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Question

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is 60 cm, what is the length of the closed pipe?

A
30 cm
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B
15 cm
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C
120 cm
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D
240 cm
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Solution

The correct option is B 15 cm
Given that, the length of the open pipe, lo=60 cm

Let the length of the closed pipe be lc.

Now, fundamental frequency of closed organ pipe is

f1=V4 lc

The fundamental frequency of open organ pipe is V2 lo and first over tone is

f2=2V2 lo=Vlo

From the question : f1=f2

V4 lc=Vlo

lc=lo4=604=15 cm

Hence, option (B) is correct.
Why this question ?

Concept : Frequency of the open organ pipe is same as frequency of vibrating string fixed at both end.

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