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Sound fields above porous layers or rough acoustically hard boundaries may include airborne surface waves. The surface wave properties depend on the effective surface admittance. Analytical expressions for surface wave speeds are derived from models for the acoustical properties of rigid porous media. Surface wave effects on measurements of level difference spectra over porous asphalt are investigated and predictions of phase, group speeds, and vertical attenuation of the surface waves over externally reacting hard backed layers corresponding to a porous asphalt are compared. Predictions of surface wave characteristics above an identical vertical slit medium are compared with data obtained over arrays of parallel aluminum strips on an acoustically hard surface. Group speeds of surface waves over lattices, parallel regularly spaced strips, and snow obtained by numerical differentiation of the phase speed spectra corresponding to admittance spectra deduced from complex excess attenuation are found to compare well with those estimated from time domain data. An effective admittance, deduced from a boundary element method simulation of the excess attenuation spectrum over regularly spaced ribs so that the frequency of the peak corresponds with that in the measured spectrum, is used to estimate the group speed of the associated surface wave. [ABSTRACT FROM AUTHOR]

A modal model formulation explains many aspects of sound propagation over complex grooved surfaces. Insights that such a formulation offers about the intrinsic resonant properties of rectangular grooved surfaces shall be explored and applied to predict phenomenon such as surface waves and non-specular energy redistribution (blazing). Furthermore, the effects of filling the grooves with a porous material are investigated. A brief summary is made of the modal method and the mechanisms involved with sound propagation over rough surfaces to provide the context before exploring, in detail, how the modal method may be applied to predict various resonant behaviours of rectangularly grooved gratings. As well as their general predictive capabilities, the modal methods also provide significant insight into the wave modes diffracted by grooved surfaces under incident excitation at a low computational cost. [ABSTRACT FROM AUTHOR]

A modal model for diffraction by a contiguous array of rectangular grooves in an acoustically-hard plane is extended to predict the free space acoustic field from a point source above such a structure. Subsequently, an approximate effective impedance model for grooved surfaces is presented. Measurements have shown that these ground surfaces can be used for outdoor noise reduction but accurate modelling has required the use of computationally expensive numerical methods. The extended modal model and approximate impedance model inspired by it yield equivalent results in a fraction of the time taken by the boundary element method, for example, and could be used when designing grooved surfaces to reduce noise from road traffic. [ABSTRACT FROM AUTHOR]

Propagation of an airborne acoustic pulse from a point source above an array of regularly spaced rigid cylinders on a rigid plane has been investigated using a two-dimensional multiple scattering theory. Time domain simulations show a main arrival and a separate delayed "tail." Fourier analysis of the tail shows that, for a sufficiently sparse array of cylinders, it is composed of a series of spectral peaks resulting from constructive interference consistent with Bragg diffraction theory and amplitudes depending on the spacing and size of the cylinders. For increasingly compact distributions of cylinders, the lowest frequency peak is dominated by a quarter wavelength "organ pipe" or "gap" resonance in the space between the cylinders. Simulated pressure maps show that there is a transition region in the acoustic field with an extent that depends on the spacing and size of the cylinders. Beyond this region, individual gap resonances combine to create a field that declines exponentially with height, consistent with the behaviour of a surface wave. Data from measurements of acoustic pulses above copper cylinders on rigid fibreboard under anechoic conditions demonstrate some of the predicted characteristics. [ABSTRACT FROM AUTHOR]

Growing demand on transportation, road, and railway networks has resulted in increased levels of annoyance from road traffic. Optimized use of green surfaces in combination with vegetation may be desirable as a method for reducing the noise impact of road traffic in urban and rural environments. Sound propagation over soft ground and through crops has been studied through outdoor measurements at short and medium ranges and through predictions. At lower frequencies, ground effect is dominant, and there is little or no attenuation due to crops. At higher frequencies above 3-4 kHz, the attenuation in crops is dominant. It was also found that the ground effects and the influence of crops can be treated independently and can be added to obtain the total effect. Sound attenuation by crops is the result of multiple scattering between the stems and leaves, loss of coherence, and viscous and thermal losses due to foliage. The major contribution is associated with viscous and thermal losses. A model for sound attenuation by vegetation is proposed. Insertion losses for a typical road traffic noise source have been calculated that result either by replacing hard ground with different types of acoustically soft ground or by growing crops along the road sides. [ABSTRACT FROM AUTHOR]

