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In this paper, a new Boundary Integral Equation (BIE) is proposed for solution of the scalar Helmholtz equation. Applications include acoustic scattering problems, as occur in room acoustics and outdoor and underwater sound propagation. It draws together ideas from the study of time-harmonics and transient BIEs and spatial audio sensing and rendering, to produce an energy-inspired Galerkin BEM that is intended for use with oscillatory basis functions. Pivotal is the idea that waves at a boundary may be decomposed into incoming and outgoing components. When written in its admittance form, it can be thought of setting the Burton-Miller coupling parameter differently for each basis function based on its oscillation; this is a discrete form of the Dirichlet-to-Neumann map. It is also naturally expressed in a reflectance form, which can be solved by matrix inversion or by marching on in reflection order. Consideration of this leads to an orthogonality relation between the incoming and outgoing waves, which makes the scheme immune to interior cavity eigenmodes. Moreover, the scheme is seen to have two remarkable properties when solution is performed over an entire obstacle: i) it has a condition number of 1 for all positive-real wavenumber k on any closed geometry when a specific choice of cylindrical basis functions are used; ii) when modelling two domains separated by a barrier domain, the two problems are numerical uncoupled when plane wave basis functions are used - this is the case in reality but is not achieved by any other BIE representation that the authors are aware of. Normalisation and envelope functions, as would be required to build a Partition-of-Unity or Hybrid-Numerical-Asymptotic scheme, are introduced and the above properties are seen to become approximate. The modified scheme is applied successfully to a cylinder test case: accuracy of the solution is maintained and the BIE is still immune to interior cavity eigenmodes, gives similar conditioning to the Burton-Miller method and iterative solution is stable. It is seen that for this test case the majority of values in the interaction matrices are extremely small and may be set to zero without affecting conditioning or accuracy, thus the linear system become sparse - a property uncommon in BEM formulations.

Designing a perfect low frequency acoustic absorber with subwavelength thickness is always a challenge. Various designs including micro-perforated panels, acoustic metamaterials and metasurfaces have attracted significant interests in recent years. The present paper reports a slim subwavelength absorber based on a regular array of coupled microslits to achieve low frequency absorption. The absorption mechanism by the coupled microslits is investigated using acoustic impedance together with the reflection coefficient in the complex frequency plane. The geometry of the coupled microslits is optimized using a differential evolution algorithm to enhance the absorption in the frequency band from 300 Hz to 800 Hz under different condition. The ratio of the absorber thickness to wavelength at the lowest absorption peak is less than 3.4%, which confirms its operation in deep subwavelength regime. Finally, wide band absorption using coupled microslits is demonstrated by the experiment and simulation.

An acoustic environment simulator is a system that facilitates acoustic environment composition by controlling the parameters of sound objects (both background and sound events), allowing the user to compose and compare soundscapes against their expectations. By using the acoustic environment simulator, data regarding parameters of sound objects, such as their sound level and selection, can be obtained. Furthermore, these data can be used to understand the relationship between the sound objects and the soundscapes.\ud This paper describes the development and validation of an acoustic environment simulator, which can be used to design a complex acoustic environment in the laboratory according to the expectations of the user. Validation of the simulated soundscape, whether the composed acoustic environment has the same soundscape dimension characteristics as previous in-situ and other laboratory experiments, was conducted by reproducing acoustic environment compositions using a two-dimensional ambisonic system in the laboratory. Listener responses on semantic differential scales were reduced to three reliable soundscape dimensions by principal component analysis: Calmness/Relaxation (40%), Dynamics/Vibrancy (12%), and Communication (11%). These three soundscape dimensions are consistent with a previous study conducted in situ. The results reported here indicate that acoustic environment composition can successfully imitate the soundscape dimensions of an actual acoustic environment.

The Boundary Element Method (BEM) is a proven numerical prediction tool for computation of room acoustic transfer functions, as are required for auralization of a virtual space. In this paper, it is validated against case studies drawn from the “Ground Truth for Room Acoustical Simulation” database within a framework that includes source and receiver directivity. These aspects are often neglected but are respectively important to include for auralisation applications because source directivity is known to affect how a room is excited and because the human auditory system is sensitive to directional cues. The framework uses weighted-sums of spherical harmonic functions to represent both the source directivity to be simulated and the pressure field predicted in the vicinity of the receiver location, the coefficients of the former being fitted to measured directivity and those of the latter computed directly from the boundary data by evaluating a boundary integral. Three validation cases are presented, one of which includes a binaural receiver. The computed results match measurements closely for the two cases conducted in anechoic conditions but show some significant differences for the third room scenario; here, it is likely that uncertainty in boundary material data limited modelling accuracy.The Boundary Element Method (BEM) is a proven numerical prediction tool for computation of room acoustic transfer functions, as are required for auralization of a virtual space. In this paper, it is validated against case studies drawn from the “Ground Truth for Room Acoustical Simulation” database within a framework that includes source and receiver directivity. These aspects are often neglected but are respectively important to include for auralisation applications because source directivity is known to affect how a room is excited and because the human auditory system is sensitive to directional cues. The framework uses weighted-sums of spherical harmonic functions to represent both the source directivity to be simulated and the pressure field predicted in the vicinity of the receiver location, the coefficients of the former being fitted to measured directivity and those of the latter computed directly from the boundary data by evaluating a boundary integral. Three validation cases are presented, one o...

