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 39.0 cm long if the pipe is open at both ends. Use v = 344 m/s. fundamental Hz first overtone Hz second overtone Hz third overtone Hz (b) Find the fundamental frequency and the frequency of the first three overtones for a pipe 39.0 cm long if the pipe is closed at one end. Use v = 344 m/s. fundamental Hz first overtone Hz second overtone Hz third overtone Hz For each of the above cases, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20 to 20000 Hz? open pipe harmonic pipe closed at one end harmonic

Explanation / Answer

a) If the pipe is open at both ends, the fundamental wavelength is 2*39cm = 78cm. If v = 344m/s, the fundamental frequency is: (344m/s)/(0.78m) = 441. Hz.
The frequencies of the first three overtones are: 882. Hz, 1.32 kHz, and 1.76 kHz.

b) if the pipe is closed at one end, the fundamental wavelength is 4*39cm = 156cm. If v = 344m/s, the fundamental frequency is: (344m/s)/(1.56m) = 220.5 Hz.
The frequencies of the first three overtones are: 661.5 Hz, 1.10 kHz, and 1.54 kHz.

c) If the pipe is open at both ends, the fundamental frequency is: 441. Hz. Since 20000/441 >= 45, the 44th overtone will be heard.
If the pipe is open at one end, the fundamental frequency is: 156. Hz. Since 20000/156 >= 128, the 127th overtone will be heard.

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