Frequency- and time-domain measurements have been made on surfaces composed from parallel periodically-spaced rectangular strips (width: 0.0126 m, height: 0.0253 m) on an acoustically hard surface. The edge-to-edge spacing between the strips has been varied between 0.003 and 0.06 m. Frequency domain predictions show that when the spacing is small, these surfaces may be regarded as locally reacting rigid-framed hard-backed slit-pore layers with an effective depth slightly larger than the strip height, but when the spacing is comparable to the strip height or greater, the surfaces behave as periodically rough surfaces. Both frequency- and time-domain results show that surface waves of comparable magnitudes are created over the range of strip spacings studied but the frequency content of the acoustically induced surface waves decreases as the mean spacing is increased. It is found that surface wave dispersion is better predicted by the deduced effective impedance spectrum than by the slit-pore layer impedance model. [ABSTRACT FROM AUTHOR]

Two effective medium models are presented and used to predict complex reflection and transmission coefficients of finite periodic arrays of resonant elastic shells as well as their effective density and bulk modulus at low frequencies. Comparisons with full multiple scattering theory and measurements show that the self-consistent model fails to correctly predict the shape of the transmission/reflection curves when scatterer resonances are close to the first Bragg bandgap. The low frequency grating model, which neglects the evanescent modes and considers scattered wave propagation only in the same direction as the incident one, gives a much better agreement with both measurements and the full multiple scattering theory. Moreover, because it does not require the wavelength to strongly exceed the size of scatterers, the model gives reliable predictions even at frequencies around the first periodicity related bandgap. In contrast to the self-consistent model, the low frequency grating model is applicable when the resonant scatterers have more than two low frequency resonances. [ABSTRACT FROM AUTHOR]

The destructive interferences observed in Excess Attenuation (EA) spectra over periodically and randomly spaced roughness elements with different cross-sectional profiles (semicylindrical, rectangular and wedge-shaped strips) have been investigated. If the roughness is spaced periodically, then two or three destructive interference maxima are observed in the same frequency range as the one or two observed with randomly distributed roughness. Roughness-induced surface waves are investigated also. Their amplitudes and the frequencies at which they occur are found to depend on the roughness height, mean center-to-center spacing and the extent to which the roughness is periodic. A semianalytical Multiple Scattering Theory and a numerical method (the Boundary Element Method) have been used to make predictions of the EA spectra which are compared with measurements. In addition it is found that the effective surface impedance spectra deduced from complex EA measurements over rough surfaces exhibit resonances similar to those observed for a hard-backed porous layer. On this basis a heuristic effective impedance model for rough hard surfaces is developed and the corresponding predictions of EA spectra are compared with data. [ABSTRACT FROM AUTHOR]

This paper presents and compares three analytical methods for calculating low frequency band gap boundaries in doubly periodic arrays of resonating thin elastic shells. It is shown that both Foldy-type equations (derived with lattice sum expansions in the vicinity of its poles) and a self-consistent scheme could be used to predict boundaries of low-frequency (below the first Bragg band gap) band gaps due to axisymmetric (n=0) and dipolar (n=1) shell resonances. The accuracy of the former method is limited to low filling fraction arrays, however, as the filling fraction increases the application of the matched asymptotic expansions could significantly improve approximations of the upper boundary of band gap related to axisymmetric resonance. The self-consistent scheme is shown to be very robust and gives reliable results even for dense arrays with filling fractions around 70%. The estimates of band gap boundaries can be used in analyzing the performance of periodic arrays (in terms of the band gap width) without using full semi-analytical and numerical models. The results are used to predict the dependence of the position and width of the low frequency band gap on the properties of shells and their periodic arrays. [ABSTRACT FROM AUTHOR]