The aim of this work was to investigate the perception of soundscape reproduced by an ambisonic reproduction system on a horizontal plane, how the experience of space affected the perception of soundscape reproduction, and how the sound level adjustment on soundscape reproduction affected the perception of soundscape compared with actual conditions. There were three experiments conducted: a soundwalk in situ in Manchester (United Kingdom) city centre, listening tests in Salford (United Kingdom), and listening tests in Bandung (Indonesia). The listening tests used material recorded from four locations on the soundwalk route in Manchester. The Salford listening tests were performed at the in-situ measured sound level, and the participants were asked to adjust the sound level to the level that represents actual locations. The listening test in Bandung was conducted to understand the effect of participants who never come to the actual location to the perception of soundscape and the sound level adjustment. The listening tests in Bandung were conducted at the in situ sound level, at 9.5 dB below the in situ sound level (based on the preference sound level from the experiment in Salford), and the participants were also requested to adjust the sound level to the level that represents the actual space (to examine the consistency with the experiment in Salford). In each case, soundscape perception was measured on 19 semantic differential scales. Analysis of the semantic differential results showed that the ambisonic reproduction produced a similar subjective experience to the in situ soundwalk when the reproduction sound level was 9.5 dB lower than the actual sound level in situ. Reproduction at the actual sound level in situ produced a different dimensional space. The study shows that the sound level adjustment of soundscape reproduction in laboratory experiment produces more ecologically valid results compared to the reproduction at the actual sound level in situ.

We propose a method for efficient evaluation of surface integrals arising in boundary element methods for three-dimensional Helmholtz problems (with real positive wavenumber k), modelling wave scattering and/or radiation in homogeneous media. To reduce the number of degrees of freedom required when k is large, a common approach is to include in the approximation space oscillatory basis functions, with support extending across many wavelengths. A difficulty with this approach is that it leads to highly oscillatory surface integrals whose evaluation by standard quadrature would require at least O(k2) quadrature points. Here, we use equivalent contour integrals developed for aperture scattering in optics to reduce this requirement to O(k), and possible extensions to reduce it further to O(1)are identified. The contour integral is derived for arbitrary shaped elements, but its application is limited to planar elements in many cases. In addition, the transform regularises the singularity in the surface integrand caused by the Green’s function, including for the hyper-singular case under appropriate conditions. An open-source Matlab™ code library is available to demonstrate our routines.

Most spatial audio reproduction systems have the constraint that all loudspeakers must be equidistant from the listener, a property which is difficult to achieve in real rooms. In traditional Ambisonics this arises because the spherical harmonic functions, which are used to encode the spatial sound-field, are orthonormal over a sphere and because loudspeaker proximity is not fully addressed. Recently, significant progress to lift this restriction has been made through the theory of sound field synthesis, which formalizes various spatial audio systems in a mathematical framework based on the single layer potential. This approach has shown many benefits but the theory, which treats audio rendering as a sound-soft scattering problem, can appear one step removed from the physical reality and also possesses frequencies where the solution is non-unique. In the time-domain Boundary Element Method approaches to address such non-uniqueness amount to statements which test the flow of acoustic energy rather than considering pressure alone. This paper applies that notion to spatial audio rendering by re-examining the Kirchhoff-Helmholtz integral equation as a wave-matching metric, and suggests a physical interpretation of its kernel in terms of common acoustic power flux density between waves. It is shown that the spherical basis functions (spherical harmonics multiplied by spherical Bessel or Hankel functions) are orthogonal over any arbitrary surface with respect to this metric. Finally other applications are discussed, including design of high-order microphone arrays and the coupling of virtual acoustic models to auralization hardware.

The finite difference time domain (FDTD) method is a numerical technique that is straight forward to implement for the simulation of acoustic propagation. For room acoustics applications, the implementation of efficient source excitation and frequency dependent boundary conditions on arbitrary geometry can be seen as two of the most significant problems. This paper deals with the source implementation problem. Among existing source implementation methods, the hard source implementation is the simplest and computationally most efficient. Unfortunately, it generates a large low-frequency modulation in the measured time response. This paper presents a detailed investigation into these side effects. Surprisingly, some of these side effects are found to exist even if a transparent source implementation is used. By combing a time limited approach with a class of more natural source pulse function, this paper develops a source implementation method in FDTD that is as simple and computationally as efficient as a hard source implementation and yet capable of producing results that are virtually the same as a true transparent source. It is believed that the source implementation method developed in this paper will provide an improvement to the practical usability of the FDTD method for room acoustic simulation.

