Discussion
When an open pipe is suddenly closed at one end, the frequency of the third harmonic of the closed pipe is found to be 50 Hz more than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is
Answer: A
The fundamental frequency of the open pipe is 100 Hz.
For a pipe of length \(L\): open at both ends, \(f_{0} = \frac{v}{2L}\); closed at one end, the harmonics are odd multiples of \(\frac{v}{4L}\), so the third harmonic is \(\frac{3v}{4L} = \frac{3}{2}f_{0}\).
\[ \begin{aligned} \tfrac{3}{2}f_{0} - f_{0} &= 50 \\ \tfrac{1}{2}f_{0} &= 50 \Rightarrow f_{0} = 100\ \text{Hz} \end{aligned} \]
Check: the closed pipe's third harmonic is 150 Hz, 50 Hz above 100 Hz. Taking the closed pipe's third harmonic as \(3f_{0}\) would give 25 Hz, not offered.
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