where ρ is the density of the medium and
cc is the complex speed of sound,
The subscripts 1 and
2 denote the sides of the boundary into which the reflected and refracted ray propagate, respectively; see
Ref. 4.
At a Wall, the reflection coefficient
R can be defined explicitly or in terms of the absorption coefficient
α or characteristic impedance of absorber
Z1. In terms of the absorption coefficient,
The Wall feature also includes built-in options to compute the reflection coefficient for fluid-fluid interfaces, fluid-solid interfaces, and a fluid layer adjacent to a semi-infinite fluid domain. When treating the
Wall boundary as a
Fluid-fluid interface, the reflection coefficient is computed using
Equation 8-2 as if the wall were a material discontinuity where the fluid properties of the adjacent medium are specified, except that no refracted ray is produced.
If the Wall boundary is modeled as a
Fluid-solid interface, the reflection coefficient is instead defined as
where the subscripts p and
s refer to the propagation of compressional and shear waves in the adjacent solid domain, respectively. For example,
θp,t is the refraction angle computed using the compressional complex speed of sound in the adjacent solid domain.
If the Wall boundary is modeled as a
Layered fluid half-space, the boundary is treated as a thin layer of one fluid backed by a semi-infinite domain of a second fluid. The reflection coefficient is
where h1 (SI unit: m) is the layer thickness.
If the Rayleigh roughness model is used, the reflected intensity is multiplied by an additional factor to account for surface roughness:
where k (SI unit: rad/m) is the wave vector magnitude of the ray and
σ (SI unit: m) is the RMS roughness of the surface.
