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Noise is a growing concern in the built environment. Sound absorbers are a viable option for noise treatment. However, the characterization of their absorption coefficient in standardized measurement chambers still show challenges for high accuracy as required in practice. In recent years, experimental analysis has shown that assumptions of diffuse sound fields made in well-known reverberation chambers are unfulfilled. Specifically, that sound intensities in chamber-based measurement methods are presumed to be isotropic or diffuse. Diffusion equation models have shown dramatic changes in energy flow in the presence of highly absorptive materials under test. This has been attributed to well-documented inconsistencies reported from reverberation chamber measurements across different laboratories. This work will demonstrate that the diffusion equation model is proving to be a computationally efficient and viable method for predicting sound energy flows, garnering an increasing amount of interest from the acoustical community.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

When physical or other quantities vary in a specific way as a function of time, we say that they oscillate. A common, very broad definition of oscillation is as follows.

The wave equation as derived in Section 7.1 and used so far in this book, is valid for sound propagation in lossless media. The Helmholtz form of this equation is

The wave equations derived in the preceding chapter allow for calculation of arbitrary sound fields with any possible, physically meaningful boundary conditions. We had restricted ourselves to one-dimensional waves so far. These can, for instance, be observed in tubes with a diameter being small compared to the wavelength, that is d ≪ λ. This condition guarantees that no other waveforms than axial ones can propagate in the tube. One-dimensional propagation also means that all wave planes perpendicular to the axial direction are planes of constant phase.

The chapter deals with the wave equation in the spherical coordinate system. The wave equation as derived in Chap. 7 theoretically covers all possible sound fields in idealized fluids. However, the task of computing specific sound fields requires solutions of the wave equation for the particular boundary conditions in each case. In this chapter, we discuss some exemplary cases that can be solved analytically and are often sufficient to understand the structure of a problem, namely, the sound fields of spherical sound sources of 0th, 1st, and higher-order. Furthermore, the sound fields of line arrays of monopoles (0th-order spherical sources) are discussed in detail. It is shown that the directional characteristics of such arrays can be computed by Fourier transform of the spatial distribution of monopoles and their strengths.

In electric-field transducers mechanic forces are caused by electric fields or, in the reverse effect, electric polarization is influenced by mechanic forces. Even more than magnetic-field transducers, electric-field transducers exist in a wide variety of forms and shapes. There are transducers that are intrinsically linear and others that naturally have a quadratic force law and must be linearized. There are also irreversible controlled couplers. In this chapter we concentrate on the basic principles of electric-field transducers and discuss some illustrative examples.

For the purpose of numerical efficiency in room acoustic modeling, the physical theory of diffraction (PTD) is applied to approximate solutions of a finite-sized, rigid rectangular plate. The application of the PTD enables sound diffraction contributions from the two edge pairs of the rigid plate to be predicted separately while ignoring the edge waves around the corners in far-field. This paper discusses numerical implementations of the theoretical predictions to show the efficiency of the application of the PTD in finite-sized objects. The numerical results implemented will also be compared with preliminary experimental results carried out using an acoustical goniometer.

Localization of sound sources relative to a receiver is of great interest in many acoustical applications. Within the near field of a spherical array, spherical wave incidence can be assumed and both direction of arrival and radial distance information can be extrapolated. This work presents a two-tiered Bayesian framework, using spherical harmonics, through which the directions of arrival and radial distance of a single, or multiple sources in the near field relative to a spherical microphone array receiver can be estimated. The first tier estimates the number of sources present in the sound field, while the second tier estimates the direction of arrival and radial distance parameters. Two models for spherical wave incidence on a spherical array, both based on spherical harmonic beamforming techniques, are formulated and analyzed. This work presents analysis of the Bayesian framework and both models to demonstrate the feasibility of model-based Bayesian inference for three dimensional source localization of one or more sources in complex noise environments.

