THE NATURE OF SOUND

"Consider the air close to the surface of some vibrating object. As the surface moves outwards the air molecules next to the surface are pushed closer together (the air is compressed). The air cannot move back into its original position for the moment as the space is occupied by the advanced surface of the vibrating object and therefore a movement of air occurs away from the object." 
P.H. Parkin & H.R. Humphries, Acoustics, Noise and Buildings.

A vibrating object will produce a sequence of compressions and rarefactions in the air surrounding it. These small fluctuations in air pressure travel away from the source at relatively high speed, gradually dying off as their energy is absorbed by the medium. What we call sound is simply the sensation produced by the ear when stimulated by these vibrations.
 

If you were to graph the pressure maxima and minima at a given instant, what you get is a sound wave. It should be noted that air cannot sustain any form of shear stress so sound can only be transmitted as a longitudinal wave. Thus the graph showing a sine wave refers only to variations in pressure or compression, not to the actual displacement of air.

PROPERTIES OF SOUND

The wave motion of sound can be described in terms of Amplitude, Frequency, Velocity and Wavelength. 

Amplitude
Refers to the difference between maximum and minimum pressure.

Wavelength
Refers to the physical distance between successive compressions and is thus dependant on the speed of sound in the medium divided by its frequency:

V = l * f

[Velocity = Wavelength * Frequency]

Frequency
Refers to the number of peak-to-peak fluctuations in pressure that pass a particular point in space in one second.

Velocity
Refers to the speed of travel of the sound wave. This varies between mediums and is also dependant on temperature. Assuming air acts as an ideal gas, its velocity (V in m/s) relates to temperature (T in °C) as follows: 

V = 331.5 + (0.6 T)

(m/s)

In other materials, the speed of sound can vary quite substantially. The following table shows the speed of sound in a number of different materials.