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 than the fundamental frequency of the open pipe. The

Question

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 than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

TestHub · Accepted Answer

Length of the organ pipe is same in both the cases. Fundamental frequency of open pipe is $f_{1} = \frac{v}{2 l}$ Frequency of third harmonic of closed pipe will be.

$f_{2} = 3 (\frac{v}{4 l})$

Given that, $f_{2} = f_{1} + 100$

or $f_{2} - f_{1} = 100$

or $\frac{3}{4} (\frac{v}{l}) - (\frac{1}{2}) (\frac{v}{l}) = 100 \Rightarrow \frac{v}{4 l} = 100$

$∴$ $\frac{v}{2 l} or f_{1} = 200 Hz$

Therefore, fundamental frequency of the open pipe is 200 Hz.

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