Results of laboratory measurements of sound transmission through 5 × 10 arrays of meter long polyvinyl chloride pipes with lattice constants of 5 and 10 cm with filling fractions of 13% and 50% located either on medium density fibreboard or a layer of felt are reported. Ground effects and sonic crystal effects are found to be additive. Measurements and predictions show that, while there is little broadband advantage in a periodic configuration compared with a random one, a quasi-periodic arrangement in which the perturbation has a standard deviation equal to the scatterer diameter gives the best overall attenuation. [ABSTRACT FROM AUTHOR]

The acoustical performances of regular arrays of cylindrical elements, with their axes aligned and parallel to a ground plane, have been investigated through predictions and laboratory experiments. Semi-analytical predictions based on multiple scattering theory and numerical simulations based on a boundary element formulation have been made. Measurements have been made in an anechoic chamber using arrays of (a) cylindrical acoustically-rigid scatterers (PVC pipes) and (b) thin elastic shells. Insertion loss (IL) spectra due to the arrays have been measured without and with ground planes for several receiver heights. Data and predictions have been compared. The minima in the excess attenuation spectrum i.e., attenuation maxima due to the ground alone resulting from destructive interference between direct and ground-reflected sound waves, tend to have an adverse influence on the band gaps (BG) related to a periodic array in the free field when these two effects coincide. On the other hand, the presence of rigid ground may result in an IL for an array near the ground similar to or, in the case of the first BG, greater than that resulting from a double array, equivalent to the original array plus its ground plane mirror image, in the free field. [ABSTRACT FROM AUTHOR]

Many models for the acoustical properties of rigid-porous media require knowledge of parameter values that are not available for outdoor ground surfaces. The relationship used between tortuosity and porosity for stacked spheres results in five characteristic impedance models that require not more than two adjustable parameters. These models and hard-backed-layer versions are considered further through numerical fitting of 42 short range level difference spectra measured over various ground surfaces. For all but eight sites, slit-pore, phenomenological and variable porosity models yield lower fitting errors than those given by the widely used one-parameter semi-empirical model. Data for 12 of 26 grassland sites and for three beech wood sites are fitted better by hard-backed-layer models. Parameter values obtained by fitting slit-pore and phenomenological models to data for relatively low flow resistivity grounds, such as forest floors, porous asphalt, and gravel, are consistent with values that have been obtained non-acoustically. Three impedance models yield reasonable fits to a narrow band excess attenuation spectrum measured at short range over railway ballast but, if extended reaction is taken into account, the hard-backed-layer version of the slit-pore model gives the most reasonable parameter values. [ABSTRACT FROM AUTHOR]

Analytical and numerical approaches have been made to the problems of (a) propagation through a doubly periodic array of elastic shells in air, (b) scattering by a single elastic shell in air, and (c) scattering by a finite periodic array of elastic shells in air. Using the Rayleigh identity and the Kirchhoff-Love approximations, a relationship is found between the elastic material parameters and the size of the bandgap below the first Bragg frequency, which results from the axisymmetric resonance of the shells in an array. Predictions and laboratory data confirm that use of a suitably 'soft' non-vulcanized rubber results in substantial insertion loss peaks related to the resonances of the shells. Inclusion of viscoelasticity is found to improve the correspondence between predictions and data. In addition the possible influences of inhomogeneity due to the manufacturing of the elastic shells (i.e., the effects of gluing sheet edges together) and of departures from circular cylindrical cross-sections are considered by means of numerical methods. [ABSTRACT FROM AUTHOR]

To assess the acoustical performance of noise screens in the presence of an arbitrary sound speed profile, a numerical scheme based on a combination of the boundary integral and fast field program methods is developed. The Green's function required in the boundary integral is evaluated by a fast field formulation. The procedure is validated by comparing its predictions with other numerical results for simple cases and with measurements for indoor model experiments simulating downward refracting conditions. It is predicted that the performance of a noise screen placed 50 m from the source is reduced considerably by moderate downwind conditions. © 2001 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

