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Question

A cylindrical tube open at both ends has a fundamental frequency f in air. The tube is dipped vertically in water so that it has water up to the half height. The fundamental frequency of the air column is now
(Neglect end corrections)

A
4f
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B
3f
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C
f
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D
2f
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Solution

The correct option is C f
For open organ pipe, fundamental frequency,
f=v2l,
where l is the length of an organ pipe.
l=v2f
After the pipe is half dipped in water, it becomes a closed organ pipe and its new length is,
l=v4f
So, fundamental frequency of closed organ pipe,
f=v4l
[speed is same as medium is same]
f=v4×v4f=f

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