Approximate methods in high-frequency scattering

Two approximate methods for deriving the high-frequency scattering coefficient of twodimensional obstacles without edges are described. In the first method a simple field which satisfies approximately the boundary condition near the points of glancing incidence is found. Elsewhere the geometrical acoustics field is used. The scattering coefficient is about 7 % in error. In the second method Fourier transforms are employed to find a field which satisfies the boundary condition over a wider region. This leads to results which, for the circular cylinder, are in complete agreement with those of the exact theory.