Finite element approximation for low‐frequency sound in a room with absorption

The two‐dimensional flow of acoustic energy is calculated in a room with parallel ceilings and floors and of a rectangular floor plan in the finite element approximation. The interior surfaces of the room are assumed to be reverberant, with the exception of a locally reactive vertical strip of impedance Z=0.7 ρc located on one of walls. Solutions are obtained for a vertically oriented acoustic line source with volumetric flow rate Q per unit length and frequency ω that intersects horizontal planes in the room at the point (x(s),y(s)). The frequency response is calculated by expanding the acoustic Green’s function as the direct product of the damped room eigenmodes, as approximated by the finite element analysis. This approach allows calculation of the room response for various frequencies and source locations in the post processing phase of the finite element solution.