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Concept
Acoustic wave
Résumé
Acoustic waves are a type of energy propagation through a medium by means of adiabatic loading and unloading. Important quantities for describing acoustic waves are acoustic pressure, particle velocity, particle displacement and acoustic intensity. Acoustic waves travel with a characteristic acoustic velocity that depends on the medium they're passing through. Some examples of acoustic waves are audible sound from a speaker (waves traveling through air at the speed of sound), seismic waves (ground vibrations traveling through the earth), or ultrasound used for medical imaging (waves traveling through the body).
Acoustic wave is a mechanical wave that transmits energy through the movements of atoms and molecules. Acoustic wave transmits through liquids in longitudinal manner (movement of particles are parallel to the direction of propagation of the wave); in contrast to electromagnetic wave that transmits in transverse manner (movement of particles at a right angle to the direction of propagation of the wave). However, in solids, acoustic wave transmits in both longitudinal and transverse manners due to absence of shear moduli in such a state of matter.
Acoustic wave equation
The acoustic wave equation describes the propagation of sound waves. The acoustic wave equation for sound pressure in one dimension is given by
where
is sound pressure in Pa
is position in the direction of propagation of the wave, in m
is speed of sound in m/s
is time in s
The wave equation for particle velocity has the same shape and is given by
where
is particle velocity in m/s
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
is angular frequency in rad/s
is time in s
is wave number in rad·m−1
is a coefficient without unit
For the wave becomes a travelling wave moving rightwards, for the wave becomes a travelling wave moving leftwards.
Source officielle
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