The absorptive nature of the scattering coefficient in the stress-energy tensor formalism for room acoustics

In the stress-energy tensor formalism, the symmetry between absorption and scattering coefficients, as proven by measurements combined with simulations, is counter-intuitive. By introducing the wall admittance, we show that the scattering coefficient is partly created by the real part of the wall admittance combined with the active intensity, that is, is partly due to absorption. However, it also depends on the imaginary part of the wall admittance in combination with the reactive intensity, which confers it genuine scattering properties. In the case of plane waves impinging on planar boundary, the admittance formalism shows that reactive intensity vanishes in directions parallel to the wall; when the source is at finite distance from the wall, a residual reactive intensity subsists. However, for curved boundaries, the velocity in directions parallel to the wall is no longer proportional to the pressure, and scattering occurs.