Identity of the Rayleigh–Fourier and extinction theorem method solutions for scattering and transmission of sound at a rough fluid–solid interface

Abstract

The Rayleigh–Fourier and extinction theorem mathematical formulations are established and compared in the case of scattering from and transmission through a rough fluid–solid interface. By using the properties of the solution resulting from the extinction theorem method, it is shown that the two methods are equivalent. This result, which has already been established in the case of an interface with an impedance boundary condition, is of practical importance since it justifies the use of the Rayleigh–Fourier method instead of the rigorous extinction theorem method that is more costly in computation time. The identity of the two solutions is confirmed by numerical results presented by other authors. This conclusion, surprising in view of the well-known limited regime of validity of the Rayleigh hypothesis upon which the Rayleigh–Fourier method is based, is discussed.