The prediction of sound fields in non-diffuse spaces by a “random walk” approach

Abstract

A Markov process, representing random walks of acoustical phonons in an enclosure, is used to predict the steady state high frequency sound pressure levels in complex internal spaces, excited by an omni-directional point source. In the theory, developed from work by Gerlach, one considers the three dimensional random walks of phonons inside an enclosure of any internally complex geometry. The sound pattern is derived by considering the probability that a phonon, leaving some source, will radiate to a particular wall, undergo a certain path of successive reflections, and be radiated to a detection point. The spatial density of phonons, at a given location, arising from a large ensemble of phonons traversing different random paths, gives rise to an intensity. Knowledge of the sound intensity at a suitable number of detection points, in a regularly spaced lattice, enables the sound field inside an enclosure to be estimated. The advantages of this approach, over others is that, in determining the location of each phonon, and hence the sound intensity, room shape and mutual relationships among internal partitions, and, subsequently, the past history of the phonon, are all taken into account.