NUMERICAL MODELLING OF THE SOUND FIELDS IN URBAN STREETS WITH DIFFUSELY REFLECTING BOUNDARIES

A radiosity-based theoretical/computer model has been developed to study the fundamental characteristics of the sound fields in urban streets resulting from diffusely reflecting boundaries, and to investigate the effectiveness of architectural changes and urban design options on noise reduction. Comparison between the theoretical prediction and the measurement in a scale model of an urban street shows very good agreement. Computations using the model in hypothetical rectangular streets demonstrate that though the boundaries are diffusely reflective, the sound attenuation along the length is significant, typically at 20-30 dB/100 m. The sound distribution in a cross-section is generally even unless the cross-section is very close to the source. In terms of the effectiveness of architectural changes and urban design options, it has been shown that over 2-4 dB extra attenuation can be obtained either by increasing boundary absorption evenly or by adding absorbent patches on the façades or the ground. Reducing building height has a similar effect. A gap between buildings can provide about 2-3 dB extra sound attenuation, especially in the vicinity of the gap. The effectiveness of air absorption on increasing sound attenuation along the length could be 3-9 dB at high frequencies. If a treatment is effective with a single source, it is also effective with multiple sources. In addition, it has been demonstrated that if the façades in a street are diffusely reflective, the sound field of the street does not change significantly whether the ground is diffusely or geometrically reflective.     

Numerical modeling of the sound fields in urban squares

This paper studies the basic characteristics of sound fields in urban squares surrounded by reflecting building fa?ades and the effectiveness of architectural changes and urban design options. A radiosity model and an image source model are developed, and a parametric study is carried out in hypothetical squares. The results show that the reverberation time (RT) is rather even in a square, whereas the early decay time (EDT) is very low in the near field, and then becomes close to RT after a rapid increase. Compared to diffuse boundaries, with geometrical boundaries the RT and EDT are significantly longer and the sound pressure level (SPL) attenuation with distance is generally smaller unless the height/side ratio is high. With a boundary diffusion coefficient of 0.2, the sound field is already close to that resulting from purely diffusely reflecting boundaries. The SPL in far field is typically 6-9 dB lower if the square side is doubled; 8 dB lower if the height of building fa?ades is decreased from 50 m to 6 m (diffuse boundaries); 5 dB (diffuse boundaries) or 2 dB (geometrical boundaries) lower if the length/width ratio is increased from 1 to 4; and 10-12 dB lower if the boundary absorption coefficient is increased from 0.1 to 0.9.     

The absorption of rayleigh's sound waves in metals in a parallel magnetic field

The electron absorption coefficient has been calculated for the Rayleigh waves in a metal, with the magnetic field parallel to the boundary. Reflection of electrons from the metal surface is assumed to diffuse. For high magnetic fields the shape and width of the absorption lines have been investigated as well as maximum values of the attenuation. For low fields oscillations of the geometric and cyclotron resonance type are predicted.     

Prediction of the absorption exponent in rectangular enclosures with a single absorbent boundary

It is known that the classical theory of room acoustics cannot be strictly applied to the study of the sound field in a rectangular enclosure with only five boundaries (i.e., with a single absorbent boundary), as the sound field in the enclosure is not diffuse. A theoretical method is developed for the prediction of the absorption exponent in a rectangular enclosure with a single absorbent boundary, and the absorption exponent is used to describe the exponential decay of the sound energy. The method is based on the radiosity-based theoretical/computer model and is used for diffusely reflecting boundaries. The predicted absorption exponent is compared with the Kuttruff values and the simulation results from Monte-Carlo computations. It is found that the predicted absorption exponent of the proposed method shows better agreement with the simulation results from Monte-Carlo computations than the Kuttruff values. With the more accurately predicted absorption exponent, the slope of the energy decay curve and other acoustic parameters in an enclosure with a single absorbent boundary can be obtained accurately.     

Diffraction of sound by a rigid screen with an absorbent edge

A solution is obtained for the problem of diffraction of a plane wave sound source by a semi-infinite plane. A finite region in the vicinity of the edge has an impedance boundary condition; the remaining part of the half plane is rigid. The problem which is solved is a mathematical model for a rigid barrier with an absorbing edge. It is found that the absorbing material that comprises the edge need only be of the order of a wavelength long to have approximately the same effect on the sound attenuation in the shadow region of the barrier as a semi-infinite absorbent barrier. Also the softer the absorbent lining the greater the attenuation in the shadow of the barrier. In the illuminated region a reduction in the sound intensity level can be achieved by a suitable choice of the absorptive material of the strip and its length. It is found that the effect of the absorptive strip is lost if its length is less than two wavelengths long. For a strip length of six wavelengths or more the system is equivalent to an absorbing half plane.     

