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Multiple scattering of sound by turbulence and other inhomogeneities

Authors
Journal
Journal of Sound and Vibration
0022-460X
Publisher
Elsevier
Publication Date
Volume
27
Issue
4
Identifiers
DOI: 10.1016/s0022-460x(73)80357-8
Disciplines
  • Mathematics
  • Musicology
  • Physics

Abstract

This paper describes a multiple scattering theory of the propagation of sound through an inhomogeneous atmosphere. Two cases are considered separately, The first is that of propagation in an extensive region of low Mach number turbulence, and the second is that of propagation in an atmosphere in which the speed of sound varies randomly owing to fluctuations in temperature. Kinetic equations for the diffusion of energy in wavenumber space are derived. When account is taken of the relatively slow temporal evolution of the turbulence or temperature fields, these equations are shown to be unsymmetric in the energy exchange integrals, and indicate that there is a net transfer of energy between the sound field and the medium. The kineticequations are analysed for thecase of waves long compared to the correlation length of the inhomogeneities and for the important case of the propagation of high frequency waves. Here the three principal conclusions relate to (i) absorption of sound by the turbulence, (ii) spectral broadening of the acoustic spectrum due to interaction with a temporally evolving field, and (iii) scattering by spatial inhomogeneities. The analysis constitutes what is essentially a scattering theory; nevertheless, at very high frequencies results such as (ii) and (iii) are shown to agree precisely with predictions based on the theory of geometrical acoustics.

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