Equation for the propagation of sound waves through a medium
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In physics, the acoustic wave equation is a second-order partial differential equation that governs the propagation of acoustic waves through a material medium resp. a standing wavefield. The equation describes the evolution of acoustic pressure p or particle velocity u as a function of position x and time t. A simplified (scalar) form of the equation describes acoustic waves in only one spatial dimension, while a more general form describes waves in three dimensions. Propagating waves in a pre-defined direction can also be calculated using a first order one-way wave equation.
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.[1]
^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
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In physics, the acousticwaveequation is a second-order partial differential equation that governs the propagation of acousticwaves through a material...
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proposed a time convolution integral dissipative acousticwaveequation. On the other hand, acousticwaveequations based on fractional derivative viscoelastic...
energy, producing a sound wave. There is one fundamental equation that describes sound wave propagation, the acousticwaveequation, but the phenomena that...
where the wave amplitude appears smaller or even zero. Waves are often described by a waveequation (standing wave field of two opposite waves) or a one-way...
{\displaystyle \nabla \times \mathbf {v} =0} ), we then have the acousticwaveequation that describes the system: 1 c 2 ∂ 2 ϕ ∂ t 2 − ∇ 2 ϕ = 0 {\displaystyle...
to the acousticwaveequation, can consult Acoustics: An Introduction to Its Physical Principles and Applications Allan D. Pierce, Acoustical Soc of America...
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{\displaystyle c_{L}} is the longitudinal wave speed. This has the same form as the acousticwaveequation in one-dimension. c L {\displaystyle c_{L}}...
tensor for the acoustic field. The Lighthill equation is an inhomogenous waveequation. Using Einstein notation, Lighthill’s equation can be written as...
physics, an ion acousticwave is one type of longitudinal oscillation of the ions and electrons in a plasma, much like acousticwaves traveling in neutral...
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(2nd ed.). Heidelberg: Springer. ISBN 978-0-387-21603-4. OCLC 883383570. The WaveEquation for Sound What Is Acoustic Impedance and Why Is It Important?...
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well, for instance to describe ion acousticwaves in plasma physics. The Korteweg–de Vries equation (KdV equation) can be used to describe the uni-directional...
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oscillations, or waves, that propagate away from their source. In a fluid, small changes in pressure p can often be described by the acousticwaveequation: ∂ 2 p...
S-waves (see Seismic wave). Elimination of displacements and strains from the governing equations leads to the Ignaczak equation of elastodynamics ( ρ...
In theoretical acoustics, it is often desirable to work with the acousticwaveequation of the velocity potential Φ instead of pressure p and/or particle...
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of the Acoustical Society of America. 70 (3): 801–806. Bibcode:1981ASAJ...70..801M. doi:10.1121/1.386919. Del Grosso, V. A. (1974). "New equation for speed...
own" equation, such as the EE. The LEE and its many variations are widely used in computational aeroacoustics. Sound wave or acousticwaveequation: Start...
Rayleigh waves are a type of surface acousticwave that travel along the surface of solids. They can be produced in materials in many ways, such as by...
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