Diffraction of sound from a dipole source near to a barrier or an impedance discontinuity

Pierce's formulation for the diffraction of spherical waves by a hard wedge has been extended to the case of the sound field due to a dipole source. The same approach is also used to extend a semiempirical model for sound propagation above an impedance discontinuity due to a dipole source. The resulting formulas have been validated by comparing their numerical solutions with that computed by summing the sound fields due to two closely spaced monopole sources of equal magnitude but opposite in phase. These new formulations are then used to develop a simple model for calculating the dipole sound field diffracted by a barrier above an impedance ground. Applications of these models relate to transportation noise prediction, particularly railway noise abatement, for which dipole sources are commonly used. The numerical predictions have been found to compare reasonably well with indoor measurements using piezoceramic transducers as dipole sources.     

The use of in-situ test method EN 1793-6 for measuring the airborne sound insulation of noise barriers

The in situ measurement of the airborne sound insulation, as outlined in EN 1793-6:2012, is becoming a common means of quantifying the performance of road traffic noise reducing devices. Newly installed products can be tested to reveal any construction defects and periodic testing can help to identify long term weaknesses in a design. The method permits measurements to be conducted in the presence of background noise from traffic, through the use of impulse response measurement techniques, and is sensitive to sound leakage. Factors influencing the measured airborne sound insulation are discussed, with reference to measurements conducted on a range of traffic noise barriers located around Auckland, New Zealand. These include the influence of sound leakage in the form of hidden defects and visible air gaps, signal-to-noise ratio, and noise barrier height. The measurement results are found to be influenced by the presence of hidden defects and small air gaps, with larger air gaps making the choice of measurement position critical. A signal-to-noise ratio calculation method is proposed, and is used to show how the calculated airborne sound insulation varies with signal-to-noise ratio. It is shown that the measurement results are influenced by barrier height, through the need for reduced length Adrienne temporal windows to remove the diffraction components, prohibiting the direct comparison of results from noise barriers with differing heights.     

A review of commonly used analytical and empirical formulae for predicting sound diffracted by a thin screen

This paper reviews some useful analytical and empirical formulae that are used for the calculation of sound diffracted by a barrier. A brief historic overview of the study of spherical waves diffracted by a rigid half plane is presented also. The physical principles of sound diffraction by a thin plane are explained. The mathematical expressions are cast in a convenient form for ease of numerical implementation. Accurate analytical solutions are expressed in terms of standard mathematical functions that can be computed readily. Among the approximate solutions quoted, quite a few empirical formulations are adequate for most engineering purposes. The information presented in this paper should also be helpful for those who are interested in the study of sound diffracted by a barrier in a room or in a long industrial space.     

Thick barrier noise-reduction in the presence of atmospheric turbulence: measurements and numerical modelling

Atmospheric turbulence causes scattering of sound, which can reduce the performance of sound barriers. This is an important inclusion in prediction models to obtain a correct picture of the sound reduction at higher frequencies. Here a prediction method is applied that uses the strengths of the wind and temperature turbulence to estimate the scattered power into the shadow zone of a barrier. The predictions are compared to full-scale measurements on a thick barrier, where both acoustic and meteorological data were recorded simultaneously under both calm and windy conditions. Comparison between the measurements and the predictions indicate that the method gives reasonably accurate results for mid to high frequencies and a slight overestimation at very high frequencies.     

Performance of a noise barrier within an enclosed space

The present study involved experimental, theoretical, and numerical analyses of the insertion loss provided by rigid noise barriers in an enclosed space. The existing classical diffuse-field theory may be unable to predict the actual sound pressure level distribution and barrier insertion loss for indoor applications. Although predictions made by the ray tracing method at high frequencies are reasonably satisfactory, the method is computer-intensive and time-consuming. We propose a new formula that incorporates the effects of diffraction theory and the reflection of sound between room surfaces. Our results indicate that the present formula provides more realistic and practical predictions of the barrier insertion loss than existing approaches.     