To achieve active noise cancellation over a large area, it is often necessary to get a measure of the physical properties of the noise source to devise a counter measure. This, however, is not practical in many cases. A mathematical approach, the Difference Potential Method, can provide an alternative solution for active shielding over a large area. In this approach, the cancellation of unwanted noise requires only measurements near the boundary surface but not at the source itself, and it does not require any other information. Moreover, the solution based on difference potentials applies to bounded domains in the presence of acoustic sources inside the domain to be shielded. This paper reports on the results of experimental validation. It has been demonstrated that while preserving the wanted sound, the developed approach can cancel out the unwanted noise. The volumetric noise cancellation offered by the proposed methodology along with leaving the wanted sound unchanged is a unique feature compared to other techniques available in the literature. It can be most useful in the context of applications related to civil aviation, in particular, for eliminating the exterior noise inside the passenger compartments of both current and future generation of commercial aircraft.

Several approximate extensions of the semi-empirical De Jong model [ De Jong et al., J. Sound and Vib. 86, 23–46 (1983) ] are considered for the prediction of sound propagation over multiple impedance discontinuities. A limitation in the original formulation of the De Jong model is highlighted and a modified form that overcomes this limitation is derived based on reciprocity. This leads to the development of a model for multiple impedance discontinuities that can be used for the investigation of sound-wave propagation above a mixed, striped soft ground that is created by either porous absorbent strips, embedded grooves, or wells with different depths. The accuracy of the model is validated against the boundary element method. It is then used to evaluate the importance of the imaginary part of the admittance of the ground strips on sound attenuation along welled surface. It is shown that the attenuation performance of a surface with multiple impedance discontinuities is high when the imaginary part of the average admittance is large and negative (with an −iωt convention), but the magnitudes of the attenuation peaks are also substantially affected by diffraction from the impedance discontinuities.\ud \ud © 2006 Acoustical Society of America

This paper discusses the application of a method based on human subjective preference to the acoustic design of a Javanese gamelan performance hall. Some important distinctions between Javanese gamelan ensembles and Western classical orchestra are the tuning system, orchestral blending process, and technique of playing. The results of subjective preference test using the rank order method showed that the subjects preferred 24·25 ms for the initial time delay gap (ITDG) and the smallest value of the inter-aural cross-correlation (IACC). The preferred ITDG agree with the ITDG from the room response measured in a traditional pendopo in Indonesia, which is not a common concert hall but an open-sided hall. However, the preferred IACC is not in agreement with the measured ITDG in the pendopo.

Auralization of a space requires measured or simulated data covering the full audible frequency spectrum. For numerical simulation, this is extremely challenging, since that bandwidth covers many octaves in which the wavelength changes from being large with respect to features of the space to being comparatively much smaller. Hence, the most efficient way of describing acoustic propagation changes from wave descriptions at low frequencies to geometric ray and sound-beam energy descriptions at high frequencies. These differences are reflected in the disparate classes of algorithms that are applied. Geometric propagation assumptions yield efficient algorithms, but the maximum accuracy they can achieve is limited at low frequencies in particular. Methods that directly model wave effects are more accurate but have a computational cost that scales with problem size and frequency, thereby limiting them to small or low frequency scenarios. Hence, it is often necessary to operate two algorithms in parallel to handle the complete bandwidth. Here, we utilize Boundary Element Method as the low frequency method in such a scheme. Using the SEACEN Round Robin scenarios as case studies, this paper will discuss challenges including: representing source directivity; choosing suitable boundary condition data; encoding BEM results for binaural presentation.

This paper extends a potential-based approach to active noise shielding with preservation of wanted sound in three-dimensional settings. The approach, which was described in a previous publication [Lim et al., J. Acoust. Soc. Am. 129(2), 717-725 (2011)], provides several significant advantages over conventional noise control methods. Most significantly, the methodology does not require any information including the characterization of sources, impedance boundary conditions and surrounding medium, and that the methodology automatically differentiates between the wanted and unwanted sound components. The previous publication proved the concept in one-dimensional conditions. In this paper, the approach for more realistic conditions is studied by numerical simulation and experimental validation in three-dimensional cases. The results provide a guideline to the implementation of the active shielding method with practical three-dimensional conditions. Through numerical simulation it is demonstrated that while leaving the wanted sound unchanged, the developed approach offers selective volumetric noise cancellation within a targeted domain. In addition, the method is implemented in a three-dimensional experiment with a white noise source in a semi-anechoic chamber. The experimental study identifies practical difficulties and limitations in the use of the approach for real applications.

It is possible to obtain good absorption from Schroeder diffusers if suitable alterations to the design are made. Interestingly, previous work has shown that good absorption appears possible below the design frequency when the diffusers are poorly constructed. This has inspired the design of a profiled absorber using perforated plates in some wells; the absorber has extended bass response. The paper presents a theory for the enhanced absorption and the important design parameters are discussed. Good agreement is shown between the prediction model and impedance tube measurements. The design of this absorber was first carried out using a numerical optimization, although a simplified design procedure is also outlined which is almost as good. The results clearly show that this type of profiled absorber extends the absorption at low frequencies while maintaining the good absorption at mid frequencies as well.