Coprime arrays represent a form of sparse sensing which can achieve narrow beams using relatively few elements, exceeding the spatial Nyquist sampling limit. The purpose of this paper is to expand on and experimentally validate coprime array theory in an acoustic implementation. Two nested sparse uniform linear subarrays with coprime number of elements ( M and N) each produce grating lobes that overlap with one another completely in just one direction. When the subarray outputs are combined it is possible to retain the shared beam while mostly canceling the other superfluous grating lobes. In this way a small number of microphones ( N+M-1) creates a narrow beam at higher frequencies, comparable to a densely populated uniform linear array of MN microphones. In this work beampatterns are simulated for a range of single frequencies, as well as bands of frequencies. Narrowband experimental beampatterns are shown to correspond with simulated results even at frequencies other than the arrays design frequency. Narrowband side lobe locations are shown to correspond to the theoretical values. Side lobes in the directional pattern are mitigated by increasing bandwidth of analyzed signals. Direction of arrival estimation is also implemented for two simultaneous noise sources in a free field condition.

Efficient predictions of sound diffraction around objects are of critical significance in room-acoustic simulations. An advanced diffraction theory has recently been investigated for potential applications in room acoustics for some semi-infinite, canonical wedges and for finite-sized rectangular plates [Rozynova and Xiang, J. Acoust. Soc. Am. 144 (to be published)]. The physical theory of diffraction (PTD) still relies on both geometrical and physical principles, yet emphasizes the physical one. Important features of the PTD approach are its computational efficiency and the high degree of accuracy for the diffracted sound field. This paper reviews the fringe field predictions of canonical semi-infinite wedges and further discusses solutions of diffraction problems on finite, rigid rectangular plates. The PTD is applied to approximate the solutions of a finite-sized, rigid rectangular plate that achieves high numerical efficiency. The PTD simulation allows sound diffraction contributions to be determined independently from two pairs of edges of the rigid plate, while ignoring the edge waves around the corner in far-field. This paper uses numerical implementations of the PTD predictions to demonstrate the simulation efficiency of the PTD in finite-sized objects. The numerical simulations are also validated by some preliminary experimental results carried out using an acoustic goniometer.

This work investigates the sound energy decays and flows in the Suleymaniye Mosque in Istanbul. This is a single-space superstructure having multiple domes. The study searches for the non-exponential sound energy decay characteristics. The effect of different material surfaces and volumetric contributions are investigated using acoustic simulations and in situ acoustical measurements. Sound energy decay rates are estimated by Bayesian decay analysis. The measured data reveal double- or triple-slope energy decay profiles within the superstructure. To shed light on the mechanism of energy exchanges resulting in multi-slope decay, spatial sound energy distributions and energy flow vectors are studied by diffusion equation model (DEM) simulations. The resulting sound energy flow vector maps highlight the contribution of a sound-reflective central dome contrasted with an absorptive carpeted floor in providing delayed energy feedback. In contrast, no multi-slope energy decay pattern is observed in DEM simulations with a bare marble floor, which generates a much more diffuse sound field than in the real situation with a carpeted floor. The results demonstrate that energy fragmentation, in support of the non-exponential energy decay profile, is due to both the sound absorption characteristics of materials and to their distributions, as well as to relations between the subvolumes of the mosque's interior.

Efficient predictions of sound diffraction around objects is vital in room-acoustics simulations. Recent efforts using the Physical Theory of Diffraction (PTD) [Rozynova, A. and Xiang, N., J. Acoust. Soc. Am., 141, pp. 3785 (2017)] have been reported on some canonical objects of infinite size. This research has been further developed based on solving diffraction problems on finite, rectangular plates which are free from grazing singularities. Separate solutions are considered for diffraction from two pairs of the rigid plate edges, the edge waves around the plate corner are ignored due to the lower order of diffraction contributions in the far-field. This paper will discuss numerical implementations of the theoretical predictions to demonstrate the efficiency of the PTD in room-acoustics simulations for finite sized rectangular plates. The implemented numerical results will also be compared with some preliminary experimental results carried out with a goniometer.

Surface scattering and diffuse reflections of acoustic diffusers are of relevance in room-acoustics simulations or for characterization purposes. Polar responses of diffraction objects to acoustic plane-wave excitations can be experimentally characterized using a circular microphone array: acoustical goniometer. Recently, the Graduate Program in Architectural Acoustics at Rensselaer Polytechnic Institute has begun to explore the advanced physical theory of diffraction (PTD) [Xiang and Rozynova, J. Acoust. Soc. Am., 141, pp. 3785 (2017)]. In order to validate the PTD applied to a number of canonical shapes (rigid wedges or plates) of finite sizes, experimental investigations on the diffraction objects need to be carried out with high angular resolutions and sufficiently wide angular ranges. A large radius of the acoustical goniometer is also crucial to satisfy acoustical far-field conditions. This talk will discuss the effort in implementation and processing algorithms for various radii of portable acousti...