A mathematical model for a single screen barrier in open-plan offices

In open-plan offices, single screen barriers are widely used to separate individual workplaces as a means of improving acoustical privacy. In this paper, a general model for calculating the insertion loss of a single screen barrier in the presence of a floor and a ceiling is developed using the image source technique. In addition to the acoustical properties of the floor and ceiling, this model also takes the sound absorption of the screen, the sound transmission through the screen and the interference between the sound waves into account. This model is able to separate the contribution of reflected sound and diffracted sound from the total sound pressure level at the receiving point, which can help indicate how best to improve the acoustical design of an open office. The mean differences between the predicted 1/3 octave band insertion loss values behind the screen and the corresponding measured results are within 2 dB.     

NUMERICAL MODELLING OF MEDIAN ROAD TRAFFIC NOISE BARRIERS

Outdoor sound propagation from road traffic is modelled by solving a boundary integral equation formulation of the wave equation using boundary element techniques in two dimensions. In the first model, the source representing a traffic stream can be considered as a coherent line source of sound. The results can then be transformed to derive a pseudo-three dimensional solution to the problem. In the second model the line source is incoherent. For receivers near the ground, the second model predicted significantly higher values of ground attenuation than the first. The first model generally produced better agreement with ground attenuation results obtained using the U.K. traffic noise prediction model. For conditions when a noise barrier was present and the ground was absorbent, the incoherent line source model generally predicted significantly higher values of attenuation than those from the barrier and ground attenuation calculated separately. Over a range of receiver positions and barrier heights a similar, but less marked effect was observed when the coherent line source model was used. On dual carriageway roads, it is possible to incorporate barriers on the central reservation as a noise control measure. These are “median” noise barriers. The incoherent line source model is used to assess the performance of median barriers in reducing noise when installed alone and also with associated roadside barriers. A sound absorbent median noise barrier 1m in height produced consistent values of insertion loss of between 1 and 2dB over the range of receiver positions and ground conditions considered. When the median barrier was used in conjunction with a roadside barrier it produced a consistent improvement in insertion loss of between 1 and 2 dB over the range of conditions considered.     

A further study of a mathematical model for a screen in open-plan offices

In order to obtain a good acoustical environment in open-plan offices, the acoustic performance of a single screen needs to be well estimated. Based on the sound pressure or the sound energy summation, the models proposed by previous investigators provided the predictions of the speech intelligibility index (SII) at the receivers behind a single screen in the open-plan offices. In the development of these models, the expression describing the diffracted field of a screen was an empirical formula and the sound diffraction is assumed to be appeared in the shadow region of the screen. In the present study, the MacDonald analytical formula is applied to describe the diffracted field of a screen, and both the diffractions in the visible region and in the shadow region are considered in the proposed model though it seems that the diffraction in the visible region is small compared with that in the shadow region. The comparison of the predicted and experimental results of the Wang and Bradley and the predicted results of the improved model shows that the improved model can provide a more accurate prediction, and further calculations indicate that the improvement is mostly due to the application of the MacDonald analytical diffraction formula.     

Seismic waves and seismic barriers

The basic idea of seismic barrier is to protect an area occupied by a building or a group of buildings from seismic waves. Depending on nature of seismic waves that are most probable in a specific region, different kinds of seismic barriers are suggested. For example, vertical barriers resembling a wall in a soil can protect from Rayleigh and bulk waves. The FEM simulation reveals that to be effective, such a barrier should be (i) composed of layers with contrast physical properties allowing “trapping” of the wave energy inside some of the layers, and (ii) depth of the barrier should be comparable or greater than the considered seismic wave length. Another type of seismic barrier represents a relatively thin surface layer that prevents some types of surface seismic waves from propagating. The ideas for these barriers are based on one Chadwick’s result concerning non-propagation condition for Rayleigh waves in a clamped half-space, and Love’s theorem that describes condition of non-existence for Love waves. The numerical simulations reveal that to be effective the length of the horizontal barriers should be comparable to the typical wavelength.     

