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Reflection and Refraction of Spherical Waves

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Acoustics of Layered Media II

Part of the book series: Springer Series on Wave Phenomena ((SSWAV,volume 10))

Abstract

Our previous book [1.1] was completely focused on the problem of plane and quasi-plane waves in layered media. In the theory of acoustic wave propagation, however, it is important to take into account that the sound source is located at a finite distance from the receiver as well as from the boundaries. The most simple example of this is the classical problem about the field of a point source in the presence of an interface between two homogeneous media. In other words, it is a problem of spherical wave reflection and refraction. For electromagnetic waves this was first considered by A. Sommerfeld [1.2]. Later, fundamental works by H. Weyl, H. Ott, V. Fock, M. Leontovich, A. Baños [1.3–7] appeared. Below we shall follow mainly our own works [1.8–11] which are the further development of Weyl’s idea of the representation of a spherical wave as a superposition of plane waves. Using the same techniques, the more difficult problem of the bounded wave beam reflection can be solved as well.

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Authors and Affiliations

  1. P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Nakhimovsky pr. 36, 117218, Moscow, Russia

    Professor Leonid M. Brekhovskikh (Academician) & Dr. Oleg A. Godin

  2. School of Earth and Ocean Sciences, University of Victoria, P.O. Box 1700, V8W 2Y2, Victoria, B.C., Canada

    Dr. Oleg A. Godin

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  1. Professor Leonid M. Brekhovskikh
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  2. Dr. Oleg A. Godin
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Brekhovskikh, L.M., Godin, O.A. (1999). Reflection and Refraction of Spherical Waves. In: Acoustics of Layered Media II. Springer Series on Wave Phenomena, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03889-5_1

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  • DOI: https://doi.org/10.1007/978-3-662-03889-5_1

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