17.7

*Complex Sound Waves

Musical instruments produce sound in a way that depends on standing waves. Example 4 and Example 5 illustrate the role of transverse standing waves on the string of an electric guitar, while Example 6 and Example 7 stress the role of longitudinal standing waves in the air column within a flute. In each example, sound is produced at the fundamental frequency of the instrument.
In general, however, a musical instrument does not produce just the fundamental frequency when it plays a note, but simultaneously generates a number of harmonics as well. Different instruments, such as a violin and a trumpet, generate harmonics to different extents, and the harmonics give the instruments their characteristic sound qualities or timbres. Suppose, for instance, that a violinist and a trumpet player both sound concert A, a note whose fundamental frequency is 440 Hz. Even though both instruments are playing the same note, most people can distinguish the sound of the violin from that of the trumpet. The instruments sound different because the relative amplitudes of the harmonics (880 Hz, 1320 Hz, etc.) that the instruments create are different.
The sound wave corresponding to a note produced by a musical instrument or a singer is called a complex sound wave because it consists of a mixture of the fundamental and harmonic frequencies. The pattern of pressure fluctuations in a complex wave can be obtained by using the principle of linear superposition, as Figure 17-26 indicates. This drawing shows a bar graph in which the heights of the bars give the relative amplitudes of the harmonics contained in a note such as a singer might produce. When the individual pressure patterns for each of the three harmonics are added together, they yield the complex pressure pattern shown at the top of the picture.*

Figure 17-26 The topmost graph shows the pattern of pressure fluctuations such as a singer might produce. The pattern is the sum of the first three harmonics. The relative amplitudes of the harmonics correspond to the heights of the vertical bars in the bar graph.

In practice, a bar graph such as that in Figure 17-26 is determined with the aid of an electronic instrument known as a spectrum analyzer. When the note is produced, the complex sound wave is detected by a microphone that converts the wave into an electrical signal. The electrical signal, in turn, is fed into the spectrum analyzer, as Figure 17-27 illustrates. The spectrum analyzer then determines the amplitude and frequency of each harmonic present in the complex wave and displays the results on its screen.

Figure 17-27 A microphone detects a complex sound wave produced by a singer’s voice, and a spectrum analyzer determines the amplitude and frequency of each harmonic present in the wave.

The physics of a spectrum analyzer.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.