A parametric investigation of the performance of T-profiled highway noise barriers and the identification of a potential predictive approach

Although a considerable amount of research has been undertaken regarding the performance of T-profile noise barriers, the information available to the practicing highway engineer is confusing. For example, there is a widespread belief that the performance of a top edge, expressed as an insertion loss relative to that of the simple barrier on which it is mounted, is constant, irrespective of the relative locations of the source, barrier and receiver. In order to clarify the situation an investigation has been undertaken, using computer modelling, of the performance afforded by highway noise barriers with T-profile tops with different acoustic treatments. The relative insertion loss was found to increase systematically with increasing top width. Although the relative insertion loss afforded by a reflective T-top is small, significant attenuation can be obtained with an absorptive top. Examination of the effect on performance of the locations of source and receiver relative to that of the noise barrier indicated that, for source and receiver locations typical of those experienced for highway noise barriers, the relative insertion loss for a given width of T-top was a function of (a) the path difference between sound travelling to the receiver via the barrier top and direct sound from the source to the receiver and (b) the barrier height. Plots of relative insertion loss versus the path difference, normalised with respect to barrier heights, for a range of T-top widths and absorbent treatment, resulted in a collapse of data around well defined trend lines which offer the potential of being developed into a prediction method.     

Experimental studies of sound diffraction by moving inhomogeneities under shallow-water conditions

The experimental data on the sound propagation and diffraction by moving test inhomogeneities under lake conditions are presented. It is shown that the diffracted signals under multimode propagation are adequately described by simplified theoretical models proposed earlier. The detection of the diffracted signals against the background of a fluctuating direct signal is demonstrated for the reception by a horizontal or vertical array. It is also shown that the direct and diffracted signals observed in the lake are similar in their characteristics to the signals in a shallow sea, which allows one to use the lake experiment for testing various underwater acoustic techniques intended for shallow-sea conditions.     

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.     

The predicted barrier effects in the proximity of tall buildings

A ray model is developed and validated for the prediction of the insertion loss of barriers that are placed in front of a tall building in high-rise cities. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the barrier and fa?ade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model, as they play important roles in determining the overall sound pressure levels for receivers located between the fa?ade and barrier. Comparisons of the ray model with indoor experimental data and wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Case studies are also presented that highlight the significance of positioning the barrier relative to the noise-sensitive receivers in order to achieve improved shielding efficiency of the barrier.     

Experimental and numerical study on the propagation of impulsive sound around buildings

Propagation of impulsive sound around buildings and induced structural loading are investigated experimentally and numerically. Experiments were conducted on a rectangular building at Virginia Tech using sonic booms generated by shaped charges with an explosive weight of 0.78 kg, constructed from detonation cord. These experiments were simulated with a three-dimensional numerical model, in the context of geometrical acoustics (GA), by combining the image source method for the reflected field (specular reflections) with an extension of the Biot–Tolstoy–Medwin (BTM) method for the diffracted field. In this model, it is assumed that the acoustic propagation is linear and that all surfaces are acoustically rigid. This numerical model is validated against a boundary element (BE) solution and experimental data, showing a good overall agreement. The key advantages of this GA modeling approach for this application include the ability to model large three-dimensional domains over a wide frequency range and also to decompose the sound field into direct, reflected, and diffracted components, thus providing a better understanding of the sound-propagation mechanisms. Finally, this validated numerical model is used to investigate sound propagation around a cluster of six rectangular buildings, for a range of elevated source positions simulating sonic booms from aircraft.     

Procedures for determining the acoustic efficiency of edge-modified noise barriers

This paper describes the noise shielding efficiency of barriers with an acoustic device mounted on their top edge for reducing sound diffraction. Diffraction behind the edge-modified barrier is investigated by scale model experiments in which the positions of a source and a receiver are aligned along a circular arc around the barrier top. The result indicates that the acoustic efficiency of the edge device is a function of the angles of the source and receiver and independent of their radii. Based on this finding, a novel procedure for determining the efficiency of manufactured edge devices is established. This procedure is very beneficial for estimating the edge device efficiency by eliminating ground and meteorological effects. The measured efficiency of the device will be quite useful for the prediction of noise propagation behind the edge-modified barriers.     

