A wavenumber approach to quantifying the isotropy of the sound field in reverberant spaces

Abstract

This study proposes an experimental method for evaluating isotropy in enclosures, based on an analysis of the wavenumber spectrum in the spherical harmonics domain. The wavenumber spectrum, which results from expanding an arbitrary sound field into a plane-wave basis, is used to characterize the spatial properties of the observed sound field. Subsequently, the obtained wavenumber spectrum is expanded into a series of spherical harmonics, and the moments from this spherical expansion are used to characterize the isotropy of the wave field. The analytical framework is presented. The method is examined numerically and experimentally, based on array measurements in four chambers: two anechoic chambers (one with a single source and another with an array of 52 sources), a reverberation chamber, and the same reverberation chamber with a sample of absorbing material on the floor. The results indicate that the proposed methodology is suitable for assessing the isotropy of a sound field.

Bayesian decay time estimation in a reverberation chamber for absorption measurements

“…The quantification of the isotropy of the sound field is investigated in Ref. 41. Furthermore, this work does not deal with the quantification of double slopes like in Ref.…”

Approximating an isotropic sound field as a composition of plane waves

“…To evaluate the degree of isotropy of the synthesized sound field, we employ the isotropy indicator [3], which is denoted as ðk; tÞ ¼ jA 00 ðk; tÞj…”

“…A diffuse sound field is generally composed of two physical features: the homogeneity of a sound field inside a room and the isotropy of the directional properties of a sound field observed at a given point in a room [2]. As for isotropy, in a recent study [3], a measure called the isotropy indicator was proposed to evaluate the degree of isotropy of a sound field. This measure employs plane-wave decomposition [4] based on spherical harmonics expansion.…”

“…Specifically, the sufficient number of plane waves required to realize a nearly complete isotropic sound field is numerically discussed utilizing the plane-wave composition (PWC) and plane-wave decomposition (PWD) for the synthesis and analysis of a sound field, respectively. The degree of isotropy in a simulated sound field is evaluated using the isotropy indicator [3].…”

Directional sound field decay analysis in performance spaces

“…Since the fundamental definition of the diffuse sound field is its isotropy condition—requiring it to be composed of an infinite number of uncorrelated waves with incidence directions distributed uniformly over the spherical domain—arrays of microphones of high order prove to be a well suited analysis tool. Early works by Thiele 25 were extended to microphone array based approaches from Gover et al 26,27 and more recently Epain and Jin 24 and Nolan et al 28 However, aforementioned studies were either limited to the steady-state sound field or in the case of Gover to a very coarse temporal resolution.…”