Multiple scattering of sound by a periodic line of obstacles

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Abstract
Equations derived earlier for multiple scattering by arbitrary three-dimensional configurations are applied to a line of equally spaced identical obstacles. We develop several different representations and approximations for the field and derive the appropriate energy and scattering theorems. Spherically symmetric scatterers are considered as a special case. In general, the results are analogous to those obtained before for the two-dimensional problem of scattering by a planar grating of identical cylinders but differ essentially in that now the scattered modes are conical instead of planar. A major difference is that resonance maxima (analogous to the Wood's anomalies for the planar grating) may occur not only for wavelengths that are slightly larger than the grazing (Rayleigh) wavelengths, but also for wavelengths that are slightly smaller. We also derive closed-form approximations for small scatterers with arbitrary spacing, and then specialize the results to small spacing.

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