A surface diffusion coefficient is needed in room acoustics to enable the quality of diffusing surfaces to be evaluated. It may also facilitate more accurate geometric room acoustic models. This paper concentrates on diffusion coefficients derived from free-field polar responses. An extensive set of two- and three-dimensional measurements and predictions was used to test the worth of different diffusion coefficient definitions. The merits and problems associated with these types of coefficients are discussed, and past parameters reviewed. Two new coefficients are described. The new measure based on the autocorrelation function is forwarded as the best free-field coefficient. The strengths and weaknesses of the coefficient are defined. © 2000 Acoustical Society of America.

Computer modelling of acoustics in enclosures has developed into various forms, none of which have yet demonstrated 100% accuracy. This paper, therefore, details a study of room acoustic computer modelling that highlights weaknesses with existing modelling techniques. The study illustrates that for accurate prediction of many room acoustic parameters the modelling of surface reflections needs to be refined. Accounting for scattering in the modelling of all reflection orders would improve accuracy in the time domain and assist in the prediction of parameters such as reverberation time, early decay time and clarity index. Allowing the directivity of scattered energy to be modelled would improve spatial accuracy and prediction of lateral energy fraction. Definition of scattering parameters in the frequency domain would also improve predictive accuracy, especially at low frequencies, where geometrical modelling is particularly inappropriate. Improvements in accuracy may also be achieved by including the modelling of barrier edge-diffraction, especially for seating areas behind balcony fronts.

The scattering of sound by reflecting surfaces is an important feature in room acoustics. The boundary element method has been shown in the past to be an accurate method to calculate the scattering pattern of complex surfaces. However, this numerical method is expensive to use on large surfaces where a large number of elements is required. This paper proposes a method of reducing the number of boundary elements required to model large, but periodic, structures. The method is based on a consideration of the relationship between the field variables at two points exactly one period apart. The problem is reduced to the modeling of just one period of the structure. In cases of plane-wave incidence, the prediction using this method agrees very well with the prediction obtained by modeling the complete structure. With the point source in the near field of the surface, the incidence field is no longer periodic and the assumption of a constant periodic factor does not hold. In this case, it is shown that the method can still be used with a simple modification to the periodic formulation, and produces good agreements with the full structure predictions and with measurements.

This paper looks at the common errors that may occur when applying existing standard methods of outdoor noise calculation to realistic environments. The two methods investigated are those described in the CONCAWE report 4/81 and the international standard ISO 9613 Part 2. These standard methods are based mainly on empirical developments and are therefore limited by the environmental conditions upon which the methods were derived. Based on comparisons obtained in real outdoor measurements, this paper shows that significant errors occur when the methods are applied to situations where the ground cover changes from the assumed types, when a finite length barrier is used on soft ground, or when the meteorological condition is significant. The error tends to increase with greater interactions between the ground, barrier and meteorological conditions. The result of this paper should provide a better understanding of the limitations of these standard methods and should therefore help to reduce the chance of these methods being used in inapplicable surroundings.

The dependence of the calculation parameters that control the diffusion calculation in a room acoustics prediction computer model on auditorium sizes and shapes was investigated through a series of physical scale model experiments. Seven auditorium type scale models were used in total. The models had typical auditorium aspect ratios of around 2.5:1.8:1 and important auditorium features such as stage, balcony and raked seating. Their sizes varied from 5050 to 29 500 m3 and shapes included rectangular, fan, reversed fan, and hexagonal. The computer prediction model used a combination of randomized ray directions and secondary diffuse area source radiation to calculate diffuse reflections in its prediction of a room’s acoustic characteristics. The calculation process is controlled by two diffusion parameters: the diffuse‐reflection coefficient of surfaces and a transition order which control the on‐set of the diffusion calculation process. It was found that a diffuse‐reflection coefficient of 0.1 was appropriate for the plain walls of the scale models in the 500‐ and 1‐kHz octave bands, and this value did not change significantly with the scale models’ shapes and sizes. In the lower frequency bands the diffuse‐reflection coefficient changed from 0.1 in the smaller scale models to over 0.4 in the larger models. A slight increase was also observed in models with more complicated shapes. For the transition order a low value (0) was found to be appropriate for the low frequency bands but a higher value (1 to 3) was required in the 500‐ and 1‐kHz bands and also in situation where the specular/geometrical influence of a room was important. The average and root‐mean‐square prediction errors of the computer model using a generic set of diffusion parameters for the scale models were found to be, respectively, within 3% and 10% for RT, and 1.1 and 2 dB for sound level. For the clarity index C80, the prediction errors in the smallest model were within 1.9 and 2.2 dB, which were significantly higher than the 0.8 and 1.8 dB found in the other models.

This paper follows from an earlier experiment investigation1 on the sound reduction of single skin, trapezoidal profiled cladding systems, paying particular attention to the pronounced “dips” in the SRI at mid frequencies. Theoretical predictions were made to confirm the previous experimental findings. Finite element analysis was used to examine the vibration modes of the profiled cladding. The boundary element method was used to investigate the radiation efficiency of the vibration modes and their excitation by acoustic plane waves. Good agreement with measured vibration data was found. An analytical method for predicting the sound reduction index of single skin profiled cladding systems is proposed and is shown to compare well with measurements on all 15 cladding systems used in the experiment work. An empirical prediction model is also compared.