This paper presents an experimental study of low frequency behavior of sound propagation in acoustically coupled volumes. The experiments are carried out in an eighth-scale model of two coupled volumes with an automated high spatial-resolution scanning system. Both sound pressure and three-dimensional sound intensities are automatically measured in terms of room impulse responses at each scanning positions over densely defined two-dimensional grids covering the entire areas of the two coupled rooms that enable the analysis and visualization of sound energy and sound energy flows. Through these measurements, and with the aid of a predictive computational model, this paper will discuss low frequency modal behaviors of sound energy flows within one of two coupled volumes. As such, the distribution of potential and kinetic energies, as well as that of active and reactive sound intensities within the coupled space will be separately analyzed. The distributions of intensity vector fields are compared through computational simulation. Consequently, a discussion on possible discrepancies in modal distributions between the computational and experimental results rounds off this paper.

The need of developing accurate and cost-effective room-acoustic simulations has prompted recent investigations on edge diffractions with some progresses on solving multiple-order diffractions of finite wedges. This work explores an alternative approach based on the physical theory of diffraction [P. Ya. Ufimtsev, J. Acoust. Soc. Am. 120, 631-635 (2006)] which is well suited for solving acoustic scattering problems from reflecting objects for room-simulation purposes. Although the approaches based on the principle of geometrical acoustics (GA) are widely applied, they are less suitable for geometrical shadow boundaries. The physical theory of diffraction still relies on both geometrical and physical principles, yet emphasizes the physical one. One of the important features of this physical acoustics (PA) approach is the ability to calculate the sound field more accurately in shadow boundaries. To this end, exact and asymptotic solutions of wedge fields are discussed for secondary edge sources induced by t...

In the context of room-acoustic simulations, diffractions on obstacles with edges still post challenges. In order to create an efficient and accurate room acoustic simulation, this work focuses on solutions of diffraction on finite wedges. The solutions are based on the physical theory of diffraction [P. Ya. Ufimtsev, J. Acoust. Soc. Am. 120, 631-635 (2006)]. A detailed discussion on integral and asymptotic expressions for the diffracted field radiated by secondary wedge sources will help elaborate problem-solving strategies with the grazing incidence for exact and asymptotic solutions of wedge fields. Due to the fact that the computational load of an asymptotic solution is of orders of magnitude more efficient than that of the exact solution using the physical diffraction theory, any possible ways of reducing asymptotic errors without significantly increasing computational load will be critically important in practical room-simulations. This paper will discuss implementation based on the physical theory of diffraction. For some canonical wedge configurations, this paper will also elaborate on asymptotic errors as a function of incident source distance and direction.

Coprime linear microphone arrays consist of subarrays, each with inter-element spacing of half the wavelength observed times an integer factor. These two factors, M and N, corresponding to each subarray, are coprime, which ensures that their sensitivity completely overlaps only in the direction of the main beam. This implies a single observable wavelength, thus frequency; however, the grating lobe-mitigating effect can also be achieved for broadband sources [D. Bush, and N. Xiang, J. Acoust. Soc. Am., 138, 447-456 (2015)]. A modified Laplacian function provides a phenomenological model for broadband noise array responses, but real-world signals vary in spectral content making it prudent to develop a model which incorporates finer-resolution frequency dependence. This work also explores spatial filtering/source separation techniques for coprime linear microphone arrays. Multichannel experimental impulse response measurements with differing angles of incidence are convolved with independent speech signals. ...

Some recent concert hall designs have incorporated coupled reverberation chambers to the main hall that have stimulated a range of research activities in architectural acoustics. The coupling apertures between two or more coupled-volume systems are of central importance for sound propagation and sound energy decays throughout the coupled-volume systems. In addition, positions of sound sources and receivers relative to the aperture also have a profound influence on the sound energy distributions and decays. This work investigates the effect of aperture size on the behavior of coupled-volume systems using both acoustic scale-models and diffusion equation models. In these physical and numerical models, the sound source and receiver positions relative to the aperture are also investigated. Through systematic comparisons between results achieved from both physical scale models and numerical models, this work reveals valid ranges and limitations of the diffusion equation model for room-acoustic modeling.

