Acoustic and Electromagnetic Equations pp 9-109 | Cite as

# The Helmholtz Equation

Chapter

## Abstract

The acoustic wave equation described the propagation of the sound in a medium like the air. It results, e.g., from the equation of the compressible gas dynamic, also called the compressible Navier-Stokes equations. In the case of small displacements of the gas, a linearization of these equations leads to an equation for the displacement and the small variation of the pressure in the gas. In the case of a homogeneous medium of mean density
Where

*ρ*_{0}, this is the well-known above system of equations(2.1.1)

*c*is the speed of sound in the medium, the speed of displacement in the medium and*p*the pressure, which is supposed to be isotropic. Eliminating the displacement , we obtain a scalar wave equation for the pressure*p*:(2.1.2)

## Keywords

Dirichlet Problem Spherical Harmonic Laplace Equation Neumann Problem Helmholtz Equation
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## Copyright information

© Springer Science+Business Media New York 2001