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Range of frequency of pipes

  • Thread starter pivoxa15
  • Start date
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1. Homework Statement
The (two side open) pipes of a pipe organ range in length from 9m to 0.18m. What are the limits of the range of frequencies that can be produced by such pipes?

2. Homework Equations
For open pipes
wavelength = 2L/n, L is length of pipe, n is number of segments or antinodes


3. The Attempt at a Solution
The wavelength for the first fundamental harmonic is 18m and 0.36m respectively

The wavelength for the 2nd harmonic is 9m and 0.18m.

The wavelengths get shorter as higher harmonics are counted. Hence the frequency increases. Assuming the speed of sound is 340m/s than the lowest frequency for either pipes is 18.9Hz but the highest frequency for either pipe has no limit as the wavelength can get shorter as harmonics increase.

The back of the book answer suggested the range is 18.9Hz – 944.4Hz which are the frequency of the fundamental harmonics of both pipes. Why do they suggest this result? Surely frequencies higher than 944.4Hz can be produced by both pipes.
 

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