Spectrum estimation is a problem common to many fields of physics, science, and engineering, and it has thus received a great deal of attention from the Bayesian data analysis community. In room acoustics, the modal or frequency response of a room is important for diagnosing and remedying acoustical defects. The physics of a sound field in a room dictates a model comprised of exponentially decaying sinusoids. Continuing in the tradition of the seminal work of Bretthorst and Jaynes, this work contributes an approach to analyzing the modal responses of rooms with a time-domain model. Room acoustic spectra are constructed of damped sinusoids, and the modelbased approach allows estimation of the number of sinusoids in the signal as well as their frequencies, amplitudes, damping constants, and phase delays. The frequency-amplitude spectrum may be most useful for characterizing a room, but in some settings the damping constants are of primary interest. This is the case for measuring the absorptive properties of materials, for example. A further challenge of the room acoustic spectrum problem is that modal density increases quadratically with frequency. At a point called the Schroeder frequency, adjacent modes overlap enough that the spectrum - particularly when estimated with the discrete Fourier transform - can be treated as a continuum. The time-domain, model-based approach can resolve overlapping modes and in some cases be used to estimate the Schroeder frequency. The proposed approach addresses the issue of filtering and preprocessing in order for the sampling to accurately identify all present room modes with their quadratically increasing density.

It is well known that head rotations are instrumental in resolving front/back confusions in human sound localization. A mechanism for a binaural model is proposed here to extend current cross-correlation models to compensate for head rotations. The algorithm tracks sound sources in the head-related coordinate system, HRCS, as well as in the room-related coordinate system, RRCS. It is also aware of the current head position within the room. The sounds are positioned in space using an HRTF catalog at \(1^{\circ }\) azimuthal resolution. The position of the sound source is determined through the interaural cross-correlation, ICC, functions across several auditory bands that are mapped to functions of azimuth and superposed. The maxima of the cross-correlation functions determine the position of the sound source. Unfortunately, two peaks usually occur, one at or near the correct location and the second at the front/back reversed position. When the model is programmed to virtually turn its head, the degree-based cross-correlation functions are shifted with the current head angle to match the RRCS. During this procedure, the ICC peak for the correct hemisphere will prevail if integrated over time for the duration of the head rotation, whereas the front/back reversed peak will average out.

Acoustic landmine detection using a laser Doppler vibrometer (LDV) has demonstrated success in recent field tests. However, low detector signals and speckle noise are still challenging problems in the LDV-based acoustic-to-seismic detection of buried landmines. This letter describes the use of binary maximum-length sequences as the acoustic excitation for achieving high SNRs of scanning results. Some relevant issues associated with the detection system design and experimental field results are discussed.

Due to recent developments in concert hall design, there is an increasing interest in the analysis of sound energy decays consisting of multiple exponential decay rates. It has been considered challenging to estimate parameters associated with double-rate (slope) decay characteristics, and even more challenging when the coupled-volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this work investigates coupled-volume systems using acoustic scale-models of three coupled rooms. Two Bayesian formulations are compared using the experimentally measured sound energy decay data. A fully parameterized Bayesian formulation has been found to be capable of characterization of multiple-slope decays beyond the single-slope and double-slope energy decays. Within the Bayesian framework using this fully parameterized formulation, an in-depth analysis of likelihood distributions over multiple-dimensional decay parameter space motivates the use of Bayesian information criterion, an efficient approach to solving Bayesian model selection problems that are suitable for estimating the number of exponential decays. The analysis methods are then applied to a geometric-acoustics simulation of a conceptual concert hall. Sound energy decays more complicated than single-slope and double-slope nature, such as triple-slope decays have been identified and characterized.

In this paper, a three-dimensional transport equation model is developed to describe the sound energy propagation in a long space. Then this model is reduced to a one-dimensional model by approximating the solution using the method of weighted residuals. The one-dimensional transport equation model directly describes the sound energy propagation in the "long" dimension and deals with the sound energy in the "short" dimensions by prescribed functions. Also, the one-dimensional model consists of a coupled set of N transport equations. Only N=1 and N=2 are discussed in this paper. For larger N, although the accuracy could be improved, the calculation time is expected to significantly increase, which diminishes the advantage of the model in terms of its computational efficiency.

