Jason E. Summers

Statistical-acoustics models of energy decay in systems of coupled rooms and their relation to geometrical acoustics

An improved statistical-acoustics model of high-frequency sound fields in coupled rooms is developed by incorporating into prior models geometrical-acoustics corrections for both energy decay within subrooms and energy transfer between subrooms. The conditions under which statistical-acoustics models of coupled rooms are valid approximations to geometrical acoustics are examined by comparison of computational geometrical-acoustics predictions of decay curves in two- and three-room systems with those of both improved and prior statistical-acoustics models. The accuracy of the decay model used within subrooms is found to have a primary influence on the accuracy of predictions in coupled systems. Likewise, nondiffuse transfer of energy is shown to significantly affect decay of energy in systems of coupled rooms. The decrease in energy density of the reverberant field with distance from the source, which is predicted by geometrical acoustics, is found to result in spatial dependence of decay-curve shape for certain coupling geometries. Geometrical effects are shown to contribute to the failure of statistical-acoustics models in the case of strong coupling between subrooms; thus, previously proposed statistical-acoustics criteria cannot predict the point at which the models break down with consistent accuracy.

Adapting a randomized beam-axis-tracing algorithm to modeling of coupled rooms via late-part ray tracinga)

The ability of computational geometrical acoustics to accurately model energy decay in systems of coupled rooms is investigated both theoretically and experimentally. Unlike single-volume rooms, coupled rooms have reflection density that is not described by a single quadratic function of time. It is shown that tail-correction procedures used by beam-axis-tracing algorithms, which assume quadratic growth of reflection density, can lead to inaccurate predictions in coupled rooms. Further, beam-axis tracing implemented as ray tracing with a growing detection sphere is susceptible to error in coupled rooms when the detection sphere extends into adjacent subrooms. Marked error is anticipated in those cases for which the source and receiver are in the less reverberant of two rooms and is expected to be most severe for (1) small coupling apertures and (2) receiver positions near boundaries between subrooms. Errors are demonstrated by comparison of computational geometrical acoustics predictions with scale-model ...

Small-slope simulation of acoustic backscatter from a physical model of an elastic ocean bottom

An underwater acoustic experiment with a two-dimensional rough interface, milled from a slab of PVC, was performed at a tank facility. The purpose was to verify the predictions of numerical models of acoustic rough surface scattering, using a manufactured physical model of an ocean bottom that featured shear effects, nonhomogeneous roughness statistics, and root-mean-square roughness amplitude on the order of the acoustic wavelength. Predictions of the received time series and interface scattering strength in the 100-300 kHz band were obtained from the Bottom Reverberation from Inhomogeneities and Surfaces-Small-Slope Approximation (BORIS-SSA) numerical scattering model. The predictions were made using direct measurements of scattering model inputs-specifically, the geoacoustic properties from laboratory analysis of material samples and the grid of surface heights from a touch-trigger probe. BORIS-SSA predictions for the amplitude of the received time series were shown to be accurate with a root-mean-square residual error of about 1 dB, while errors for the scattering strength prediction were higher (2-3.5 dB). The work is part of an ongoing effort to use physical models to examine a variety of acoustic scattering and propagation phenomena involving the ocean bottom.

Experimental validation of a coprime linear microphone array for high-resolution direction-of-arrival measurementsa)

Coprime linear microphone arrays allow for narrower beams with fewer sensors. A coprime microphone array consists of two staggered uniform linear subarrays with M and N microphones, where M and N are coprime with each other. By applying spatial filtering to both subarrays and combining their outputs, M+N-1 microphones yield M⋅N directional bands. In this work, the coprime sampling theory is implemented in the form of a linear microphone array of 16 elements with coprime numbers of 9 and 8. This coprime microphone array is experimentally tested to validate the coprime array theory. Both predicted and measured results are discussed. Experimental results confirm that narrow beampatterns as predicted by the coprime sampling theory can be obtained by the coprime microphone array.

Accounting for delay of energy transfer between coupled rooms in statistical-acoustics models of reverberant-energy decaya)

A statistical-acoustics model for energy decay in systems of two or more coupled rooms is introduced, which accounts for the distribution of delay in the transfer of energy between subrooms that results from the finite speed of sound. The method extends previous models based on systems of coupled ordinary differential equations by using functional differential equations to explicitly model dependence on prior values of energy in adjacent subrooms. Predictions of the model are illustrated for a two-room coupled system and compared with the predictions of a benchmark computational geometrical-acoustics model.

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

Confusion can result because the two best-known statistical-acoustics models of energy decay in coupled rooms give variant predictions, despite being derived from identical base assumptions. It is shown here that the model given by Cremer and Müller is formally identical to the model given by Kuttruff and that differences between the models arise only if Cremer and Müllers approximate solution method is followed. An exact formulation of Cremer and Müllers model is given explicitly and its predictions are shown to agree with those of Kuttruffs model.

Reverberant acoustic energy in auditoria that comprise systems of coupled rooms

A frequency-dependent model for reverberant energy in coupled rooms is developed and compared with measurements for a 1:10 scale model and for Bass Hall, Ft. Worth, TX. At high frequencies, prior statistical-acoustics models are improved by geometrical-acoustics corrections for decay within sub-rooms and for energy transfer between sub-rooms. Comparisons of computational geometrical acoustics predictions based on beam-axis tracing with scale model measurements indicate errors resulting from tail-correction assuming constant quadratic growth of reflection density. Using ray tracing in the late part corrects this error. For mid-frequencies, the models are modified to account for wave effects at coupling apertures by including power transmission coefficients. Similarly, statical-acoustics models are improved through more accurate estimates of power transmission measurements. Scale model measurements are in accord with the predicted behavior. The edge-diffraction model is adapted to study transmission through...

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

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 random-incidence power transmission coefficient. These estimates agree well with independent measurements of circular apertures in thin, hard screens. When used to predict the effects of diffraction in a schematic representation of typical coupled-room auditoria, new mid-frequency models suggest that effects of diffraction on decay curves, while smaller than variations due to input-parameter uncertainty, are large enough to be audible.

Measurement of audience seat absorption for use in geometrical acoustics software

Systematic errors in the high frequency predictions of geometrical acoustics software can result from the use of seat absorption coefficients derived by traditional measurement methods based on diffuse-field assumptions. This analysis treats in-situ measurement methods in which seat absorption coefficients are calculated by a diffuse-field model from reverberation time measurements made in auditoria. Computer models illustrate that the nonuniform distributions of absorption in auditoria result in significant differences between the absorption coefficients derived by an in-situ measurement method and the true random-incidence absorption coefficients. Proposals are made for methods to be used when measuring seat absorption coefficients for use in geometrical acoustics software.

Assessing the accuracy of auralizations computed using a hybrid geometrical‐acoustics and wave‐acoustics method

When based on geometrical acoustics, computational models used for auralization of auditorium sound fields are physically inaccurate at low frequencies. To increase accuracy while keeping computation tractable, hybrid methods using computational wave acoustics at low frequencies have been proposed and implemented in small enclosures such as simplified models of car cabins [Granier et al., J. Audio Eng. Soc. 44, 835–849 (1996)]. The present work extends such an approach to an actual 2400‐m3 auditorium using the boundary‐element method for frequencies below 100 Hz. The effect of including wave‐acoustics at low frequencies is assessed by comparing the predictions of the hybrid model with those of the geometrical‐acoustics model and comparing both with measurements. Conventional room‐acoustical metrics are used together with new methods based on two‐dimensional distance measures applied to time‐frequency representations of impulse responses. Despite in situ measurements of boundary impedance, uncertainties in...