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Helmholtz Formula and Rayleigh Hypothesis

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Wave Scattering from Rough Surfaces

Part of the book series: Springer Series on Wave Phenomena ((SSWAV,volume 17))

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Abstract

This chapter concerns two problems. First, we consider the Helmholtz formula which enables us to express the field at any point of some region through boundary values of this field and its normal derivative. Section 3.1 presents a simple derivation of the Helmholtz formula when it directly follows from the differentiation rule for discontinuous functions. The advantage of this derivation is a clear demonstration of the Helmholtz formula ambiguity which is used in the following chapters. Section 3.1 also discusses some consequences of the formula and derives integral equations for surface density at the boundary.

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References

  1. J.W.S. Rayleigh: The Theory of Sound (Dover, New York 1945) vol. 2

    Google Scholar 

  2. B.A. Lippman: J. Opt. Soc. Am. 43, 408 (1953)

    Article  Google Scholar 

  3. R. Petit, M. Cadilhac: C.R. Acad. Sc. Paris 262, 468–471 (1966)

    Google Scholar 

  4. R.F. Millar: Proc. Camb. Phil. Soc. 65, 773–791 (1969)

    Article  Google Scholar 

  5. R.F. Millar: Proc. Camb. Phil. Soc. 69, 217–225 (1971)

    Article  Google Scholar 

  6. P.M. van den Berg, J. T. Fokkema: J. Opt. Soc. Am. 69, 27–31 (1979)

    Article  Google Scholar 

  7. H.W. Marsh: J. Acoust. Soc. Am. 35, 1835–1836 (1963)

    Article  Google Scholar 

  8. N.R. Hill, V. Celli: Phys. Rev. B 17, 2478–2481 (1978)

    Article  CAS  Google Scholar 

  9. A.G. Voronovich: Dokl. Akad. Nauk. SSSR 273, 85–89 (1983)

    Google Scholar 

  10. R.F. Millar: Radio Sci 8, 785–796 (1973)

    Article  Google Scholar 

  11. H. Ikuno, K. Yasuura: IEEE Trans. AP-21, 657–662 (1973)

    Google Scholar 

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Authors and Affiliations

  1. Environmental Technology Laboratory, National Oceanic and Atmospheric Administration, 325 Broadway, Boulder, CO, 80303-3328, USA

    Professor Alexander Voronovich

Authors
  1. Professor Alexander Voronovich
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© 1999 Springer-Verlag Berlin Heidelberg

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Voronovich, A. (1999). Helmholtz Formula and Rayleigh Hypothesis. In: Wave Scattering from Rough Surfaces. Springer Series on Wave Phenomena, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59936-1_3

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  • DOI: https://doi.org/10.1007/978-3-642-59936-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64187-9

  • Online ISBN: 978-3-642-59936-1

  • eBook Packages: Springer Book Archive

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