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Physical Fundamentals of Sound Fields

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Part of the T-Labs Series in Telecommunication Services book series (TLABS)


The present chapter outlines the mathematical and physical tools that are employed in the subsequent chapters. It is not written in a tutorial style but serves rather as a reference. The wave equation and its solutions in Cartesian as well as in spherical coordinates are introduced. Then, a number of useful representations of sound fields such as the wavenumber domain, spherical harmonics expansions, the angular spectrum representation, and alike are presented. The basis for the solutions to the problem of sound field synthesis is set by a discussion of useful integral relations such as the Rayleigh Integral and the Kirchhoff Helmholtz Integral.


  • Plane Wave
  • Spherical Harmonic
  • Sound Pressure
  • Sound Source
  • Helmholtz Equation

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  • DOI: 10.1007/978-3-642-25743-8_2
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Ahrens, J. (2012). Physical Fundamentals of Sound Fields. In: Analytic Methods of Sound Field Synthesis. T-Labs Series in Telecommunication Services. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-642-25742-1

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