Raymond A. Serway and John W. Jewett. “Physics for Scientists and Engineers with modern physics“, 8th edition, Brooks/Cole, Belmont, USA (2010)

Part 2. Oscillations and Mechanical Waves

Most of the waves we studied in previous sections are constrained to move along a one-dimensional medium. For example, a one-dimensional sinusoidal wave is a purely mathematical construct moving along the x axis. The sinusoidal wave in a string is constrained to move along the length of the string. We have also seen waves moving through a two-dimensional medium, such as the ripples on the water surface in the introduction to Part 2 and the waves moving over the surface of the ocean in previous lectures. In this session, we investigate mechanical waves that move through three-dimensional bulk media. For example, seismic waves leaving the focus of an earthquake travel through the three-dimensional interior of the Earth.

We will focus our attention on sound waves, which travel through any material, but are
most commonly experienced as the mechanical waves travelling through air that result in
the human perception of hearing. As sound waves travel through air, elements of air are
disturbed from their equilibrium positions. Accompanying these movements are changes
in density and pressure of the air along the direction of wave motion. If the source of the
sound waves vibrates sinusoidally, the density and pressure variations are also sinusoidal. The mathematical description of sinusoidal sound waves is very similar to that of sinusoidal waves on strings, as discussed in previous session.

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 one another, even when separated by many kilometres.

(3) Ultrasonic waves have frequencies above the audible range. You may have used a “silent” whistle to retrieve your dog. Dogs easily hear the ultrasonic sound this whistle emits, although humans cannot detect it at all. Ultrasonic waves are also used in medical imaging.

This session begins with a discussion of the pressure variations in a sound wave, the speed of sound waves, and wave intensity, 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. The effects of the motion of sources and listeners on the frequency of a sound are also investigated.