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An open organ pipe filled with air has a...

An open organ pipe filled with air has a fundamental frequency 500 Hz. The first harmonic of another organ pipe closed at one end and filled with carbon dioxide has the same frequency as that of the first harmonic of the open organ pipe. Calculate the length of each pipe. Assume that the velocity of sound in air and in carbondioxide to be 330 and 264 m/s respectively.

Text Solution

Verified by Experts

The correct Answer is:
33 cm and 13.2 cm
For air
`(lamda_(1))/(2)=L_(1)rArr lamda_(1)=2L_(1)`
`V_(1)=330rArrV_(1)=f lamdarArr 330=500(2L_(1))`
`rArr L_(1) = 33 cm`
For `CO_(2)CO_(2)=(lamda_(2))/(4)=L_(2)`
`lamda_(2)=4L_(2),v_(2)=264`
`rArrv_(2)=flamda_(2)rArr264=500(4L_(2))`
`rArr L_(2)=13.2 cm`
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