In this paper, the accuracy and efficiency of the previously discussed one-dimensional transport equation models [Y. Jing et al., J. Acoust. Soc. Am. 127, 2312-2322 (2010)] are examined both numerically and experimentally. The finite element method is employed to solve the equations. Artificial diffusion is applied in the numerical implementation to suppress oscillations of the solution. The transport equation models are then compared with the ray-tracing based method for different scenarios. In general, they are in good agreement, and the transport equation models are substantially less time consuming. In addition, the two-group model is found to yield more accurate results than the one-group model for the tested cases. Lastly, acoustic experimental results obtained from a 1:10 long room scale-model are used to verify the transport equation models. The results suggest that the transport equation models are able to accurately model the sound field in a long space.

The subtraction method is a technique critical to several important acoustic measurements. It involves subtracting a reference measurement including only direct sound from one with direct sound and a reflection, to isolate the reflection. The process is very sensitive to environmental conditions, such as changes in temperature, air movement, and microphone positioning. These variations cause small time differences between the reference and reflection measurements, which prevent complete subtraction of the direct sound; the residual direct sound then pollutes analysis of the isolated reflection. This work evaluates methods to compensate for differences to achieve minimal interference from the residual direct sound.

Visualizations, based on a diffusion equation model, are presented for both steady-state and transient sound energy. For steady-state sound-pressure level distributions, animations created by scanning from the primary room to the secondary room reveal discontinuous transitions of sound energy caused by a location change from the wall area to the aperture area. Animations of time-dependent energy flow directions visualize the energy flows across coupled spaces. This study also reveals a “reversal” characteristic of energy flow directions which seems to be dependent on the size and location of the aperture.

While dealing with magnetic-field transducers in this chapter and electric-field transducers in the next, we will demonstrate that the force-law relationship between the mechanic force, F, and the coupled electric quantity, u or I, is either linear or quadratic. A linear force law, characterized by F ~u or F ~i, is observed when the energy content of the magnetic or electric field does not vary when the movable component changes position. A quadratic force law, characterized by F ~u2 or F ~i2, appears when the movable component meets the electric or magnetic field at a boundary, implying that the energy of the field varies when the movable component changes position. The force in the boundary area is given by the relationships described below that can be derived by imagining a small virtual shift of the border area. We have

So far in this book we dealt with sound propagation in terms of the wave equation. This procedure becomes very complicated, however, when treating sound fields inside rooms with complicated shapes like concert halls or churches. An approximate method called geometrical acoustics is often useful in these cases.

In the last chapter the sound field produced by point-source arrangements was calculated by linear superposition of individual spherical sound fields. For continuously loaded line arrays we further substituted the source strength of the individual sources with a length-specific source-strength load, \(\underline{q}_{\,0}'(x)\). The source-strength load has the dimension [volume-velocity/length].

In the preceding chapter, we dealt with simple linear, time-invariant mechanic and acoustic networks and their electric analogies. In general, these networks can be quite complicated and may assume any number of degrees of freedom. Yet, regardless of how sophisticated the networks are, the energy and power transported in these networks is either mechanic, acoustic, or electromagnetic. Acoustic power and energy are of mechanic nature. Thus the terminological distinction between mechanical, \(\underline{F}\), \(\underline{v}\), and acoustical coordinates, \(\underline{p}\), \(\underline{q}\), is purely operational. In this chapter, we shall present the possibility of coupling electrical and mechanical domains, which results in a coupling of electric and mechanic energy and power. This topic is extremely important for modern acoustics.

So far in this book we have dealt with vibrations. These are processes that vary as functions of time. We were able to describe relevant types of vibrations with common differential equations. This chapter now focuses on waves, which are processes that vary with both time and space. Their mathematical description requires partial differential equations.

The wave equation, \(\nabla^2 p = \ddot{p} / c^2\) as derived in Sections 7.1 and 7.2 theoretically determines all possible sound fields in idealized fluids, that is, gases and liquids. The special task of computing sound fields for particular cases requires solutions of the wave equation for particular boundary conditions. In general, this task can be mathematically expensive, but there are helpful computer programs available, some of which are based on numerical methods like the finite-element method, FEM, or the boundary-element method, BEM. In praxi, approximations are often sufficient to understand the structure of a problem.

