A longitudinal wave that is transmitted through a solid, liquid, or gaseous material as a result of the mechanical vibrations of the particles forming the material. The direction of motion of the particles is parallel to the direction of propagation of the wave, and the wave therefore consists of compressions and rarefactions of the material. The term ‘sound wave’ is sometimes used specifically for those waves with a frequency falling within the audible range of the human ear, i.e. from about 20 hertz to 20 kilohertz. Waves of frequency greater than about 20 kHz are ultrasonic waves.
In a crystalline solid an acoustic wave is transmitted as a result of the displacement of the lattice points about their mean position, and the modes of propagation are constrained by the interatomic forces active between the lattice points. The wave is transmitted as an elastic wave through the crystal lattice. The angular frequency, ω, of the wave is related to the wave vector K by the relation
where m is the mass of an atom, Cp the force constant between planes of atoms separated by p, where p is an integer, and a is the spacing between atomic planes. The range of physically realizable waves that may be transmitted is
The limits of this range define the first Brillouin zone for the crystal lattice, and at these limits travelling waves cannot be propagated; standing waves are formed. The energy of the lattice vibrations is quantized. The quantum of energy is the phonon, which is analogous to the photon of energy of an electromagnetic wave. The phonon energy is given by , where is the frequency and is equal to .
A travelling acoustic wave in a solid can be produced by applying mechanical stress to the crystal or as a result of magnetostriction or of the piezoelectric effect. The resulting phonons can interact with mobile charge carriers present in the material. The interaction can be considered as an electric vector, analogous to the electric vector associated with an electromagnetic wave, that extends for about a quarter wavelength distance orthogonal to the direction of propagation of the wave.
http://www.acoustic-glossary.co.uk/sound-waves.htm A useful glossary of the terms associated with acoustic waves