Acoustic beaming and reflexion from wave-bearing surfaces

The field radiated by an acoustic monopole in the presence of an infinite membrane, or plate, is studied, with emphasis on the case when fluid loading effects are small and when a free wave in the surface has supersonic phase speed relative to the fluid. Coupling between fluid and surface is then specified by a Mach angle θ M and by a fluid loading parameter ε, with ε [Lt ] 1. Asymptotic expressions for the field are derived which are uniform in the observation angle θ, measured from the surface. Previous descriptions have suggested the formation of a strong two-dimensional beaming effect along the surface of the Mach cone θ = θ M . Here it is shown that this effect is a spurious consequence of nonuniform asymptotics. A beam is indeed formed, and persists without attenuation or distortion to large distances k 0 R ∼ ε −2 . However, the beam amplitude is small compared with that of the three-dimensional reflected field, while at distances k 0 R [Gt ] ε −2 only the reflected wave survives. Some interesting features of the reflexion coefficient and of the field near to the membrane are also discussed. In particular, it is shown that the pressure field generated by a subsonic surface wave is also confined to a conical zone, the transition across the generators of the cone being described by Fresnel functions of a familiar kind.