A ray model for hard parallel noise barriers in high-rise cities

A ray model is developed and validated for prediction of the insertion loss of hard parallel noise barriers placed in an urban environment either in front of a row of tall buildings or in a street canyon. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the ground, barrier and fa?ade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model as they play important roles in determining the overall sound pressure levels for receivers located between the fa?ade and the near-side barrier. Comparisons of the ray model with a wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Results of scale model experimental studies are also presented. It is demonstrated that the ray model agrees tolerably well with the scale model experimental data.     

预测声屏障插入损失的抛物方程法及其初始声场研究

Salomons建立的抛物方程(CNPE)方法可以预测非均匀环境中的声屏障插入损失。但是该方法在声屏障与声源距离较近时会产生较大误差。文中通过理论分析发现产生该问题的原因在于CNPE方法所使用的Gauss初始场仅适用于小仰角(10°以内)范围内的声波。为解决Gauss初始场引起的问题,推导了可以用于较大仰角声波的更高阶数的Gauss初始场。通过数值仿真对比了不同阶数的初始场在CNPE方法中的效果。结果表明:4阶初始场是最适合CNPE方法的初始场,将该初始场与CNPE方法相结合,可以准确预测当声屏障与声源距离较近时的插入损失.      

计入地面附加衰减的声屏障插入损失估算方法*

基于理论推导和计算,给出了公路声屏障声学设计中,在考虑地面附加衰减情况下计算插入损失的方法。该方法综合考虑了有限长线声源无限长声屏障绕射声衰减量、有限长线声源地面衰减量及遮蔽角对插入损失的影响。通过与《声屏障声学设计和测量规范》（HJ/T90-2004）的计算结果的对比,验证了本文所给方法的精确性及可行性,并对规范所给地面衰减修正量进行了商榷。最后,给出了当预测点位于有限长路段中央法线上时,通过计算线声源地面衰减量得到计算插入损失所需参数值,再计算插入损失的简便方法。本研究为存在地面附加衰减情况下有限长声屏障插入损失计算提供了一个新的参考方法。     

Tunneling times for opaque barriers

We propose new criteria to evaluate the average time spent by particles in a tunneling barrier. First we construct asojourn time, on the basis of statistical information provided by quantum mechanics, which seems to be an appropriate measure of the time spent byall particles within the barrier. A simple, stochastic treatment is then used to deal with the particles that actually traverse the barrier, in order to study their interaction time. The results obtained show that opaque barriers have important effects on the particlesbefore they enter the potential region, confirming previously published numerical findings. No arbitrarily high effective velocities appear anywhere in the present treatment.     

Noise attenuation by a hard wedge-shaped barrier

This paper is concerned with the problem of sound screening by a wedge-like barrier. The sound source is assumed to be point like, and the receiver is located in the shadow of the source sound field, so that according to geometrical optics only the field diffracted by the edge of the barrier is considered. First, for the hard wedge in space, three models are used for calculating the amplitude of the edge-diffracted field. These are the uniform theory of diffraction (UTD), the Hadden-Pierce model, both in the frequency domain, and the Biot-Tolstoy theory of diffraction which is a time domain formulation. It is first shown that even at relatively low frequencies, the frequency domain models perform quite satisfactorily as compared to the exact time domain theory. Hence, and due to its relative simplicity the UTD is proposed as an accurate calculation scheme for solving problems with edge diffraction by hard wedges. It is also proved from theoretical calculations that the amplitude of the edge-diffracted field increases for an increasing angle of the wedge, and consequently the hard half-plane gives the lowest field amplitude in the shadow zone. Some applications are then considered for evaluating the performance of a barrier on a flat ground, either completely hard or with mixed homogeneous boundary conditions. An improvement of the scheme for calculating the sound field in the all-hard case is achieved through considering the multiple diffraction, in this case only to the second order, between the top of the wedge barrier and its base. The results show that for usually occurring situations, increasing the angle of the hard wedge barrier affects negatively its efficiency through diminishing its insertion loss. These conclusions are also supported by the results of some experimental measurements conducted at a scale-model level.