Prediction and uncertainty quantification of the diffuse sound absorption of finite absorbers

This contribution presents a numerical approach to predict diffuse sound absorption. Conventionally, this is done by considering an infinite absorber coupled to an acoustic halfspace. However, the diffuse absorption coefficient for a finite absorber can be quite different from the corresponding infinite-size value due to what is referred to in literature as the size or edge effect. A finite size correction has been developed previously, but it is only applicable to homogeneous absorbers, neglects boundary conditions, and is based on a computationally costly numerical integration. This contribution presents an alternative approach which overcomes these drawbacks. In this approach, a deterministic model of the absorber, e.g., constructed with the finite element or modal transfer matrix method, is coupled to a diffuse model of the room through the diffuse field reciprocity relation. The theoretical uncertainty on this diffuse sound absorption that is inherent in the diffuse field assumption can also be quantified, or more precisely, the variance of the sound absorption that can be theoretically expected across a diverse ensemble of rooms of the same volume. It is demonstrated that the diffuse absorption coefficient corresponds to the average of the absorption coefficient across an ensemble of rooms, implying that the former is of practical use even at low frequencies. The methodology is experimentally validated for porous and membrane absorbers.