This paper proposes a modified boundary condition to improve the room-acoustic prediction accuracy of a diffusion equation model. Previous boundary conditions for the diffusion equation model have certain limitations which restrict its application to a certain number of room types. The boundary condition employing the Sabine absorption coefficient V. Valeau et al., J. Acoust. Soc. Am. 119, 1504‐1513 2006 cannot predict the sound field well when the absorption coefficient is high, while the boundary condition employing the Eyring absorption coefficient Y. Jing and N. Xiang, J. Acoust. Soc. Am. 121, 3284‐3287 2007; A. Billon et al., Appl. Acoust. 69, 2008 has a singularity whenever any surface material has an absorption coefficient of 1.0. The modified boundary condition is derived based on an analogy between sound propagation and light propagation. Simulated and experimental data are compared to verify the modified boundary condition in terms of room-acoustic parameter prediction. The results of this comparison suggest that the modified boundary condition is valid for a range of absorption coefficient values and successfully eliminates the singularity problem. © 2008 Acoustical Society of America. DOI: 10.1121/1.2805618

This letter presents a modified diffusion model using an Eyring absorption coefficient to predict the reverberation time and sound pressure distributions in enclosures. While the original diffusion model [Ollendorff, Acustica 21, 236–245 (1969); J. Picaut et al., Acustica 83, 614–621 (1997); Valeau et al., J. Acoust. Soc. Am. 119, 1504–1513 (2006)] usually has good performance for low absorption, the modified diffusion model yields more satisfactory results for both low and high absorption. Comparisons among the modified model, the original model, a geometrical-acoustics model, and several well-established theories in terms of reverberation times and sound pressure level distributions, indicate significantly improved prediction accuracy by the modification.

Multiple domed superstructures with different volumetric and material attributes are previously investigated using in-situ acoustical measurements and acoustical simulation methods for analyzing their contributions to multi-slope energy decay formation. Relevant acoustical parameters including decay rates and decay times are computed by applying the Bayesian decay analysis. Initial results indicate double- or triple-slope decay characteristics for specific measurement configurations for selected cases. The ongoing research is aimed at explaining the probable reasons of multiple decay formation as observed in such single space enclosures. Diffusion equation modeling (DEM) and intensity probe measurements are utilized to observe spatial sound energy distributions and energy flow vectors. Both computed and measured flow vectors indicate the contribution of central dome to the later energy feedback. For a specific case the trial by DEM over virtual model with floor with marble instead of carpet resulted in a ...

Sound energy distributions and flows within single-space rooms can be exploited to understand the occurrence of multi-slope decays. In this work, a real-size monumental worship space is selected for investigations of non-exponential sound energy decays. Previous field tests in this single-space venue indicate multi-slope formation within such a large volume and the multiple-dome upper structure layout. In order to illuminate/reveal the probable reasons of non-exponential sound energy decays within such an architectural venue, sound energy distributions and energy flows are investigated. Due to its computational efficiency and advantages in spatial energy density and flow vector analysis, a diffusion equation model (DEM) is applied for modeling sound field of the monumental worship space. Preliminary studies indicate good agreement for overall energy decay time estimations among experimental field and DEM results. The energy flow vector and energy distribution analysis indicate the upper central dome-struc...

Probability as logic is used to estimate the surface velocity of a patch of soil driven by an incident acoustic wave. The data used by the estimation procedure is obtained from a laser Doppler vibrometer (LDV). The output of the LDV is an intermediate-frequency carrier that is frequency- modulated by the soil surface velocity. Additionally, the LDV output is amplitude modulated by an undesirable variation in the returned laser signal due to dynamic optical speckle. The effect of the amplitude modulated by an undesirable variation in the returned laser signal due to dynamical optical speckle. The effect of the amplitude modulation on the estimate of the soil surface velocity is illustrated with results obtained using the Markov chain Monte Carlo method.

Direction-of-arrival estimation using microphone arrays is relatively simple with low signal-to-noise ratio, but precise location estimation amongst noise requires many sensors to reduce beam width. Coprime linear microphone arrays allow for narrow beams with fewer sensors. A coprime microphone array is made up of two overlapping uniform linear arrays with M and N sensors, where M and N are coprime. By applying spatial filtering with both arrays and combining their outputs, M + N sensors can yield MN directional bands. In this work, a coprime microphone array is used to estimate the location of multiple uncorrelated narrowband sources hidden in noise.