The sound reduction of single-skin trapezoidal profiled metal cladding systems often displays pronounced “dips” in mid frequency range. Because of their magnitude and frequency range, these “dips” can be a critical limiting factor in a cladding system's performance towards insulating noise from industrial premises. This paper investigates in detail the sound reduction of these cladding systems. A series of sound reduction measurements employing a systematic and comprehensive change of profile geometry involving 15 cladding systems was conducted to examine the effect of the profile geometry on the sound reduction “dips”. It is suggested that the “dips” are caused by resonant vibration modes that are local to the geometry of a profile corrugation. Vibration measurements on cladding sheets excited by a diffuse field in a transmission suite and on free hanging cladding sheets excited by a normal incidence plane wave in an anechoic chamber were conducted to test and confirm the explanation.

The scattering from quadratic residue diffusers has been predicted using methods based on the Helmholtz–Kirchhoff integral equation. The methods consisted of two boundary integral methods, and two more approximate solutions utilizing Kirchhoff’s boundary conditions. The predictions were compared to measurements made in both the near and far fields. An accurate boundary integral method which works below and above the well cutoff frequency has been found. The limitations of the more approximate methods have been defined. The approximations behind the quadratic residue diffuser’s design have been tested. The important assumption of a phase change local reacting admittance over each well face was found to be good over a wide range of frequencies. The frequency limit of this approximation has also been defined.

New measurements have been made on the low-frequency attenuation of an impulse excitation over-seating in an unoccupied concert hall and on scale model seats. Two new attributes of the phenomenon were found the attenuation varied over time and the width of the seating area was also important. Because of this, the underlying mechanism of the attenuation may be best understood in the time domain. A scheme for reducing the attenuation with floor-mounted resonant absorbers was evaluated practically, and it was found that this might be incorporated into a hall ventilation system. Large effects attributed to the attenuation were found in graphs of clarity, centre time and strength versus frequency in the concert hall.

This paper describes a simple model for the calculation of finite length barrier insertion loss. The model is based on the concept of minimum diffracted paths. It makes use of Maekawa's empirical curve to estimate the attenuation associated with each diffracted path. However, instead of summing the energy contributions of the diffracted waves as suggested by Maekawa (Applied Acoustics, 1 (1968) 157-73), a new formulation of the phase relationships between the waves is developed to allow pressure summation. The result is a model which is simple to use and yet has accuracy substantially better than Maekawa's energy summation method, in predicting both narrow and octave band insertion loss of finite length barriers. Extensive model experiments are used to verify the model. It is believed that the model is both simple and accurate enough to replace Maekawa's energy summation method in engineering practice.

This paper describes an active sound control methodology based on difference potentials. The main feature of this methodology is its ability to automatically preserve “wanted” sound within a domain while canceling “unwanted” noise from outside the domain. This method of preservation of the wanted sounds by active shielding control is demonstrated with various broadband and realistic sound sources such as human voice and music in multiple domains in a one-dimensional enclosure. Unlike many other conventional active control methods, the proposed approach does not require the explicit characterization of the wanted sound to be preserved. The controls are designed based on the measurements of the total field on the boundaries of the shielded domain only, which is allowed to be multiply connected. The method is tested in a variety of experimental cases. The typical attenuation of the unwanted noise is found to be about 20 dB over a large area of the shielded domain and the original wanted sound field is preserved with errors of around 1 dB and below through a broad frequency range up to 1 kHz.\ud \ud © 2011 Acoustical Society of America

A simple model of diffraction is developed that can predict accurately the insertion loss of finite length barriers. The model is based on the geometric theory of minimum diffracted paths. Assumptions are made on the phase and amplitude of each diffracted wave to obtain a new and rather simple formulation of the solution. It provides a clear picture of the sound attenuation performance of a barrier as a function of barrier length. Extensive model experiments are used to verify the model. The model’s accuracy in predicting the overall pattern of the narrow‐band insertion loss is found to be comparable to that of an integral equation method, although the latter method produces better prediction in the fine details of the sound field. The model is much simpler than and as accurate as other methods that apply the usual geometric solutions to each diffracted path, and represents a major improvement on Maekawa’s energy summation method for octave band finite barrier calculations.

The result of the prediction of the ringing noise of a 1/3 scale model of a drop hammer in a rectangular room is presented. The noise prediction uses a numerical technique developed in an earlier work [Y. W. Lam and D. C. Hodgson, J. Acoust. Soc. Am. 88, 1993–2000 (1990)]. The technique is based on the Helmholtz integral equation with a modified Green’s function to account for the effect of the enclosure. The vibration data required by the noise prediction technique was obtained by finite element predictions and impact response experiments. It was found that the noise prediction shows good agreement with measurements in general, but at certain frequencies noise other than the ringing noise was found to contribute significantly towards the measured noise levels.

