Acoustical properties of homogeneous planar surfaces in room acoustics: A theoretical review

Abstract

This work reviews the fundamental boundary conditions used in room acoustics from a theoretical perspective. In particular, it is assumed that sound propagates in air as plane waves and the boundaries are planar walls. Moreover, the walls are assumed to be infinite in lateral extent and have uniform properties along their surface. These two conditions ensure that sound waves are reflected wholly specularly, as opposed to being scattered as well; the assumption of infinite lateral extent avoids scattering from the edges of the walls, and the assumption of uniform properties avoids scattered radiation caused by the inhomogeneity of the wall. Parameters used in describing the acoustical properties of the walls are introduced and, using the wave equation, expressions are derived for them in terms of the wall impedance. Theoretical relations between the parameters are then discussed based on (i) physical restrictions such as energy conservation and the causality condition and (ii) simplifying assumptions used in room acoustics such as local reaction of surfaces and the minimum-phase condition. Finally, some practical aspects of these theoretical relations are discussed using simple examples.