Chapter Thirteen - Radiation and scattering of sound by the boundary integral method

Abstract

This chapter starts with definitions of the Huygens–Fresnel Principle; Rayleigh integrals, Green's function; Kirchhoff–Helmholtz boundary integral; and Green's function in different coordinate systems. Then comes a succession of applications: radiation from a pulsating cap in a rigid sphere; reflection of a point source near a plane; radiation of a rigid circular piston in an infinite baffle; radiation from a resilient circular disk without a baffle and with an infinite baffle; radiation from a rigid circular piston in a finite circular open baffle and a finite circular closed baffle. This is followed by a definition of the Babinet–Bouwkamp principle, with applications to several cases. Continuing, we have radiation from an infinitely long oscillating ribbon in an infinite baffle and the far-field pressure distribution as a spatial frequency spectrum of the source velocity distribution. The chapter concludes with a definition of the bridge product theorem, with applications to radiation from a rigid rectangular piston in an infinite baffle and to mutual radiation impedance between circular pistons in an infinite baffle.