ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A plane acoustic wave is incident upon an infinite, rough, impenetrable surface S. The aim is to find the scattered field by deriving a boundary integral equation over S, using Green's theorem and the free-space Green's function. This requires careful consideration of certain integrals over a large hemisphere of radius r; it is known that these integrals vanish as r→∞ if the scattered field satisfies the Sommerfeld radiation condition, but that is not the case here—reflected plane waves must be present. It is shown that the well-known Helmholtz integral equation is not valid in all circumstances. For example, it is not valid when the scattered field includes plane waves propagating away from S along the axis of the hemisphere. In particular, it is not valid for the simplest possible problem of a plane wave at normal incidence to an infinite flat plane. Some suggestions for modified integral equations are discussed. © 1998 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.532359
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