Investigation of the validity of radiosity for sound-field prediction in cubic rooms

This paper explores acoustical (or time-dependent) radiosity using predictions made in four cubic enclosures. The methods and algorithms used are those presented in a previous paper by the same authors [Nosal, Hodgson, and Ashdown, J. Acoust. Soc. Am. 116(2), 970-980 (2004)]. First, the algorithm, methods, and conditions for convergence are investigated by comparison of numerous predictions for the four cubic enclosures. Here, variables and parameters used in the predictions are varied to explore the effect of absorption distribution, the necessary conditions for convergence of the numerical solution to the analytical solution, form-factor prediction methods, and the computational requirements. The predictions are also used to investigate the effect of absorption distribution on sound fields in cubic enclosures with diffusely reflecting boundaries. Acoustical radiosity is then compared to predictions made in the four enclosures by a ray-tracing model that can account for diffuse reflection. Comparisons are made of echograms, room-acoustical parameters, and discretized echograms.     

Application of audience-seats characteristics to the sound field analysis for large enclosures

The analysis of the sound field of a hall including the effect of audience seats has difficulties in computing time and memory. Although extensive investigations have been conducted for analyzing sound fields, there is scarcely any report dealing with the sound field including this effect. The main cause may be the complex shape and amount of materials of the audience seats. However, there is a possibility that periodical grooved structures like seat rows can be replaced by an appropriate imaginary boundary with an impedance of quasi-local reaction at the top of seats. The purpose of this research is to reduce the calculation load of acoustical analysis by treating the seat rows as an imaginary-impedance boundary which is almost equivalent to the characteristics of audience seats. The SDE filter, which can express excess attenuation caused by seat rows, is proposed and some applications to both the geometrical and wave theoretical methods are presented. To examine the validity of this method, some numerical examples calculated using an image method are discussed in comparison with the measured data. Furthermore, the numerical results of its application to the boundary element method are presented and discussed in terms of its effectiveness and validity.     

Time-domain impedance formulation for transmission line matrix modelling of outdoor sound propagation

Outdoor sound propagation modelling has attracted considerable attention in the past and has lead to many analytical and numerical models. More recently, the increase of computational power has led to consider time-domain methods that enable to consider transient phenomena. Among these models, the transmission line matrix (TLM) method has been proposed, but the sound absorption at boundaries appears to be a somewhat underdeveloped aspect of this approach. In this paper, a specific implementation of impedance boundary condition is proposed. The method is based on the approximation of the impedance as a sum of linear systems, which allows the formulation of an equivalent impedance model in the time-domain. The proposed implementation is applied for two common impedance models of porous material. Numerical simulations have been carried out in the case of sound propagation over a flat ground with and without an impedance discontinuity, and for several values of specific airflow resistivity. TLM numerical predictions expressed in terms of excess attenuation relative to free field show a good agreement with analytical solutions.     

Eigenfrequency spacing analysis and eigenmode breakdown for semi-stadium-type 2-D fields

This paper describes eigenfrequency statistics including modal patterns and degrees of freedom for a semi-stadium-type 2-D field. The authors numerically investigated sound fields surrounded by 2-D semi-stadium-type boundaries as examples of boundaries where chaotic properties are hidden, in order to understand the characteristics of complex sound fields and to gain new insight into sound-field design. One limit of the semi-stadium boundaries is a rectangular boundary that gives a regular field, while another limit is a stadium boundary in which the chaotic property emerges. The numerical results show that eigenfrequency spacing in all the cases can be expressed as a family of Γ distributions extended to a non-integer degree of freedom. This fractal degree of freedom can be interpreted as the degree of freedom of the sound field. For the regular limit case, i.e., a rectangular case, the distribution is the exponential distribution with the freedom of unity, while in the chaotic case, i.e., the stadium case, it is the Wigner distribution with a degree of freedom of two. The authors, however, analyze the semi-stadium sound fields. The analysis of the fluctuations in the distribution function for the eigenfrequencies showed that the skewness decreases as the boundary approaches the stadium condition. Modal patterns also clearly showed breaks of the regular pattern of nodal lines in a rectangular case as the boundary was deformed from the rectangular to the stadium condition. The breaks of the modal pattern could be also confirmed by decreasing of the skewness for the sound pressure distribution.     

