This article is from the Acoustics FAQ, by Andrew Silverman with numerous contributions by others.
Sound is the quickly varying pressure wave within a medium. We usually mean audible sound, which is the sensation (as detected by the ear) of very small rapid changes in the air pressure above and below a static value. This "static" value is atmospheric pressure (about 100,000 Pascals) which does nevertheless vary slowly, as shown on a barometer. Associated with the sound pressure wave is a flow of energy. Sound is often represented diagrammatically as a sine wave, but physically sound (in air) is a longitudinal wave where the wave motion is in the direction of the movement of energy. The wave crests can be considered as the pressure maxima whilst the troughs represent the pressure minima.
How small and rapid are the changes of air pressure which cause sound? When the rapid variations in pressure occur between about 20 and 20,000 times per second (ie at a frequency between 20Hz and 20kHz) sound is potentially audible even though the pressure variation can sometimes be as low as only a few millionths of a Pascal. Movements of the ear drum as small as the diameter of a hydrogen atom can be audible! Louder sounds are caused by greater variation in pressure - 1 Pascal, for example, will sound quite loud, provided that most of the acoustic energy is in the mid-frequencies (1kHz - 4kHz) where the ear is most sensitive.
What makes sound? Sound is produced when the air is disturbed in some way, for example by a vibrating object. A speaker cone from a hi-fi system serves as a good illustration. It may be possible to see the movement of a bass speaker cone, providing it is producing very low frequency sound. As the cone moves forward the air immediately in front is compressed causing a slight increase in air pressure, it then moves back past its rest position and causes a reduction in the air pressure (rarefaction). The process continues so that a wave of alternating high and low pressure is radiated away from the speaker cone at the speed of sound.
 
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