Theory of Sound Barriers: Diffraction of Plane, Cylindrical and Spherical Waves on a “Hard-Soft” Half Plane

Abstract

When designing sound barriers, it is important to clarify the following problems: feasibility of partial or full coverage of the barrier surface with absorbent material or formation of barriers using sound-scattering surfaces. The study of the indicated applied problems for plane barriers leads to the necessity of formulating and solving the problems of diffraction of sound waves on a half-plane with boundary conditions of different type (various) on the half-plane sides. The solution of such problems by traditional methods is significantly complicated in comparison with the consideration of similar problems under the boundary conditions of the same type on the entire boundary of the scattering body and often leads to hardly determinable results. Simple methods for solving problems on diffraction of acoustic waves on a half-plane with Neumann boundary conditions on the one side of the half-plane and Dirichlet boundary conditions on another side are presented in the present article. For plane incident waves, the proposed method is based on the usage of the method of separation of variables with the subsequent summation of the Fourier — Bessel series. In the case of cylindrical and spherical waves, the method for obtaining solution consists in utilizing the results found for plane waves in combination with the Keller’s geometrical theory of diffraction. New analytical solutions of the diffraction problems for plane, cylindrical, and spherical waves on a hard-soft half-plane are obtained. These solutions are valid in the far-field diffraction region (that is, at large distances from the barrier edge and have the same “simplicity” as the solutions corresponding for the boundary conditions of the same type. This circumstance makes them convenient for comparative analysis in applications of sound barriers.