三维浅海下弹性结构声辐射预报的有限元-抛物方程法

利用多物理场耦合有限元法对结构和流体适应性强、抛物方程声场计算高效准确的特点,提出了三维浅海波导下弹性结构声振特性研究的有限元-抛物方程法.该方法采用多物理场耦合有限元理论建立浅海下结构近场声辐射模型,计算局域波导下结构声振信息,并提取深度方向上复声压值作为抛物方程初始值;然后采用隐式差分法求解抛物方程以步进计算结构辐射声场.重点介绍了该方法对浅海下结构声辐射计算的准确性、高效性以及快速收敛性后,对Pekeris波导中有限长弹性圆柱壳的声振特性进行了分析.研究得出,当圆柱壳靠近海面(海底)时,其耦合频率比自由场下的要高(低),当潜深达到一定范围时,与自由场耦合频率基本趋于一致;在低频远场,结构辐射场与同强度点源声场具有一定的等效性,且等效距离随着频率增加而增加;由于辐射声场受结构振动模态、几何尺寸和简正波模式影响,结构辐射场传播的衰减规律按近场声影响区、球面波衰减区、介于球面波和柱面波衰减区、柱面波衰减区四个扩展区依次进行.     

In situ measurements of surface impedance and absorption coefficients of porous materials using two microphones and ambient noise

An in situ measurement method is proposed for obtaining the normal surface impedance and absorption coefficient of porous materials using two microphones located close to the material without a specific sound source such as a loudspeaker. Ambient environmental noise that does not excite distinct modes in the sound field is employed as the sound source. Measurements of the normal surface impedance of glass wool and rockwool have been made using this method in various sound fields. The repeatability and wide applicability of the method are demonstrated by comparing results of measurements in one room with different noise conditions and in three other environments (corridor, cafeteria and terrace). The assumed diffuse nature of the sound field on the material is validated by using absorption characteristics obtained experimentally at oblique incidence. This method allows simple and efficient in situ measurements of absorption characteristics of materials in a diffuse field.     

The influence of absorption factors on the sensitivity of a virtual room’s sound field to scattering coefficients

Currently there is limited information on what scattering coefficients (SCs) to assign materials in geometrical room acoustic computer models. As a result, room modelers rely on general guidelines and intuition when assigning SCs. How sensitive is the predicted sound field to the user’s choice of scattering coefficients? The sound field’s sensitivity depends on its diffusivity (without SCs); the more diffuse the room’s sound field is, the less sensitive the virtual room is to the selection of SCs. In rooms with no fittings to diffuse sound energy, the sound field diffusivity is influenced by (1) room shape, (2) volume, (3) amount and (4) location of absorption, and (5) the choice of SCs. This investigation focuses only on the latter three factors. A rectangular room is modeled in ODEON v6.5 with 10 absorption schemes. These schemes vary in terms of the area of mirrored reflective surfaces, average absorption coefficient, and standard deviation of absorption. The amount of diffuse reflections at each room boundary as dictated by the SC is increased uniformly in each room. Changes in the room sound field, in particular in the reverberation time (T30), are examined at each step. Sound field diffusivity, and consequently a virtual room model’s sensitivity to SCs, is found to depend most on the area of mirrored reflective surfaces. Also, a proposed quantity called the Scattering Sensitivity Index appears to predict sound field diffusivity.     

The propagation of sound in narrow street canyons

This paper addresses an important problem of predicting sound propagation in narrow street canyons with width less than 10 m, which are commonly found in a built-up urban district. Major noise sources are, for example, air conditioners installed on building facades and powered mechanical equipment for repair and construction work. Interference effects due to multiple reflections from building facades and ground surfaces are important contributions in these complex environments. Although the studies of sound transmission in urban areas can be traced back to as early as the 1960s, the resulting mathematical and numerical models are still unable to predict sound fields accurately in city streets. This is understandable because sound propagation in city streets involves many intriguing phenomena such as reflections and scattering at the building facades, diffusion effects due to recessions and protrusions of building surfaces, geometric spreading, and atmospheric absorption. This paper describes the development of a numerical model for the prediction of sound fields in city streets. To simplify the problem, a typical city street is represented by two parallel reflecting walls and a flat impedance ground. The numerical model is based on a simple ray theory that takes account of multiple reflections from the building facades. The sound fields due to the point source and its images are summed coherently such that mutual interference effects between contributing rays can be included in the analysis. Indoor experiments are conducted in an anechoic chamber. Experimental data are compared with theoretical predictions to establish the validity and usefulness of this simple model. Outdoor experimental measurements have also been conducted to further validate the model.     

Enhancing micro-perforated panel attenuation by partitioning the adjoining cavity

The sound attenuation performance of micro-perforated panels (MPP) with adjoining air cavity is investigated for a plenum. The sound field inside of a plenum is compared for two cases. In the first case, the plenum is treated with an MPP and adjoining air cavity without any partitioning. For the second case, the adjoining air cavity is partitioned into a number of sub-cavities. The resulting sound pressure fields indicate that partitioning the adjoining air cavity increases the overall sound attenuation due to the MPP by approximately 4 dB. The explanation for this phenomenon was investigated by measuring the sound pressure level on planes in front of the MPP. Additionally, boundary element analyses were conducted to simulate the effect of the MPP and adjoining cavity with and without partitioning on the sound field in the plenum. It was demonstrated that a MPP can be modeled as a transfer impedance and that partitioning the adjoining cavity enhances attenuation to acoustic modes that propagate transverse to the MPP.     

