How does the frequency of a diaphragm vary?

[walshlg]

I've been looking at "how to" vids that show how an air horn works: basically a thin diaphragm of metal, or even balloon rubber, is made to vibrate by passing compressed air over its surface.

Can anyone tell me how you control the frequency of the vibration to control the tone produced. Q:
1 ) From the spring equation I guess that the frequency is proportional to sqrt(1/mass), does that sound right?
2) How does this vary with the diameter of the disk?
3) Any other tips on dimensions and clearances? I'd like to get just ultrasonic, eg. 30KHz.

P.S. yes, I see that there are lots of vibration modes but I'm looking for the strongest, I assume its (1,0)

 

[Vailanor]

1) The frequency of the vibration is determined by a combination of the mass of the diaphragm and the stiffness of the spring that holds it in place. The equation you mentioned is correct, though it only applies to the resonance frequency (i.e. the frequency at which the diaphragm vibrates most strongly). The actual frequency that is produced will depend on the pressure of the air passing over the diaphragm, as well as the dimensions of the horn itself (see below). 2) The diameter of the disk does affect the frequency of the vibration, but not in a linear way. The larger the disk, the lower the frequency. 3) To make an air horn that produces ultrasonic frequencies, the best tip is to reduce the size of the diaphragm as much as possible. This will increase the frequency of the vibration. You also want to ensure that the horn has a small opening, as this will increase the air pressure which will further increase the frequency. Finally, you should make sure that the spring and the diaphragm are as stiff as possible, as this will allow the diaphragm to vibrate more quickly.