Searching for a theoretical relation between reverberation and the scattering coefficients of surfaces in a room

Jean-Jacques Embrechts (1)

1 Université de Liège

The Sabine formula gives an opportunity to relate the reverberation time to the global absorption properties of a room. On the other hand, the scattering properties of surfaces also influence the reverberation. However, if the physical principles governing this influence are already known, there's presently not such a clear link between the "quantity" of scattering, the scattering coefficients of surfaces and reverberation. This link, like the Sabine formula, would help to specify the scattering properties of surfaces in room acoustics projects. This paper does not give a general solution to the problem, but it is rather a reflection based on existing research and a tentative of approach based on the acoustic radiative transfer (or transport) equation. This equation is first of all expressed for room acoustics problems, especially concerning the boundary conditions which explicitly include the surfaces' scattering coefficients. It is then applied to a diffuse sound field, showing that the scattering coefficients do not explicitly influence reverberation under such a strong assumption. In a second application, the transport equation is applied to a room containing a pair of parallel surfaces. In that case, the influence of scattering coefficients is described.

Mots clés: Room acoustics; Surface scattering; Reverberation

Domaines: Acoustique [physics.class-ph]

Jean-Jacques Embrechts. Searching for a theoretical relation between reverberation and the scattering coefficients of surfaces in a room. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810603⟩