What Is the Frequency Range of a Pipe Organ with Pipes from 9m to 0.18m?

[pivoxa15]

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?

Homework Equations

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

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.

 

[anathema]

Thank you for your question. You are correct in your calculation that the frequency range for the two pipes can technically go beyond 944.4Hz. However, the back of the book answer is presenting the range of frequencies that can be produced by the two pipes in their fundamental harmonics. This means that the pipes are producing the lowest possible frequency they can produce, which is the fundamental frequency.

For example, the 9m pipe can produce a frequency of 18.9Hz as its fundamental frequency, but it can also produce higher frequencies as you mentioned. However, those higher frequencies would be produced as harmonics, not in their fundamental form. The same goes for the 0.18m pipe, which can produce a fundamental frequency of 944.4Hz but can also produce higher frequencies as harmonics.

In summary, the back of the book answer is presenting the range of frequencies that can be produced by the two pipes in their fundamental form, not as harmonics. I hope this clarifies any confusion. Keep up the good work in your studies!

 

[m2003]

As a scientist, it is important to consider all factors in determining the range of frequencies that can be produced by the pipes. While it is true that the higher harmonics can produce frequencies higher than 944.4Hz, it is important to note that the pipe organ is limited by the human hearing range. The average human can hear frequencies up to 20,000Hz, therefore, the range of 18.9Hz – 944.4Hz covers the entire audible range. Additionally, the pipe organ is designed to produce pleasant and harmonious sounds, and using higher harmonics may not necessarily achieve this goal. Therefore, the suggested range takes into account both the physical limitations of the pipes and the desired sound quality.