A First Course in Fluid Dynamics

Background

The basic facts of the propagation and generation of sound are well known. Sound is a pressure disturbance in air (or water) which travels at a rather high speed. Sound is generated in regions of fluid motion; sometimes a motion of solid boundaries is involved, as in a drum; sometimes not, as in a flute. Sound is received in our ears (or by a microphone) where the pressure oscillations are converted into electrical signals.

The speed of sound is typically around 330–40m s−1 in still air near ground level, and around 1400–50ms−1 in water. Sound also travels through solid materials in the form of elastic waves; we cannot do the theory for such waves here, though it is of the same general type as what we shall do. Often the speed of sound in solids is much higher than the speed of sound in air.

The pressure fluctuations in sound in air are typically between 10−4 and 1 N m−2, so that the ratio of pressure fluctuations to ambient pressure in the atmosphere lies between

10−9 and 10−5.

The smallness of this quantity is one of the basic facts in the simple theory of sound. It is quite possible to get much higher pressure fluctuations, in explosions or in jet engines, so that the ratio of pressures is not small: the simple theory of sound cannot apply to such cases.

The frequencies of audible sound waves lie between about 20 Hz and 2 × 104 Hz. Below about 20 Hz, oscillations are felt by the body rather than heard by the ear, and so may not be classed as sound waves, though they are still described by the same mathematics – sometimes the word infrasound is used. Similarly, oscillations above 2 × 104 Hz cannot be heard by everyone; again, the mathematics is mainly the same, and the word ultrasound is used.