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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 closed organ pipe is 20 cm the length of the open organ pipe is

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a
13.2 cm
b
8 cm
c
12.5 cm
d
16 cm

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detailed solution

Correct option is A

For closed organ pipe, third harmonic is 3v4l For open organ pipe, fundamental frequency is v2l'Given, third harmonic for closed organ pipe = fundamental frequency for open organ pipe.∴  3v4l=v2l'⇒l'=4l3×2=2l3where l and l' are the lengths of closed and open organ pipes respectively.∴  =2×203=13.33 cm

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