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Q.

If the third harmonics of a closed organ pipe is equal to the fundamental frequency of an open organ pipe, compute the length of the open organ pipe (in cm) if the length of  the closed organ pipe is 30cm.

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answer is 20.

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Detailed Solution

Let l2  be the length of the open organ pipe, with l1=30cm the length of the closed oragan pipe.
It is given that the third harmonic of closed organ pipe is equal to the fundamental frequency of open organ pipe.
The third harmonic of a closed organ pipe is f2=vλ2=3v4l1=3f1
The fundamental frequency of open organ pipe is f1=vλ1=v2l2
Therefore,

v2l2=3v4l1l2=2l13=20cm

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