Sources of Musical Sound
المؤلف:
Professor John W. Norbury
المصدر:
ELEMENTARY MECHANICS & THERMODYNAMICS
الجزء والصفحة:
p 203
1-1-2017
2134
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.
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