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An open pipe is suddenly closed at one e...

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by `100 Hz` then the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

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The correct Answer is:
A
Length of the organ pipe is same in both the cases. Fundamental grequency of open pipe is `f_(1) = (nu)/(2l)` and frequency of third harmonic of closed pipe will be
`f_(2) = 3((nu)/(4l))`
Given that, `f_(2) = f_(1) + 100`
or `f_(2) - f_(1) = 100`
or `(3)/(4) ((nu)/(l)) - ((1)/(2)) ((nu)/(l)) = 100`
rArr `(nu)/(4l) = 100 H_(Z)`
:. `(nu)/(2l)` or `f_(1) = 200 H_(Z)`
Therfore, fundamental frequency of the open pipe is `200 H_(Z)`.
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