An open pipe is suddenly closed at one end. As a result, the frequency of third harmonic of the closed pipe is found to be higher by $100 ext{ Hz}$ than that of the fundamental frequency of the open pipe. The fundamental frequency of the open pipe will be [BHU 2012]

Question

An open pipe is suddenly closed at one end. As a result, the frequency of third harmonic of the closed pipe is found to be higher by $100	ext{ Hz}$ than that of the fundamental frequency of the open pipe. The fundamental frequency of the open pipe will be [BHU 2012]

Aicharya · Accepted Answer

Let $l$ be the length of the pipe and $v$ be the velocity of sound in the air column, then the fundamental frequency of an open pipe $= \frac{v}{2l}$ Fundamental frequency of closed pipe $= \frac{v}{4l}$ Frequency of third harmonic of closed pipe $= \frac{3v}{4l}$ According to given condition, $\frac{3v}{4l} = \frac{v}{2l} + 100$ $\Rightarrow \frac{v}{2l} = 200	ext{ Hz}$

An open pipe is suddenly closed at one end. As a result, the frequency of third harmonic of the closed pipe…

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