How do I find the length of a pipe I need in order to reach a certain frequency? Physics Help?

Question

I have to make an open-ended instrument and I want to make something similar to a windchime that you hit with a stick. I need to know the length I need to cut the pipes in order to play three notes. I want the notes to be 440HZ 523HZ and 659HZ. does the radius of the pipe affect it in any way. If someone can show me how you come up with the proper length to get these frequencies with work I will give them best answer. Thanks

Answer 1

If I remember correctly from my ancient physics course, a tube open at both ends resonates at a base wavelength equal to the length of the tube.
Velocity, frequency, and wavelength are related by
v = fλ
λ = v/f
v = 343 m/s @ 20°C

. f . . cm . . in
440 39.0 15.4
523 32.8 12.9
659 26.0 10.2

Answer 2

The previous answer addresses the problem of the resonant frequencies of the column of air in a pipe open at both ends (i.e., a flute), not the problem of the resonant frequencies of the pipe itself, which is what this question is asking. (The previous answer is also incorrect; the fundamental wavelength of the air column in a open pipe is *twice* the length of the pipe).

This is not a simple problem because there are different possible vibrational modes for a pipe (i.e., bending, "breathing", torsional) and their frequencies depend on both the dimensions of the tube, and the material properties of the tube (the elastic modulus of the material). Furthermore, you need to match the frequency of the tube's resonant vibrations to the frequency of resonant vibrations of the column of air in the tube.

You can use the on-line calculator at the source below to get a first estimate of the dimensions of aluminum, copper, or steel tubes that will "chime" at specified frequencies, but you will almost certainly need to "tune" the tubes by removing material to shorten them.

See sources for additional good information on designing chimes.