Estimating Mid-Frequency Effects of Aperture Diffraction on Reverberant-Energy Decay in Coupled-Room Auditoria

Abstract

Effects of aperture diffraction on reverberant energy decay in coupled-room auditoria are estimated at mid frequencies, defined as frequencies above the Schroeder frequencies of subrooms, but having wavelengths of the order of the characteristic dimensions of apertures. Hybrid models are developed that account for wave effects at apertures but treat sound fields in subrooms using high-frequency models. The models give more accurate estimates of the randomincidence power transmission coefficient. These estimates agree well with independent measurements of circular apertures in thin, hard screens. When used to predict the effects of 1 This paper is an expanded version of "Midfrequency modeling of coupled-room performance spaces by computation of transmission coefficients of apertures and arrays of apertures," which was presented at the

Grouped Feedback Delay Networks With Frequency-Dependent Coupling

“…This transmission coefficient is only valid for small values of ka. At high frequencies, the transmission coefficients of all apertures approach the geometrical limit η = 1 [31]. The transition occurs around ka ≈ 5 [31].…”

“…We rely on the diffraction model proposed by Miles in [30]. The variations in the power transmission coefficients of the coupling apertures can affect variations in the shapes of decay curves, as shown in [31].…”

“…The energy transmission coefficient, ζ, through an aperture connecting two rooms is a function of the angle of incidence with respect to the normal, η, aperture size, a and the wave number, k [31]. When the wavelength is comparable to the size of the aperture, diffraction (bending of waves around the aperture) can be observed.…”

“…With increasing mixing in an FDN, reflections from all directions will be incident on the aperture. Assuming an isotropic diffuse field, we can integrate the transmission coefficient over all angles of incidence and elevation angles to find only a frequencydependent value [31],…”

Technical Note: Remark on the Formal Identity of Two Statistical-Acoustics Models of Coupled Rooms

“…More general forms of Cremer and Müller's explicit symbolic expressions, which incorporate features of the improved statistical-acoustics model introduced in Reference [5], are given in Reference [6]. The models can be further extended to account for midfrequency effects of diffraction through coupling apertures by following the methods of Reference [7].…”