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A note on reflection of spherical waves.

Gunnar Taraldsen1

  • 1Acoustic Research Center, Department of Electronics and Telecommunications, Norwegian University of Science and Technology (NTNU), O.S. Bragstads Plass, N-7465 Trondheim, Norway. Gunnar.Taraldsen@sintef.no

The Journal of the Acoustical Society of America
|July 16, 2005
PubMed
Summary

This study simplifies wave reflection analysis by showing that solutions for sources and receivers at the boundary are sufficient for general cases. This theoretical advance may offer practical applications in acoustics and electromagnetics.

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Area of Science:

  • Physics
  • Acoustics
  • Electromagnetics

Background:

  • Sommerfeld (1909) and Weyl (1919) provided solutions for spherical wave reflection from a plane surface.
  • Existing knowledge suggests a general solution requires a solution for sources at the boundary.

Purpose of the Study:

  • To demonstrate that the general solution for spherical wave reflection can be derived from solutions where both source and receiver are at the boundary.
  • To explore the theoretical implications and potential practical applications of this simplified approach.

Main Methods:

  • Analysis of exact and asymptotic solutions for spherical wave reflection.
  • Mathematical derivation to show sufficiency of boundary-case solutions.

Main Results:

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  • It is demonstrated that having the general solution for the case where both source and receiver are at the boundary is sufficient to solve the general case.
  • Sommerfeld's approximate solution is shown to yield Ingard's approximate solution for arbitrary source and receiver heights.

Conclusions:

  • The study simplifies the theoretical framework for spherical wave reflection.
  • This approach, while primarily theoretical, may lead to practical applications in fields like acoustics and electromagnetics.