Coevolutionary arms races between predators and prey can lead to a diverse range of foraging and defense strategies, such as countermeasures between nocturnal insects and echolocating bats. Here, we show how the fine structure of wing scales may help moths by slightly increasing sound absorbance at frequencies typically used in bat echolocation. Using four widespread species of moths and butterflies, we found that moth scales are composed of honeycomb-like hollows similar to sound-absorbing material, but these were absent from butterfly scales. Micro-reverberation chamber experiments revealed that moth wings were more absorbent at the frequencies emitted by many echolocating bats (40–60 kHz) than butterfly wings. Furthermore, moth wings lost absorbance at these frequencies when scales were removed, which suggests that some moths have evolved stealth tactics to reduce their conspicuousness to echolocating bats. Although the benefits to moths are relatively small in terms of reducing their target strengths, scales may nonetheless confer survival advantages by reducing the detection distances of moths by bats by 5–6%.

When two trains of nonlinear internal waves roughly align, their lead waves form effective boundaries of an acoustic duct in which energy is trapped. This type of propagation may be considered a scattering process resulting from the broken internal wave fronts between the lead waves. A traditional approach uses adiabatic normal modes and sound speed perturbations to calculate energy propagation along horizontal rays. An alternate is a radiative transport method in which acoustic vertical modes carry energy and a two‐dimensional (2D) transport equation describes horizontal propagation. This model has parameters that are related to waveguide properties and are found from physical internal wave features. One parameter incorporates the significant curvature observed in many internal wave fronts. The two solution approaches are compared and contrasted. Data from the Shallow Water ‘06 Experiment are used to specify internal wave parameters and to compare with model calculations. [Work supported by the ONR.]

The current interest of couple‐volume systems in performing art spaces has motivated research to better understand and predict multiple‐sloped sound energy decays. This work investigates sound energy decay characteristics of coupled spaces using scale model measurements and diffusion‐equation modeling results. The experimental and numerical study is aimed to reveal possible ranges of decay parameters when investigating source and receiver positions in the primary room and aperture sizes. The receiver positions over large areas in the primary room are investigated to identify the presence of a spatial dependence and variations of decay parameters on the source position as it changes with respect to the aperture. Both scale model measurements and diffusion‐equation model results are analyzed using Bayesian probability inference in order to estimate decay orders (number of multiple slopes) and to quantify multiple‐slope decay parameters including individual decay levels, level differences, and decay times of...

There has been an increasing need in analyzing sound energy decays consisting of more than one decay slope, so‐called non‐single‐exponential decays. It has been considered very challenging to estimate parameters associated with double‐slope decay characteristics, even more challenging when the coupled‐volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this work reports investigations using both acoustical scale‐models and numerical models of three coupled volumes. Two levels of Bayesian inference: model selection and parameter estimation, have been applied to detection and characterization of sound energy decays. Experimental results measured in acoustical scale models and numerical results from diffusion‐equation‐based models are used to validate the Bayesian analysis methods. The analysis methods are then applied to geometric‐acoustics simulations of a conceptual concert hall. This work demonstrates that the analysis method...

This paper presents an experimental study on steady‐state sound pressure levels and reverberation times in a tenth long‐space scale model. The purpose of this work is to validate a recently developed one‐dimensional transport equation model for acoustic predictions in long spaces. A series of measurements has been conducted in the scale model to reveal receiver‐position dependence of measured and modeled parameters in the long spaces. Experimental results at different octave bands are obtained. This paper will compare the acoustically measured results with that of simulations.

In many areas of acoustics, the degree to which a sound field is mixed, diffuse, or spatially uniform is important in understanding the system. In the case of performance spaces, it influences the audience’s perception of the performance. More generally, it may have implications on the assessment of measurements taken in a space since often the evaluation of room‐acoustic measurements relies on diffuse field assumptions. Several techniques have been proposed to quantify the diffuseness in a space, and one of the more recent methods will be investigated in this paper. Signals measured with a combined pressure and particle velocity sensor are used to calculate energy density and average intensity. The degree of diffuseness is then associated with the relationship between these two quantities. This paper discusses aspects of the relevant theory and practical implementation.