Explicit short-wave representations and Ray Tracing method for reflections from curved surfaces in room acoustics

A short-wave asymptotic method is proposed to solve the problem of multiple reflections of sound rays from curved surfaces, as well as from a system of curved surfaces. At the beginning, we give a brief survey of the proposed method for single reflection. Then this general approach is demonstrated in the case of spherical and cylindrical canonical surfaces. To provide a more physical impression of a rather mathematical development, we give a comparison of the analytical asymptotic formulas with the results obtained by the Ray Tracing method (RTM), in the case of canonical geometries. Further, there is given a brief survey of analogous method in the case of double reflection, for surfaces of a general geometry, which is clarified again for double reflection from the surfaces of canonical shapes. At last, we give some general conclusions which may be important in practical aspect.