Uncertainty quantification of the diffuse sound field assumption in sound insulation predictions

The transmission loss of a partition depends on the sound fields in the adjoining rooms, which are often taken to be diffuse. A diffuse sound field is a random field, representing a conceptual ensemble of rooms with the same volume and reverberation time, but otherwise any possible arrangement of boundaries and small objects that have a wave scattering effect. Uncertainty due to random wave scattering is therefore inherently present in diffuse transmission loss values. In this work, closed-form expressions are presented for quantifying this uncertainty, such that it becomes possible to estimate by how much the transmission loss of a particular room-wall-room system may deviate from the nominal, ensemble average value which corresponds to omnidirectional incidence and halfspace radiation. The first expression is exact yet its evaluation requires knowledge of the dynamic stiffness of the partitioning structure and of the radiation impedances of the surrounding fluids. The second expression is approximate and depends on energetic quantities only, so it is also applicable in an experimental setting. The expressions are validated in a Monte-Carlo simulation study involving a single wall.