Some Extension Topics

Pressure in a Sound Wave

It is variations of pressure which is what affects our ears - i.e. what our ears physically respond to. A sound wave consists of pressures above and below the normal undisturbed pressure in the gas. At a point in space:

Pinstantaneous = Ptotal instantaneous - Pstatic

i.e. the instantaneous sound pressure at a point is the total instantaneous pressure at that point minus the static pressure. Static pressure is the normal atmospheric pressure in the absence of sound.

The effective sound pressure ("sound pressure") at a point is the root mean square value of the instantaneous sound pressure over a complete cycle at that point. The unit is the dyne per square centimetre. The maximum variation of pressure above or below its normal value is sometimes called the pressure amplitude.

The sound pressure in a spherical sound wave falls off inversely as the distance from the sound source.

Particle Displacement and Particle Velocity in a Sound Wave

The passage of a sound wave passing through a gas medium produces a displacement of the particles or molecules of gas from their normal positions, i.e. their positions in the absence of the wave in question.

The particle displacement of the medium through which the sound waves of speech and music pass is a very small fraction of a millimetre. For e.g. in normal conversational speech at a distance of 3 metres from the speaker, the particle amplitude or displacement of the air is of the order of a 2 millionth of a centimetre.

The particle or molecule in the medium (for e.g. air) oscillates at the frequency of the sound wave. The velocity of such a particle or molecule which is being displaced is termed the particle velocity.

The relation between sound pressure and particle velocity is given by:

Psound = pcu

where,

Psound = sound pressure, in dynes per square centimetre.
p = density of air, in grams per square centimetre
c = velocity of sound, in centimetres per second
u = particle velocity, in centimetres per second

The amplitude or displacement of the particle from its position in the absence of a sound wave is given by

where,

d = particle amplitude, in centimetres
u = particle velocity, in centimetres per second
f = frequency, in Hz.