The accuracies and computational times of theoretical methods used to predict the scattering from rigid plane and curved reflectors have been evaluated. These methods were based on different solutions of the Helmholtz-Kirchhoff integral equation. The prediction results were compared to measurements. It was found that a boundary integral method provided accurate predictions for both panel types. For the more approximate prediction methods their limitations were defined in terms of the accuracy achieved and the range over which the methods were applicable. These methods were also used to investigate the use of a cut-off frequency to describe the limit above which specular type reflections dominate the scattering. It was found to be applicable only close to the geometric scattering angle.

Using simple numerical techniques, this paper shows that the fluid-structural coupled response of piston type transducers in underwater arrays can be easily determined. Transfer matrix methods are used to establish the equations that describe the structural behaviour of the transducer. Acoustic mutual impedances between transducers are calculated using the Helmholtz integral equations. A matrix equation is then formed coupling the mutual impedance with the structural response of the transducers. The solution of the equation gives the coupled response of the transducers. The technique can be applied to receiver as well as to transmitter arrays and the effect of steering and shading can also be included. The theory is developed for arrays with finite arbitrary baffles with locally reacting surfaces. A more convenient solution of the limiting case of planar arrays in infinite rigid baffles is discussed in detail and is used to simulate the performances of several arrays which are compared to the ideal uncoupled performances. The prediction of the sensitivity of an array is compared with the measurements.

The flextensional transducer is one of the more efficient, low frequency underwater projectors. High power output is achieved by the large volume displacement produced by the flexural resonance of the elliptical shell. Taking advantage of their normal operational behaviour, this paper presents a simplified analytical model of flextensional transducers. The model is based on the assumptions of elliptical beam bending and cylindrical shell radiation similar to the mathematical model presented by G.A. Brigham in 1974. The method of solution is revised according to the special features of the transducer to give a substantially simpler numerical solution which is suitable for implementation on desktop computers. Numerical results of the model were compared with the numerical and experimental results reported by Brigham and the author's own finite element modelling results.

In outdoor sound propagation, an inherent problem of the ray tracing method is its inability to determine the sound pressure level in the shadow zone, where geometrical rays do not penetrate. This is a serious problem in a turbulent atmosphere where significant sound energy will be scattered into the shadow. Empirical corrections that are determined from measurements or numerical simulations are limited to situations within the bounds of the empirical corrections. This paper describes a different approach where the ray tracing model is modified analytically into a scattered ray model. Rays are first diffracted from the shadow boundary, which is determined by the geometrical ray paths. The diffracted rays are then scattered by turbulence in their way to the receiver. The amount of scatter is determined from turbulence statistics that are determined from a Gaussian turbulence model. Most of the statistics are determined analytically except one element, which is determined empirically from numerical simulations. This turbulence scattered ray model is shown to have good accuracy against calculations based on the parabolic equation, and against previously published measurement data. It was found that the agreement is good both with and without turbulence, at distance up to 2 km from the shadow boundary.\ud \ud © 2009 Acoustical Society of America

A numerical technique is presented for the prediction of the sound field due to an arbitrary vibrating body in a rectangular enclosure. The method, based on the Helmholtz integral equation, is claimed to have the potential for designing a realistic machine structure in enclosed surroundings. It is assumed that the vibration of the machine surface is known either from experiment or from a finite‐element calculation. The accuracy of the technique is verified by using it to predict the sound field from a vibrating sphere in a rectangular enclosure for which the analytical solution is known. The potential of its application to realistic problems is shown by comparing its predictions of the radiation from a vibrating box in a commonly encountered rectangular room with experimental results.

The paper describes an investigation about the acoustic performance of noise barriers with quadratic residue diffuser (QRD) tops, and with T-, Arrow-, Cylindrical and Y-shape profiles. A 2D boundary element method (BEM) is used to calculate the barrier insertion loss. The results of rigid and with absorptive coverage are also calculated for comparisons. Using QRD on the top surface of almost all barrier models presented here is found to improve the efficiency of barriers compare with using absorptive coverage at the examined receiver positions. T-shape and Arrow-shape barriers are also found to provide better performance than other shapes of barriers. The best shape of barriers for utilising QRD among the tested models is the T-shape profile barrier. It is found that reducing the design frequency of QRD shifts the performance improvement towards lower frequency, and therefore the most efficient model for traffic noise is a barrier covered with a QRD tuned to around 400 Hz.\ud \ud © Elsevier Ltd. All rights reserved.

The basic principle of common room acoustics computer models is the energy-based geometrical room acoustics theory. The energy-based calculation relies on the averaging effect provided when there are many reflections from many different directions, which is well suited for large concert halls at medium and high frequencies. In recent years computer modelling has become an established tool in architectural acoustics design thanks to the advance in computing power and improved understanding of the modelling accuracy. However concert hall is only one of many types of built environments that require good acoustic design. Increasingly computer models are being sought for non-concert hall applications, such as in small rooms at low frequencies, flat rooms in workplace surroundings, and long enclosures such as underground stations. In these built environments the design issues are substantially difference from that of concert halls and in most cases the common room acoustics models will needed to be modified or totally re-formulated in order to deal with these new issues. This paper looks at some examples of these issues. In workplace environments we look at the issues of directional propagation and volume scattering by furniture and equipment instead of the surface scattering that is common assumed in concert hall models. In small rooms we look at the requirement of using wave models, such as boundary element models, or introducing phase information into geometrical room acoustics models to determine wave behaviours. Of particular interest is the ability of the wave models to provide phase information that is important not only for room modes but for the construction of impulse response for auralisation. Some simulated results using different modelling techniques will be presented to illustrate the problems and potential solutions.

