Scattering by large resonant cavity structures

The scattering of a plane wave from a two-dimensional, sound hard, cavity i s considered where the length of the cavity is large compared to the wavele ngth. The cavity may contain an obstacle or have walls which slowly change on a scale that is long compared to the wavelength, but short compared to t he overall length of the cavity. The structure may be terminated by either or short or another hanged aperture. Using a generalized S-matrix, a new formula is derived for the scattering c ross-section, sigma, of the structure. This formula contains the mathematic al description of all the multiple interactions between the aperture and th e contents of the cavity. Approximating the inverse of a certain matrix by the first term of a geometric series, yields an approximation sigma(A) whic h has been derived by researchers studying the scattering cross-sections of jet engine inlets. This approximation only takes into account one scatteri ng interaction and provides excellent results, because for these applicatio ns, the width of the waveguide is much larger than a wavelength. For other important applications where the width and the wavelength are comparable, i t produces unacceptable errors. Several examples are presented which compare the errors produced by the app roximate theory to the more exact one derived in this paper. It is shown th at the two agree when the waveguide width becomes sufficiently large and di verge in the other extreme. (C) 1999 Elsevier Science B.V. All rights reser ved.