S
ound waves are the most common example of longitudinal waves. They travel
through any material medium with a speed that depends on the properties of the
medium. As the waves travel through air, the elements of air vibrate to produce
changes in density and pressure along the direction of motion of the wave. If the
source of the sound waves vibrates sinusoidally, the pressure variations are also sinu-
soidal. The mathematical description of sinusoidal sound waves is very similar to that
of sinusoidal string waves, which were discussed in the previous chapter.
Sound waves are divided into three categories that cover different frequency
ranges. (1) Audible waves lie within the range of sensitivity of the human ear. They can
be generated in a variety of ways, such as by musical instruments, human voices, or
loudspeakers. (2) Infrasonic waves have frequencies below the audible range. Elephants
can use infrasonic waves to communicate with each other, even when separated by
many kilometers. (3) Ultrasonic waves have frequencies above the audible range. You
may have used a “silent” whistle to retrieve your dog. The ultrasonic sound it emits is
easily heard by dogs, although humans cannot detect it at all. Ultrasonic waves are also
used in medical imaging.
We begin this chapter by discussing the speed of sound waves and then wave inten-
sity, which is a function of wave amplitude. We then provide an alternative description
of the intensity of sound waves that compresses the wide range of intensities to which
the ear is sensitive into a smaller range for convenience. We investigate the effects of
the motion of sources and/or listeners on the frequency of a sound. Finally, we explore
digital reproduction of sound, focusing in particular on sound systems used in modern
motion pictures.
17.1 Speed of Sound Waves
Let us describe pictorially the motion of a one-dimensional longitudinal pulse moving
through a long tube containing a compressible gas (Fig. 17.1). A piston at the left end
can be moved to the right to compress the gas and create the pulse. Before the piston is
moved, the gas is undisturbed and of uniform density, as represented by the uniformly
shaded region in Figure 17.1a. When the piston is suddenly pushed to the right (Fig.
17.1b), the gas just in front of it is compressed (as represented by the more heavily
shaded region); the pressure and density in this region are now higher than they were
before the piston moved. When the piston comes to rest (Fig. 17.1c), the compressed
region of the gas continues to move to the right, corresponding to a longitudinal
pulse traveling through the tube with speed v. Note that the piston speed does not
equal v. Furthermore, the compressed region does not “stay with” the piston as the
piston moves, because the speed of the wave is usually greater than the speed of the
piston.
The speed of sound waves in a medium depends on the compressibility and density
of the medium. If the medium is a liquid or a gas and has a bulk modulus B (see
513
(d)
v
(c)
v
(b)
(a)
Compressed region
Undisturbed gas
Figure 17.1 Motion of a longitudi-
nal pulse through a compressible
gas. The compression (darker re-
gion) is produced by the moving
piston.