Abstract
Van Bladel has reduced the problem of low-frequency scattering through an aperture in a soft screen to a sequence of static integral equations. Analytical solutions are known at the moment for a circular and an elliptic aperture only. A new analytical method is proposed here which is valid for the apertures of arbitrary shape. The method is based on an integral representation for the reciprocal distance between two points obtained by the author earlier. Specific approximate formulae are derived for evaluating the average value of the zeroth-order term in the low-frequency expansion for an aperture in the shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the numerical solutions known in the literature, and a good agreement is confirmed.
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