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Question

The fundamental frequency of an open organ pipe is n. The pipe is vertically immersed in water such that half of its length is submerged. The fundamental frequency of air column in this position will be

A
n/3
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B
n/2
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C
n
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D
2n
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Solution

The correct option is C n
Let velocity of sound in air be v.
Open organ pipe:

Let Length of the pipe be L.

Fundamental frequency i.e m=1, ν1=n=v2L

When the pipe is immersed in water, it acts like a closed organ pipe.

Length of the air column, l=L2

Frequency of different modes in closed organ pipe, νp=(2p1)v4l

Fundamental frequency i.e p=1 , ν1=v4×L2=v2L=n

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