Atmospheric turbulence is an important factor that limits the amount of attenuation a barrier can provide in the outdoor environment. It is therefore important to develop a reliable method to predict its effect on barrier performance. The boundary element method (BEM) has been shown to be a very effective technique for predicting barrier insertion loss in the absence of turbulence. This paper develops a simple and efficient modification of the BEM formulation to predict the insertion loss of a barrier in the presence of atmospheric turbulence. The modification is based on two alternative methods: (1) random realisations of log-amplitude and phase fluctuations of boundary sources and (2) de-correlation of source coherence using the mutual coherence function (MCF). An investigation into the behaviours of these two methods is carried out and simplified forms of the methods developed. Some systematic differences between the predictions from the methods are found. When incorporated into the BEM formulation, the method of random realisations and the method of MCF de-correlation provide predictions that agree well with predictions by the parabolic equation method and by the scattering cross-section method on a variety of thin barrier configurations.\ud \ud © Elsevier Ltd. All rights reserved.

The relationship between the measured acoustic absorption coefficient of an array of theater chairs and the ratio of the perimeter length to plan area of the array is considered. It is shown that the linear relationship measured by Bradley in a reverberation chamber and reported in ‘‘Predicting theater chair absorption from reverberation chamber measurements’’ [J. Acoust. Soc. Am. 91, 1514–1524 (1992)] is to be expected from simple theory. This means that any nonlinear influence of diffracted energy on the relationship is small. Bradley is also unduly harsh on the usefulness of a chair absorption measurement method involving screens. A sample result is given, showing that this method can predict in‐situ theater chair absorption with reasonable accuracy.

The quadratic residue diffuser was originally designed for enhanced scattering. Subsequently, however, it has been found that these diffusers can also be designed to produce exceptional absorption. This paper looks into the absorption mechanism of the one-dimensional quadratic residue diffuser. A theory for enhanced absorption is presented. Corresponding experiments have also been done to verify the theory. The usefulness of a resistive layer at the well openings has been verified. A numerical optimization was performed to obtain a better depth sequence. The results clearly show that by arranging the depths of the wells properly in one period, the absorption is considerably better than that of a quadratic residue diffuser. © 2000 Acoustical Society of America.

The most popular models to predict sound propagation in architectural spaces involve the tracing of rays, images, or beams. Most current beam-tracing methods use conical or triangular beams that may produce overlaps and holes in the predicted sound field. Hence a new method has been developed whereby the shape of reflected beams is governed by the shape of reflecting surfaces so as to produce a geometrically perfect description of the sound propagation for halls with occluding surfaces. The method also facilitates the calculation of diffuse sound propagation by managing the energy transfer from a specular model to a diffuse model. This adaptive beam-tracing method compares well with other methods in terms of speed and accuracy.

Prediction models are at the heart of modern acoustic engineering. Current commercial room acoustic simulation software almost exclusively approximates the propagation of sound geometrically as rays or beams. These assumptions yield efficient algorithms, but the maximum accuracy they can achieve is limited by how well the geometric assumption represents sound propagation in a given space. This comprises their accuracy at low frequencies in particular. Methods that directly model wave effects are more accurate but they have a computational cost that scales with problem size and frequency, effectively limiting them to small or low frequency scenarios. This paper will report the results of initial research into a new full-bandwidth model which aims to be accurate and efficient for all frequencies; the name proposed for this is the "Wave Matching Method". This builds on the Boundary Element Method with the premise that if an appropriate interpolation scheme is designed then the model will become 'geometrically dominated' at high frequencies. Other propagation modes may then be removed without significant error, yielding an algorithm which is accurate and efficient. This paper will present the general concepts of wave matching and the results from some numerical test cases.

Active noise shielding based on the Difference Potential Method has been developed and validated in previous publications. The key ability of the method, to provide global noise cancellation while automatically preserving wanted sound in multi-connected domains, has been demonstrated clearly in 1D experiments. In this paper, the tests are extended to 3D. The shielded domain is a 1mx1mx1m box with 1-3 sides open. Up to 4 control sources were used on each of the open sides to shield the domain from external noise. Noise attenuation of around 10dB was achieved up to about 350 Hz. The attenuation is lower than the >20dB attenuation achieved in previous 1D experiments. A reason for this is the sensitivity of the cancellation to the positioning of sensors and controls and the physical size of the control sources. Furthermore, up till now the method relies on separate measurements of the total sound field without the control sources. In realistic applications where noise and wanted sound are non-stationary, the ...

