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Question

The first overtone frequency of a closed organ pipe is equal to the second overtone frequency of an open organ pipe. If the length of the open pipe is 80 cm, what is the length of the closed organ pipe?

A
20 cm
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B
40 cm
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C
60 cm
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D
80 cm
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Solution

The correct option is B 40 cm
Modes of vibration of air column in a closed organ pipe is given by,
fn=(2n+1)v4LC

So for first overtone or third harmonic
f1=3v4Lc

Modes of vibration of air column in an open organ pipe is given by,
fn=nv2Lo

For second overtone or third harmonic
f3=3v2Lo

From the data given in the question,

3v4Lc=3v2Lo

2Lc=Lo

Given that,
Length of the open organ pipe, Lo=80 cm
Lc=802=40 cm.

Thus, option (b) is the correct answer.

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