Attenuation of the Specular Echo by an Immersed Elastic Galois Grating

摘要

Number theory play s an important role in the context of architectural acoustics (see the works of M.R. Schroeder [1,2]). More particularly, quadratic-residue sequences have been extensively studied and used (see [1,2,3] and references therein) because they assist in designing diffusing surfaces (quadratic-residue gratings) permitting uniform scattering of sound. In contrast, Galois sequences constructed from primitive elements of finite-number Galois fields and associated Galois gratings which permit sound attenuation in one direction [1, 2] have not really interested acousticians. As far as we know, the concept of a Galois grating has never been introduced in underwater acoustics. However, such a concept could be very important in the context of the search for new anechoic devices. In this research note, we present theoretical and experimental results concerning ultrasonic wave diffraction by an immersed elastic Galois grating. This grating is a one-dimensional plane diffusor, taken to be semi-infinite and the surface design is based on primitive elements from the finite Galois field G'F(23) [1,2].