Predicted attenuation of sound in a rigid-porous ground from an airborne source

An approximate analytical formula has been derived for the prediction of sound fields in a semi-infinite rigid-porous ground due to an airborne source. The method starts by expressing the sound fields in an integral form, which can subsequently be evaluated by the method of steepest descents. The concept of effective impedance has been introduced by using a physically plausible assumption. The integral can then be simplified and evaluated analytically. The analytical solution can be expressed in a closed form analogous to the classical Weyl-Van der Pol formula that has been used for predicting sound fields above a rigid-porous ground. Extensive comparisons with the wave-based numerical solutions according to the fast field formulation and the direct evaluation of the integral have been conducted. It has been demonstrated that the analytical formula is sufficiently accurate to predict the penetration of sound into a wide range of outdoor ground surfaces.     

The diffraction of sound by an impedance sphere in the vicinity of a ground surface

The problem of sound diffraction by an absorbing sphere due to a monopole point source was investigated. The theoretical models were extended to consider the case of sound diffraction by an absorbing sphere with a locally reacting boundary or an extended reaction boundary placed above an outdoor ground surface of finite impedance. The separation of variables techniques and appropriate wave field expansions were used to derive the analytical solutions. By adopting an image method, the solutions could be formulated to account for the multiple scattering of sound between the sphere and its image near a flat acoustically hard or an impedance ground. The effect of ground on the reflected sound fields was incorporated in the theoretical model by employing an approximate analytical solution known as the Weyl-van der Pol formula. An approximation solution was suggested to determine the scattering coefficients from a set of linearly coupled complex equations for an absorbing sphere not too close to the ground. The approximate method substantially reduced the computational time for calculating the sound field. Preliminary measurements were conducted to characterize the acoustical properties of an absorbing sphere made of open cell polyurethane foam. Subsequent experiments were carried out to demonstrate the validity of the proposed theoretical models for various source/receiver configurations around the sphere above an acoustically hard ground and an impedance ground. Satisfactory comparative results were obtained between the theoretical predictions and experimental data. It was found that the theoretical predictions derived from the approximate solution agreed well with the results obtained by using the exact solutions.     

Controlled experiments of the diffraction of sound by a curved surface

Controlled measurements of the sound field from a point source above a curved surface are described. The measurements were made in the frequency range between 0.3 and 10 kHz, in the case of a rigid boundary and a surface of finite impedance. Receiver positions include all of the area within, and above, the shadow zone and for various source heights. Particular attention is given to the region across the shadow boundary. The measurements are compared to diffraction theory expressed in terms of a residue series, or creeping wave solution. The calculation is extended by removing restrictive approximations and by carrying the computation to higher-order terms. A numerical algorithm allows the extension to the general case of a finite impedance. Above the shadow boundary, the sound field is calculated using geometrical theory that accounts for reflections from a curved surface. Deep within the shadow, theory and measurements agree to, typically, 0.5 dB. The same agreement is obtained between measurements and the geometrical theory well above the shadow boundary. In the vicinity of the shadow boundary, both theories agree to within 0.5 dB but differ from the measured results by 2 to 5 dB. Finally, the theory is compared to measurements obtained outdoors above a grass covered curved ground with no refraction and above flat ground with refraction.     

Sound reduction by barriers on the ground

An existing theory on the propagation of spherical sound waves over ground with a finite acoustic impedance is to a large extent verified by field measurements over different types of ground surfaces. It is then shown that it is reasonable to combine this theory with ordinary diffraction theory to get a solution of the mixed problem with a barrier on the ground. Full-scale measurements have been carried out with a 3 m high wall and the results show good agreement with the predicted values. It is also shown that it is generally of minor importance whether a thin screen is sound absorbing or not.     

Normal mode solution for low-frequency sound propagation in a downward refracting atmosphere above a complex impedance plane.