Experimental study of sound propagation in a street

This paper presents an experimental study of the sound propagation in a street, performed during July 2002, in order to measure impulse responses at numerous locations in a street canyon, and, for several positions of the sound source. A specific attention has been paid on the processing of the experimental data, in order to obtain accurate values of the reverberation time and the steady-state sound pressure level, including also the compensation of the atmospheric attenuation. In total, 11 592 useful data have been collected during this experiment, and are available by contacting the corresponding author. Reverberation times and sound levels, in the narrow street, are then analyzed and compared, for the 4 source positions in the street. This experimental study gives interesting results on the behavior of the sound field in the street.     

Sound propagation in a street

The propagation of sound in a street has previously been treated almost exclusively by the use of ray-tracing techniques. As a result, the effects of scattering from objects and protrusions in the street have not been taken adequately into account. In this paper, the sound field is analysed in terms of its propagating modes. The use of this technique allows the effect of scattering to be calculated, assuming a rather simplified model of a scattering surface. Although a number of important assumptions are made, the predicted attenuations at points down a street are in good agreement with results obtained from model studies. These attenuation curves are also similar in form to ihose obtained in full-scale tests.     

Geometrical resonance of the Rayleigh sound wave absorption as a method for direct measurements of the electron specular reflection coefficient from the metal surface

A theory of resonant absorption of the Rayleigh sound waves in metals has been developed for the case of weak magnetic fields (i.e. the Pippard type geometrical oscillations). The amplitude and shape of resonance lines have been studied in relation to the nature of electron reflection from the surface. It has been shown that observations of the geometrical resonance oscillations may serve for investigating directly surface reflectivity of the metal with respect to conduction electrons.     

The effect of turbulence damping on acoustic wave propagation in tubes

The attenuation of sound due to the interaction between a low Mach number turbulent boundary layer and acoustic waves can be significant at low frequencies or in narrow tubes. In a recent publication by the present authors the acoustics of charge air coolers for passenger cars has been identified as an interesting application where turbulence attenuation can be of importance. Favourable low-frequency damping has been observed that could be used for control of the in-duct sound that is created by the engine gas exchange process. Analytical frequency-dependent models for the eddy viscosity that controls the momentum and thermal boundary layers are available but are restricted to thin acoustic boundary layers. For cases with cross-sections of a few millimetres a model based on thin acoustic boundary layers will not be applicable in the frequency range of interest.In the present paper a frequency-dependent axis-symmetric numerical model for interaction between turbulence and acoustic waves is proposed. A finite element scheme is used to formulate the time harmonic linearized convective equations for conservation of mass, momentum and energy into one coupled system of equations. The turbulence is introduced with a linear model for the eddy viscosity that is added to the shear viscosity. The proposed model is validated by comparison with experimental data from the literature.     

Relaxation of sound fields in rooms of diffusely reflecting boundaries and its application in acoustical radiosity simulation

The acoustical radiosity method is a computationally expensive acoustical simulation algorithm that assumes an enclosure with ideal diffuse reflecting boundaries. Miles observed that for such an enclosure, the sound energy decay of every point on the boundaries will gradually converge to exponential manner with a uniform decay rate. Therefore, the ratio of radiosity between every pair of points on the boundaries will converge to a constant, and the radiosity across the boundaries will approach a fixed distribution during the sound decay process, where radiosity is defined as the acoustic power per unit area leaving (or being received by) a point on a boundary. We call this phenomenon the "relaxation" of the sound field. In this paper, we study the relaxation in rooms of different shapes with different boundary absorptions. Criteria based on the relaxation of the sound field are proposed to terminate the costly and unnecessary radiosity computation in the later phase, which can then be replaced by a fast regression step to speed up the acoustical radiosity simulation.     

Analysis of sound attenuation in a duct with a solid or porous splitter

The equivalent singularity method is developed for the analysis of sound propagation in a duct with a thin solid or point-reacting porous splitter of a finite streamwise length. The method consists in representing the splitter by a singular plane of pressure dipoles and mass sources, distributions of which are determined so that the boundary condition at the splitter surfaces is satisfied. The boundary condition is expressed in terms of two admittance parameters giving relations between pressures and normal displacements of fluid particles at the upper and lower surfaces of the splitter. Computed results are presented to illustrate the dependence of the sound power transmitted through the splitter section on the acoustic properties, length and location of the splitter and the flow Mach number. A principal cause of the sound attenuation due to a splitter is found to be the conversion of the acoustic energy into the wake vortex energy convected downstream. A solid splitter or a porous splitter of small admittance shows tuning effects—with a peak or multiple peaks in the attenuation spectrum. The tuning frequencies can be controlled by the splitter location.