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acoustic wave equation
In physics, the acoustic wave equation governs the propagation of acoustic waves through a material medium. The form of the equation is a second order partial differential equation. The equation describes the evolution of acoustic pressure or particle velocity ''u'' as a function of position ''r'' and time . A simplified form of the equation describes acoustic waves in only one spatial dimension, while a more general form describes waves in three dimensions.
The acoustic wave equation was an important point of reference in the development of the electromagnetic wave equation in Kelvin's master class at Johns Hopkins University.〔William Thomson, Lord Kelvin (1904) Lecture notes taken by A. S. Hathaway, (Molecular dynamics and the wave theory of light ), page 80, Cambridge University Press, link from Internet Archive〕
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 or the survey paper.〔S. P. Näsholm and S. Holm, "On a Fractional Zener Elastic Wave Equation," Fract. Calc. Appl. Anal. Vol. 16, No 1 (2013), pp. 26-50, DOI: 10.2478/s13540-013--0003-1 (Link to e-print )〕
==In one dimension==
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