only odd harmonics are present]

For n=1 , f1=3204=80 Hz
n=2 , f2=3×3204=240 Hz
n=3 , f3=5×3204=400 Hz
n=4 , f4=7×3204=560 Hz

Among the give options, options (a), (b) and (d) are the only modes of vibrations matching with that of a closed organ pipe.

Physics

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