First slide

Stationary waves

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 fundamental frequency of open pipe, then the fundamental frequency of open pipe is:

Moderate

A

480 Hz
B

300 Hz
C

240 Hz
D

200 Hz

Solution

Fundamental frequency of open organ pipe $= \frac{v}{2 l}$
Frequency of third harmonic of closed pipe $= \frac{3 V}{4 l}$
$∴ \frac{3 v}{4 l} = 100 + \frac{v}{2 l} \Rightarrow \frac{3 v}{4 l} - \frac{2 v}{4 l} = \frac{v}{4 l} = 100 \Rightarrow \frac{V}{2 l} = 200 Hz .$

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