A spherical harmonics basis for quantifying the isotropy of sound fields in reverberant enclosures

Abstract

This study examines an experimental method for evaluating isotropy in reverberant sound fields, based on an analysis in the spherical harmonics domain. The methodology relies on estimating the wavenumber (or angular) spectrum of the sound field in the room, to characterize the magnitude of the waves arriving from definite directions at the observation point. Subsequently, the obtained wavenumber spectrum is expanded into a series of spherical harmonics, and the multipole moments from the spherical expansion are used to characterize the isotropy of the sound field. This spherical harmonic basis is best suited for characterizing isotropy, as it provides an unequivocal characterization of the symmetry of the wave field. The work examines how theoretical considerations compare with experimental results obtained in various rooms with diverse diffuse field conditions. The experimental results are based on automated measurements using a scanning robot. In addition, the corresponding spatial distribution of the active soundintensity field is determined, making it possible to benchmark the proposed methodology with direct observations of the energy flows in the sound field.