Acoustic wave

Acoustic waves are a type of longitudinal waves that propagate by means of adiabatic compression and decompression. Longitudinal waves are waves that have the same direction of vibration as their direction of travel. Important quantities for describing acoustic waves are sound pressure, particle velocity, particle displacement and sound intensity. Acoustic waves travel with the speed of sound which depends on the medium they're passing through.

Acoustic waves are longitudinal waves that exhibit phenomena like diffraction, reflection and interference. Sound waves however don't have any polarization since they oscillate along the same direction as they move.

The acoustic wave equation describes the propagation of sound waves. The acoustic wave equation for sound pressure in one dimension is given by

where

The wave equation for particle velocity has the same shape and is given by

where

For lossy media, more intricate models need to be applied in order to take into account frequency-dependent attenuation and phase speed. Such models include acoustic wave equations that incorporate fractional derivative terms, see also the acoustic attenuation article.

D'Alembert gave the general solution for the lossless wave equation. For sound pressure, a solution would be

where

For ${\displaystyle R=1}$ the wave becomes a travelling wave moving rightwards, for ${\displaystyle R=0}$ the wave becomes a travelling wave moving leftwards. A standing wave can be obtained by ${\displaystyle R=0.5}$.

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