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The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the open organ pipe is 20 cm, the length of the closed organ pipe is ____ cm.

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answer is 30.

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Detailed Solution

$f_{o o p} = 3 f_{c o p} \Rightarrow \frac{v}{2 l_{o o p}} = \frac{3 v}{4 l_{c o p}} \Rightarrow l_{c o p} = \frac{3}{2} \times l_{o o p} = \frac{3}{2} \times 20 = 30 cm$

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