Find the fundamental frequency and the frequency of the first three overtones of

Question

Find the fundamental frequency and the frequency of the first three overtones of a pipe 55.0 cm long, if the pipe is open at both ends.

Find the fundamental frequency and the frequency of the first three overtones of a pipe 55.0 cm long, if the pipe is closed at one end.

If the pipe is open at both ends, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0 Hz to 2.00×104 Hz?

If the pipe is closed at one end, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0 Hz to 2.00×104 Hz?

Explanation / Answer

a) If the pipe is open at both ends, the fundamental wavelength is 2*55cm = 110cm. If v = 344m/s, the fundamental frequency is: (344m/s)/(1.10m) = 312.72 Hz.

The frequencies of the first three overtones are: 625.45Hz, 938.18Hz, and 1250.91Hz.

b) if the pipe is closed at one end, the fundamental wavelength is 4*55cm = 220cm. If v = 344m/s, the fundamental frequency is: (344m/s)/(2.20m) = 156.36Hz.
The frequencies of the first three overtones are: 312.73Hz, 469.091 Hz, and 625.45Hz.

c) If the pipe is open at both ends, the fundamental frequency is: 312.72 Hz. Since 20000/312.72 >= 63.95, 63 overtones will be heard.

If the pipe is open at one end, the fundamental frequency is: 156.36. Hz. Since 20000/156.36>= 127.91, the 127 overtones will be heard.

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