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If the third harmonics of a closed organ...

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 if the length of the closed organ pipe is 30 cm

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Let `l_(2)` be the length of the open organ pipe , with `l_1 = 30` cm the length of the closed organ pipe . It is given that the third harmonic of closed pipe is equal to the fundamental frequency of open organ pipe . The third harmonic of a closed organ pipe is
`f_(2) = (v)/(lambda_(2)) = (3v)/( 4 l_(1)) = 3f_(1)`
The fundamental frequency of open organ pipe is `f_(1) = (v)/(lambda_(1)) = (v)/(2 l_(2))`
Therefore , `(v)/(2l_(2)) = (3v)/(4l_(1)) implies l_(2) = (2l_(1))/(3) = 20` cm
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