The development of the fast field and parabolic equation solutions to the wave equation has made it possible to solve for the combined effects of refraction in a layered atmosphere and the interaction of sound with a complex impedance ground surface. In many respects the numerical methods have advanced beyond our understanding of the basic phenomena. In an earlier study [J. Acoust. Soc. Am. 89, 107-114 (1991)], the residue series solution for upward refraction was investigated and provided insight into the nature of the interaction of refraction and ground reflection. In this paper results are presented of a similar normal mode solution for downward refraction above a complex impedance ground surface. This model is used to investigate when the surface wave is excited for downward refraction conditions and to develop criteria for the maximum range of cylindrical decay as a function of phase and magnitude of the ground impedance and the magnitude of the sound velocity gradient.     

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.     

Efficient calculation of two-dimensional periodic and waveguide acoustic Green's functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.     

Acoustic analysis of a rectangular cavity with general impedance boundary conditions

A Fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls. The sound pressure is expressed as the combination of a three-dimensional Fourier cosine series and six supplementary two-dimensional expansions introduced to ensure (accelerate) the uniform and absolute convergence (rate) of the series representation in the cavity including the boundary surfaces. The expansion coefficients are determined using the Rayleigh-Ritz method. Since the pressure field is constructed adequately smooth throughout the entire solution domain, the Rayleigh-Ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions. To unify the treatments of arbitrary nonuniform impedance boundary conditions, the impedance distribution function on each specified surface is invariantly expressed as a double Fourier series expansion so that all the relevant integrals can be calculated analytically. The modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions, including nonuniform impedance distributions.     

Air-ground interaction in long range propagation of low frequency sound and vibration—field tests and model verification

An extensive program of intermediate and long range impulsive sound propagation field tests have been conducted. The test program and the performed measurements are presented. Particular focus is given on the air-ground interaction and its effect on low frequency sound and vibration propagation. It is found that the pressure wave interaction with the viscoelastic Rayleigh wave in the ground may have a significant effect on the ground impedance and the sound and vibration propagation. This introduces an important mechanism not covered in commonly used ground impedance models. Numerical simulation models have been developed and verified against the test data. The ground impedance does not only effect the sound pressure propagation. If either acoustically induced ground vibration, or ground to building transmitted vibration, is to be considered, the acousto-seismic impedance has a dramatic effect on the level of ground vibration induced by a given sound pressure. For a site where Rayleigh wave interaction appears at the dominant frequencies of the sound pressure, the ground vibration may be greater than a factor 100 (40 dB) than at a site with ground conditions not making the interaction happen.     

A linearized Eulerian sound propagation model for studies of complex meteorological effects

Outdoor sound propagation is significantly affected by the topography (including ground characteristics) and the state of the atmosphere. The atmosphere on its part is also influenced by the topography. A sound propagation model and a flow model based on a numerical integration of the linearized Euler equations have been developed to take these interactions into account. The output of the flow model enables the calculation of the sound propagation in a three-dimensionally inhomogeneous atmosphere. Rigid, partly reflective, or fully absorptive ground can be considered. The linearized Eulerian (LE) sound propagation model has been validated by means of four different scenarios. Calculations of sound fields above rigid and grass-covered ground including a homogeneous atmosphere deviate from analytic solutions by < or = 1 dB in most parts of the computed domain. Calculations of sound propagation including wind and temperature gradients above rigid ground agree well with measured scale model data. Calculations of sound propagation over a screen including ground of finite impedance show little deviations to measured scale model data which are probably caused by an insufficient representation of the complex ground impedance. Further calculations included the effect of wind on shading by a screen. The results agree well with the measured scale model data.     

