Low-frequency prediction of steady-state room response for different configurations of designed absorbing materials on room walls

A technique commonly used for improving room acoustics consists in increasing a total sound damping in a room. This objective can be achieved by using different configurations of a porous material for acoustical treatment of a room. In this work, that problem is analyzed theoretically by exploiting a modal representation of the impulse response (IR) function for steady-state sound field predictions. A formula for the IR function was obtained by solving a wave equation for an enclosure with complex-valued boundary conditions of walls. On the walls where the acoustic treatment is applied, these boundary conditions are related to the characteristic impedance, effective speed of sound and thickness of the porous material used for padding. Two different porous materials were considered in the analyses of the room with acoustic treatment, and to this end, the required effective properties were calculated for a rigid foam with a designed periodic microstructure, as well as for a poroelastic foam with specific visco-elastic properties of the skeleton.