Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013
14
Figure 2.13 Fundamental wavelength in open and closed pipes
The situation is different if the pipe is closed at the end opposite to the one
into which it is blown. In this case, air pressure rises to its maximum at the closed
end. The bottom part of Figure 2.13 shows that in this situation, the closed end
corresponds to the crest of the fundamental wavelength. Thus, the fundamental
wavelength is four times the length of the pipe.
Because the wave in the pipe is traveling through air, it is simply a sound
wave, and thus we know its speed approximately 1130 ft/s. With this
information, we can calculate the fundamental frequency of both closed and open
pipes, given their length.
Let
L
be the length of an open pipe, and let
c
be the speed of sound. Then the
fundamental frequency of the pipe is .
Equation 2.5
Let
L
be the length of a closed pipe, and let
c
be the speed of sound. Then the
fundamental frequency of the pipe is .
Equation 2.6
This explanation is intended to shed light on why each instrument has a characteristic
sound, called its timbre. The timbre of an instrument is the sound that results from its
fundamental frequency and the harmonic frequencies it produces, all of which are integer
Practical
Exercise:
Helmholtz
Resonators
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