A Chebyshev–Lagrangian method for acoustic analysis of a rectangular cavity with arbitrary impedance walls

A general Chebyshev–Lagrangian method is proposed to obtain the analytical solution for a rectangular acoustic cavity with arbitrary impedance boundary conditions. The originality of the present paper is the successful attempt of applying orthogonal polynomials, such as Chebyshev polynomials of the first kind, to the analysis of a rectangular sound field with general wall impedance. The sound pressure is uniformly expressed as triplicate Chebyshev polynomial series which is independent in each direction. The Chebyshev polynomial series solution is obtained using the Rayleigh–Ritz procedure after considering the influence of boundary impedance on the cavity as the work done by the impedance surfaces in the Lagrangian function. The accuracy and reliability of the proposed method are validated against the analytical solutions and some numerical results available in the literature. Excellent orthogonality and complete properties of the Chebyshev polynomials ensure the rapid convergence, numerical stability, high accuracy of the current solution. The simplicity and low computational cost of the present approach make it preferable to obtain the results of complex models even in the relative high frequency range by choosing enough truncated terms in the sound pressure expression. Numerous cases with various uniform or non-uniform impedance boundary conditions are analyzed numerically and some of the results can be used as benchmark. It is shown that the impedance boundary condition can effectively influence or modify the acoustic characteristics and response of a cavity.     

A numerical approach to sound levels in near-surface refractive shadows

The present study formulates a consistent method to simulate the outdoor, near-surface sound propagation through realistic refractive conditions. The correlated atmospheric stratification and turbulence properties are derived from standard meteorological quantities through flux-profile similarity relationships. The propagation of a monochromatic sound field is simulated in presence of the turbulence and stratification effects and an impedance ground. The propagation model uses a numerical solution of a second-order moment parabolic equation, which is introduced and evaluated. The so-formed coupled atmospheric-acoustic model is used to systematically investigate the sound levels in near-surface refractive shadows. In an illustrative propagation scenario, the shadow zone sound levels are predicted to show significant variations with the meteorological conditions. Specifically, the sound levels decrease with the adverse wind, as a consequence of enhanced mean upward refraction. Conversely, they increase with the absolute value of the surface heat flux, as a consequence of enhanced turbulence scattering. Implications for the assessment of the sound levels in shadow zones are discussed.     

Extended sources radiation and laplace type integral representation: Application to wave propagation above and within layered media

In has been shown that the sound field reflected by the plane boundary of a layered ground can always be described by a specularly reflected wave, and layer potentials. Despite its generality, this representation is not quite suitable for numerical computation. Dealing with a very simple case, Weyl, and later on Ingard and Thomasson, proposed a representation of the solution in which the layer potential terms are replaced by the sum of surface wave and a Laplace type integral. Such an integral is very convenient for numerical purposes. In this paper, it is shown that this kind of representation can be obtained for a very wide class of sound propagation problems above or within layered media: a half-space bounded by a locally reacting surface, a finite layer of porous medium, a porous medium with depth-varying porosity, a thin elastic plate; wave propagation in shallow water with an impedance bottom. Many other applications could be developed.     

Determination of sound reduction indices in the presence of flanking transmission

Unlike the standard sound insulation test method, which requires diffuse sound fields in both source room and receiving room, the sound intensity method only requires the source room to be diffuse. Flanking may, in some cases, cause large errors in the sound reduction indices obtained by the standard method, even if the flanking power is measured separately and subtracted from the total power. The sound intensity method allows selective determination of sound reduction indices for test objects surrounded by flanking surfaces, provided the measurement surface in the receiving room is defined in such a way that it encloses nothing but the test object.     

Directional properties of an array of sound receivers positioned in an impedance screen recess

Expressions for calculating the directional characteristics of an array of sound receivers positioned in a waveguide with impedance walls are obtained from the solution to the problem on the diffraction of a plane sound wave by the waveguide open end with impedance flanges. The waveguide can be of a finite length, and, in this case, it can be considered as an open cavity in an impedance screen. The solution of the integral equation for the sound pressure distribution over the opening area is reduced to the solution of an infinite system of algebraic equations for the coefficients of the field expansion in normal waveguide waves. Examples of calculated directional characteristics are presented for arrays with receivers positioned at different distances from the opening and for different values of the impedances of the waveguide walls and flanges.     

