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The fundamental frequency of a closed or...

The fundamental frequency of a closed organ pipe is equal to first overtone frequency of an open organ pipe. If the length of the open pipe is `36cm`, what is the length `(` in cm `)` of the closed pipe ?

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The correct Answer is:
9
Let `l_(1)` be the length of closed pipe
`l_(2)=36cm=` length of open pipe
Fundamental frequency of closed pipe
`n_(1)=(upsilon)/(4l_(1))`
Frequency of first overtone of open pipe,
`n_(2)=2xx(upsilon)/(2l_(2))=(upsilon)/(l_(2))=(upsilon)/(36)`
As `n_(1)=n_(2):. (upsilon)/(4l_(1))=(upsilon)/(36), 4l_(1)=36`
`l_(1)=(36)/(4)=9cm`
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