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Question
A pipe open at both the ends has a fundamental frequency of 600 Hz. The first overtone of a pipe closed at one end has the same frequency as the first overtone of the open pipe. How long are the two pipes?
(Given: v = 330 m/s)
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Solution
Data: Open pipe, n0 = 600 Hz, nc, 1 = n0, 1 (first overtones)
For an open pipe, the fundamental frequency,
n0 = `"v"/("2L"_"0")`
∴ The length of the open pipe is
L0 = `"v"/("2n"_"0")=330/(2xx600)` = 0.275 m
For the open pipe, the frequency of the first overtone is
2n0 = 2 x 600 = 1200 Hz
For the pipe closed at one end, the frequency of the first overtone is `(3"v")/"L"_"0"`
By the data, `"3v"/"4L"` = 1200
∴ LC = `(3xx330)/(4xx1200)` = 0.206 m
The pipe is 27.5 cm in length when open on both ends and 20.6 cm when closed on one end.
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