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