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Determine the fundamental frequency for a 42.5 cm long pipe, open at one end and closed...

Determine the fundamental frequency for a 42.5 cm long pipe, open at one end and closed at the other. A taut string has a mass of 2 g, a length of 4.0 m and is under a tension of 5120 N. Determine which of the harmonics of the pipe, if any, are resonant with the harmonics of the string. [The speed of sound in air is 340

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Answer #1

Fundamental frequency for given pipe:

For string: m = 2 g = 0.002 kg, L = 4.0 m, T = 5120 N

The harmonics are given as

Here n can be 1, 2, 3, 4 etc.., thus the frequencies can be 400 Hz, 800 Hz, 1200 Hz, 1600 Hz etc.

For pipe, the allowed frequencies are 200 Hz, 600 Hz, 1000 Hz, 1400 Hz, 1800 Hz and so on.

Therefore, no harmonics are resonant with the string.

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