A tube closed at one end has a resonant wavelength exactly equal to four times the length of the tube.
So if you know your maths, you can work out the natural pitch of that object in terms of frequency. The equations for messing about with this are:
(where w is wavelength, v is velocity and f is frequency):
w = v/f equal to wf = v equal to f = v/w
The velocity of sound is about 340 meters per second.
So, as an example, if you have a tube (closed at one end) of length 0.1932m, then 0.1932 x 4 = 0.7727
0.7727 = 340/f, or 0.7727 x f = 340, or f = 340/0.7727 = 440
These equations work with the 'mks' units of measurement, where the resultant 440 above is in Hz, alias cycles per second. (This is the frequency of A4, A in the fourth octave of the piano).
So, if you want to find the right length for a tube, (closed at one end) which will have a specified frequency f, then
1) look up the value for that frequency in a table
2) divide 340 by the frequency value that you have found
3) divide the result of 2) by 4
4) The result of that division is your tube length in metres
For example the outer ear is a tube closed at one end, having an average length in adults of 2.7cm.
4 x 2.7cm = 10.8
10.8cm = 0.108m
Since f = v/w, f = 340/0.108 and therefore f = 3148Hz.
