Physics for Geologists, Second edition

11 Acoustics: sound and other waves
Sound
Mechanical vibrations (i.e. elastic waves) with frequencies between about
50 Hz and 24 kHz can be detected by the human ear, and so constitute the
audible range (much as there is a visible spectrum of colours in the range
of electromagnetic radiation). The pure tones of music are very precisely
related to frequencies, with middle C being 263 Hz.
A blow on a bell sets the bell vibrating. The part moving out compresses
the air a little, and a wave is propagated; when it moves in, the air is rarefied
a little and it too is propagated. Sound in air, water and other fluids (e.g.
the outer core of the Earth), consists of compression-dilation waves. When
these reach your ear, sympathetic movements are induced in your eardrum
with exactly the same frequencies, and you hear the note belonging to that
frequency. The amplitude of the wave is not maintained, mainly because
energy is dispersing over the expanding surface of a sphere (nearly), which
increases in area as the square of the distance from the source as it propagates
from the source. So the wave is attenuated, and the sound gets weaker with
distance from the source. You can dampen the sound by touching the bell.
The size of the bell determines the note emitted when it is struck.
Laplace showed that the speed or velocity of sound in a gas is given by
where p is the pressure, p is the mass density of the gas and y is the ratio of
the specific heat capacity of the gas at constant pressure to its specific heat
capacity at constant volume, cp/c,. This is strictly valid for ideal gases that
obey Boyle's law (known as Mariotte's law in some countries). For gases
with molecules consisting of only one type of atom, called monatomic gases,
such as H2 and 0 2, y = 1.67; for diatomic gases, such as C02, y = 1.41.
For polyatomic gases, the ratio is close to unity. For ideal gases, p/p = RT,
where R is the gas constant and T is the absolute temperature; and the mass
density is directly proportional to the pressure. So the speed of sound in a gas
is independent of pressure or density but proportional to the square root of
Copyright 2002 by Richard E. Chapman