The two-dimensional problem of the diffraction of a plane acoustic shock wave by a cylindrical obstacle of arbitrary cross section is considered. An integral equation for the surface values of the pressure is formulated. A major portion of the solution is shown to be contributed by terms in the integral equation which can be evaluated explicitly for a given cross section. The remaining contribution is approximated by a set of successive, nonsimultaneous algebraic equations which are easily solved for a given geometry. The case of a square box with rigid boundaries is solved in this manner for a period of one transit time. The accuracy achieved by the method is indicated by comparison with known analytical solutions for certain special geometries.

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