There is a need for a more accurate laboratory measurement method to predict auditorium seat absorption. The traditional method tends to overpredict the absorption of the exposed front and sides of seating blocks. An alternative reverberation chamber method was studied that involves the use of barriers to obtain realistic measurements of front and side absorption. This method was validated by comparing measurements of seats made in a reverberation chamber with in situ absorption data for the same seats, calculated from reverberation time measurements in ten auditoria with and without the seats present. The accuracy of the alternative method was satisfactory in all cases, although a severe lack of diffusion in two of the halls hindered the validation process. It was found that using a frequency‐constant edge correction strip to account for side and front absorption could lead to significant errors in auditorium absorption prediction.

Several human subjects were involved in a subjective test using the paired comparison method to determine the preferred initial time delay gap (ITDG) for listening to Javanese gamelan music (gendhing) in a concert hall. To provide comparisons, acoustic measurements in several pendopos in Indonesia have also been carried out. Pendopo is an open‐sided hall, where the Javanese gamelan is usually played. The measurements were conducted using the room impulse response method, with a maximum length sequences (MLS) signal as its sound source. The ITDG of four pendopos are presented in this paper. The results of subjective preference testing showed that there are preferences for short ITDG, although evidence for a single value of preference was not conclusive. These results agree with the ITDG from the room responses measured in the pendopos, which are not common concert halls but open‐sided halls.

A new adaptive beam‐tracing algorithm was developed and implemented into a computer model to predict the propagation of sound in enclosed spaces. Unlike previous beam‐tracing methods, the model predicts a near perfect geometrical representation of a propagating sound field by adaptively tailoring it to the shape of the reflecting surfaces. Using this adaptive approach, problems such as gaps and overlaps between beams, and the ambiguity of reflection direction when a beam hits more than one surface can be eliminated. In addition, the beam tracing can start with only a small number of beams. Child beams are generated automatically upon each reflection to adapt to the complexity of the room. This method runs faster than traditional beam and ray‐tracing methods in the early part and faster than the image method in the later part of the reverberation process. Diffuse reflections are handled by a radiant exchange process and combined with the specular reflections to calculate the impulse response of a room. Thi...

As the centennial of Sabine’s research, which founded modern architectural acoustics, is celebrated, the need for an experimental measurement standard to characterize scattering surfaces is becoming acute. These data are needed to characterize and rank potential diffusing surfaces and to improve the accuracy of geometrical room modeling programs. Two approaches are currently being studied. One measures the 2‐D or 3‐D directional distribution of scattered sound for a given angle of incidence and frequency. This is used to determine the diffusion parameter, which characterizes the uniformity of the angular response. The other determines the ratio of nonspecular scattered energy to total scattered energy, for directional or randomly incident sound. This yields the scattering coefficient, which contains no diffusivity information, but can be used in geometrical modeling programs. A goal of this research is to determine both diffusivity and scattered energy ratios from a single method, which is also theoretica...

Lightweight profiled metal cladding systems generally have poor acoustic insulation characteristics, and traditional theories for evaluating noise transmission through building elements are usually not applicable to double‐skin profiled systems because of their orthotropic nature. Based on extensive experimental observations, a new method for predicting the sound reduction index (SRI) of commercial double‐skin cladding systems is proposed. The method combines existing theory for orthotropic flat plates with finite element analysis to account for the pronounced ‘‘dips‘‘ in the SRI at midfrequencies, which are caused by the resonances of the profile geometry. The predicted SRI was shown to compare well with measurements on 15 cladding systems used in the experimental work. The method was further extended to cover commercial double‐skin cladding constructions. Analytical equations were formulated to account for the orthotropic nature of the cladding sheets, the sound bridging through fixing supports, and the sound reduction through the in‐fill insulation. Comparisons of predictions against sound reduction measurements were made on a wide range of commercial cladding products. Good agreement between predictions and measurements was found.

Potential flow equations for the combined rectilinear flow and a source are used to model the discharge of a jet into a porous media such as the condition in a fixed bed before spouting occurs. The equations derived are compared with data obtained using a measurement technique developed for determining the superficial velocity profile in a packed bed. This technique does not disturb the packing nor the actual flow field at the point where the data is required. The analytical results are also compared with the results of jet flow studies in the literature. In addition, by assuming ideal situations, an equation was derived for minimum spouting which closely resembles equations for predicting minimum spouting that are available in the literature. On emploie les equations du potential d'ecoulement, pour un ecoulement rectiligne combine a une source pour modeliser la decharge d'un jet dans un milieu poreux tel que celui qu'on rencontre dans un lit fixe avant le debut du “spouting”. On compare les equations obtenues avec le resultat etabli en employant une methode de mesure mise au point pour la determination du profil de vitesse superficielle dans un lit garni. Cette methode n'affecte pas le garnissage ni le veritable champ d'ecoulement au point o-l'on prend les donnees. On compare les resultats analytiques avec ceux d'etudes d'ecoulements de jets donnes dans la litterature. En outre, en supposant des situations ideales, on etablit une equation pour le seuil de “spouting” qui ressemble beaucoup aux equations disponibles dans la litterature pour predire les seuils de “spouting”.