Sources of Musical Sound

There it is explained how standing sound waves occur in pipes filled with air. The various maxima and minima locations of the standing waves correspond to maximum and minimum pressures in the pipe.

Example For a pipe open at both ends, determine the relationship between the length of the pipe L and the frequencies of the various harmonics.

Solution There is a pressure node at the closed end and an anitnode at the open end. The relations between the wavelength ¸ and the pipe length L for the various harmonics as

etc. These can be written in general as

Example Repeat the previous example for a pipe open at only one end.

Solution Obviously

etc. These can be written in general as

Now recall that . Thus for the pipe open at both ends

and for the pipe open at one end,

These are very important formulas for the design of wind musical instruments, such as a flute or recorder. Note that a longer instrument (larger L) will give a lower frequency.