Measurements of echoes with a stationary random sound source

The separation of the direct wave issued from a stationary random sound source and echoes reverberated by surfaces is made by computing the Fourier transform of the transfer function of two microphone signals. Two methods are described for different positions of the microphones and are illustrated by experimental results concerning (i) free field measurements of ground reflexion coefficients, and (ii) measurements of echoes which are reverberated by the linings of an anechoic chamber.     

水下高斯界面背向散射超声散斑场的相位奇异

为了精确描述超声散斑场的特性,提出了采用计算机模拟产生超声散斑场的方法.利用模拟产生的高斯相关随机表面,获得了这类表面远场超声散斑场,同时得到了声强分布和相位分布.与实验产生的散斑场进行对比,建立了超声散斑场接收的实验系统,取与计算模拟相同的参数,获得了实验散斑场.通过对比发现:计算机模拟产生的超声散斑场相位存在奇异点,奇异点周围相位分布类似漩涡,计算机模拟产生的散斑场与实验得到的散斑场强度分布相似,强度值比实验产生的散斑场强度大,携带有用信息的高亮散斑较多,暗点较少,更利于研究和分析.     

Effective impedance spectra for predicting rough sea effects on atmospheric impulsive sounds

Two methods of calculating the effective impedance spectra of acoustically hard, randomly rough, two-dimensional surfaces valid for acoustic wavelengths large compared with the roughness scales have been explored. The first method uses the complex excess attenuation spectrum due to a point source above a rough boundary predicted by a boundary element method (BEM) and solves for effective impedance roots identified by a winding number integral method. The second method is based on an analytical theory in which the contributions from random distributions of surface scatterers are summed to obtain the total scattered field. Effective impedance spectra deduced from measurements of the complex excess attenuation above 2D randomly rough surfaces formed by semicylinders and wedges have been compared to predictions from the two approaches. Although the analytical theory gives relatively poor predictions, BEM-deduced effective impedance spectra agree tolerably well with measured data. Simple polynomials have been found to fit BEM-deduced spectra for surfaces formed by intersecting parabolas corresponding to average roughness heights between 0.25 and 7.5 m and for five incidence angles for each average height. Predicted effects of sea-surface roughness on sonic boom profiles and rise time are comparable to those due to turbulence and molecular relaxation effects.     

Coupled integral equations for sound propagation above a hard ground surface with trench cuttings

A set of coupled integral equations is formulated for the investigation of sound propagation from an infinitesimal harmonic line source above a hard ground surface corrugated with cuttings. Two half-space Green's functions are employed in the formulation. The first one defined for the upper half space is used to reduce the problem size and eliminate the edge effect resulting from the boundary truncation; the other one for the lower half space is to simplify the representation of the Neumann-Dirichlet map. As a result, the unknowns are only distributed over the corrugated part of the surface, which leads to substantial reduction in the size of the final linear system. The computational complexity of the Neumann-Dirichlet map is also reduced. The method is used to analyze the behavior of sound propagation above textured surfaces the impedance of which is expectedly altered. The effects of number and opening of trench cuttings, and the effect of source height are investigated. The conclusions drawn can be used for reference in a practical problem of mitigating gun blast noise.     

一种浅海声矢量场干涉结构提取方法

针对浅海Pekeris环境下声矢量场的干涉特征,基于简正波理论分析了在频率-距离域上声强谱、质点振速自谱、复声强谱和波阻抗谱干涉结构的形成机理,探讨了对干涉结构的波导不变量表征,并进行了宽带辐射声场干涉结构的海上测量试验。仿真研究和海试数据分析均表明,在频率-距离域上,上述4类物理量都会呈现稳定的、可用波导不变量β表征的干涉结构,而复声强独有的纯干涉分量更能体现波导的干涉效应。最后引入多尺度线性滤波器对海试实测LOFAR图进行处理,处理结果表明该滤波器可有效地增强干涉特征,更利于检测和提取干涉图案中的条纹信息。