Jonathan A. Hargreaves

A transient boundary element method model of Schroeder diffuser scattering using well mouth impedance

Room acoustic diffusers can be used to treat critical listening environments to improve sound quality. One popular class is Schroeder diffusers, which comprise wells of varying depth separated by thin fins. This paper concerns a new approach to enable the modeling of these complex surfaces in the time domain. Mostly, diffuser scattering is predicted using steady-state single frequency methods. A popular approach is to use a frequency domain boundary element method (BEM) model of a box containing the diffuser, where the mouth of each well is replaced by a compliant surface with appropriate surface impedance. The best way of representing compliant surfaces in time domain prediction models, such as the transient BEM is, however, currently unresolved. A representation based on surface impedance yields convolution kernels which involve future sound, so is not compatible with the current generation of time-marching transient BEM solvers. Consequently, this paper proposes the use of a surface reflection kernel for modeling well behavior and this is tested in a time domain BEM implementation. The new algorithm is verified on two surfaces including a Schroeder diffuser model and accurate results are obtained. It is hoped that this representation may be extended to arbitrary compliant locally reacting materials.

Low frequency sound propagation in activated carbon

Activated carbon can adsorb and desorb gas molecules onto and off its surface. Research has examined whether this sorption affects low frequency sound waves, with pressures typical of audible sound, interacting with granular activated carbon. Impedance tube measurements were undertaken examining the resonant frequencies of Helmholtz resonators with different backing materials. It was found that the addition of activated carbon increased the compliance of the backing volume. The effect was observed up to the highest frequency measured (500 Hz), but was most significant at lower frequencies (at higher frequencies another phenomenon can explain the behavior). An apparatus was constructed to measure the effective porosity of the activated carbon as well as the number of moles adsorbed at sound pressures between 104 and 118 dB and low frequencies between 20 and 55 Hz. Whilst the results were consistent with adsorption affecting sound propagation, other phenomena cannot be ruled out. Measurements of sorption isotherms showed that additional energy losses can be caused by water vapor condensing onto and then evaporating from the surface of the material. However, the excess absorption measured for low frequency sound waves is primarily caused by decreases in surface reactance rather than changes in surface resistance.

A transient boundary element method for acoustic scattering from mixed regular and thin rigid bodies

Boundary Element Methods (BEMs) may be used to predict the scattering of sound by obstacles, which has accelerated the prototyping of new room acoustic treatments such as diffusers. Unlike the more popular frequency domain method, the time domain BEM is usually solved in an iterative manner which means it can exhibit instability, a crucial impediment to its widespread use. These instabilities are primarily associated with the resonance of cavities formed by closed surface sections, but may also be caused by discretisation or integration error corrupting physical damped resonances. Regular BEM implementations cannot model objects with thin sections due to a phenomenon known as Thin Shape Breakdown. This paper develops an algorithm which combines an accepted approach for modelling thin plates with the Combined Field Integral Equation which eradicates cavity resonances, thereby permitting models of mixed regular and thin bodies. Accuracy and stability are tested by comparison to verified frequency domain BEMs, examination of the transient response, and pole decomposition. This is done for a simple obstacle and a Schroeder diffuser, which comprises a series of wells separated by thin fins. The approach is successful but universal stability cannot be guaranteed for the diffuser. It is suggested that instability is caused by the lightly damped resonances of the wells being corrupted into divergent behaviour by numerical errors.

An energy interpretation of the Kirchhoff-Helmholtz boundary integral equation and its application to Sound Field synthesis

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.

Simulating acoustic scattering from atmospheric temperature fluctuations using a k-space method

This paper describes a numerical method for simulating far-field scattering from small regions of inhomogeneous temperature fluctuations. Such scattering is of interest since it is the mechanism by which acoustic wind velocity profiling devices (Doppler SODAR) receive backscatter. The method may therefore be used to better understand the scattering mechanisms in operation and may eventually provide a numerical test-bed for developing improved SODAR signals and post-processing algorithms. The method combines an analytical incident sound model with a k-space model of the scattered sound close to the inhomogeneous region and a near-to-far-field transform to obtain far-field scattering patterns. Results from two test case atmospheres are presented: one with periodic temperature fluctuations with height and one with stochastic temperature fluctuations given by the Kolmogorov spectrum. Good agreement is seen with theoretically predicted far-field scattering and the implications for multi-frequency SODAR design are discussed.

Towards a full-bandwidth numerical acoustic model

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 “geometricall...

Acoustical properties of nanoporous activated carbon fibres

This work continues a series of studies on the link between the microstructure of multiscale materials and their acoustical properties [1]-[3]. Granular activated carbons are excellent low frequency sound absorbers. Two factors contribute to this. (i) They have three scales of heterogeneities: millimetric grains and micrometric and nanometric inner-grain pores. (ii) The presence of sorption in nanometric pores leads to a decrease of static bulk modulus and, consequently, of the effective low-frequency sound speed. Activated carbon felts also show promising low-frequency sound absorption but have simpler microstructure. They do not contain inner-fibre micrometric pores, but still have inner-fibre nanometric pores. This, combined with a relatively regular fibre arrangement, makes them ideal for studying the effect of sorption on their acoustical properties. In this work, parameters describing the microstructure and sorption kinetics are measured independently for several types of felts with different levels...

Simulation of acoustic environments for binaural reproduction using a combination of geometrical acoustics and Boundary Element Method

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 han...

A time domain boundary element method for compliant surfaces

The best way of representing compliant surfaces in time domain prediction models, such as the transient Boundary Element Method (BEM), is currently unresolved. This is not true of frequency‐domain, time‐invariant models, where the common practice is to represent the characteristics of a material by its surface impedance. A BEM may be used to predict the scattering of sound, and reduces the problem of modelling a volume of air to one involving surfaces conformal to the obstacles. Surface impedance is a convenient concept for inclusion in the frequency domain BEM as it abstracts the obstacles characteristics into a property of the conformal surface. The time domain BEM predicts transient scattering of sound, and is usually solved in an iterative manner by marching on in time from known initial conditions. For surface impedance data to be utilised it must be Fourier transformed from a frequency dependent multiplication into a temporal convolution. This approach typically yields convolution kernels which inv...

A stable transient boundary element method (BEM) for diffuser scattering

Boundary element methods (BEM) may be used to model scattering from hard rigid surfaces such as diffusers. They have the advantage over volumetric methods that only the surface need be meshed and the surface velocity potential found. Unlike the more widely used single frequency methodology, transient BEM discretizes integral equations to produce an iterative system that is marched on in time from known initial conditions to calculate how the velocity potential varies over time. This iterative process can be unstable, and this is one reason why transient BEM is not more widely used. Previous works on transient BEMs have focused on idealized surfaces, such as spheres and plates. However, little is published on the performance of these methods for more complex surfaces of interest, such as Schroder diffusers. Consequently, this paper presents an implicit scheme suitable for a surface comprising thin and solid sections. Such an implicit scheme has the benefits of not constraining time‐step duration to the sma...