An efficient numerical method of deducing ground-surface impedance from measurements of short-range propagation from a point source is proposed. The method involves finding the root of a complex equation and uses the fact that the classical approximation for the spherical wave-reflection coefficient near grazing incidence is an analytic function of the impedance. Examples of fitting measured excess-attenuation spectra are given. Methods for ensuring the uniqueness of the resulting impedance fits are discussed. Subsequent deductions of parameters in a two-parameter impedance model are also considered and exemplified. © 1999 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

A new ray-tracing method for predicting the sound field near a flat impedance ground in a refracting atmosphere is developed that includes the effect of vector wind and turbulence explicitly. Improvements on previous ray-tracing schemes include the use of a generalized Snell's law, an integration by means of a Gaussian quadrature, and a bracketing method for finding the ray paths. For the turbulence calculations, the interray coherence is determined from turning point heights rather than from integrals along the ray paths. A more efficient algorithm is developed for computing the sound field above an impedance plane in a realistic atmosphere. Despite the inherent limitations of the ray-trace approach, particularly in respect of logarithmic wind profiles, the algorithm is valid over a wide range of practical situations. © 1998 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Laboratory and outdoor measurements are reported of the relative sound pressure level spectrum over hard surfaces containing either random or periodically spaced arrays of 2-D roughnesses. The resulting data have been compared with predictions obtained analytically and with numerical predictions of a boundary element code. Effective impedances of the rough surfaces have been calculated from the boss theory developed by Twersky. A classical asymptotic approximation for propagation near grazing incidence from a point source over an impedance boundary has been modified, heuristically, to allow for diffraction grating effects. The resulting predictions are found to be in tolerable agreement with the data except for close and random packing. The boundary element code is found to give superior results for larger roughnesses, but computational restrictions on element size reduce its usefulness for roughnesses with small width or height. © 1998 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

The sound field due to an arbitrarily oriented quadrupole above an impedance ground is investigated. To simplify the analysis, the atmospheric and topographical effects on sound propagation are ignored. Two different methods are developed to calculate the sound field. First, an asymptotic method is used to derive a close-form analytic solution. Second, a fast field program (quad-FFP) has been developed for numerical computations of the sound field. It is found that numerical results from both methods agree well. In a recent development, it has been shown that the analytic solution of the sound field due to an arbitrarily oriented dipole can be written in the classical form similar to that due to a monopole. However, it is not possible to write the solution in such a form for the case of an arbitrarily oriented quadrupole, but rather the total sound pressure is augmented by two extra terms which are particularly important at a small separation between the source and receiver. © 1997 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

A closed-form analytic solution has been derived for an arbitrarily oriented dipole placed above an impedance plane. Asymptotic approximations for the total sound field can be written in a form similar to the classical formula for a monopole. Analytic approximations derived for horizontal and vertical dipoles give predictions that agree well with those obtained from a program of the fast field type. The asymptotic results have been confirmed also by laboratory measurements. Compared with numerical methods, the analytic approximations offer the combined advantages of easier physical interpretation and a much reduced computational time. It is found that the variation of the sound-pressure level from a vertical dipole above an impedance plane differs significantly from that due to a monopole above this plane, particularly as a result of differences in the ground wave component. However, the excess attenuation due to a horizontal dipole is found to be rather similar to that for a monopole except for source and receiver heights that are comparable with range. © 1997 Acoustical Society of America. [ABSTRACT FROM AUTHOR]

Measurements of the excess attenuation of sound from a point source over artificially rough surfaces in an anechoic chamber are compared with predictions from modified forms of theories by Howe [J. Sound Vib. 98, 83-94 (1985)] and by Tolstoy [J. Acoust. Soc. Am. 72, 960-072 (1982)]. The modified theories agree with each other and are in tolerable agreement with data over hard or nearly hard boundaries. The modified Tolstoy formulation, which allows the roughnesses to have an impedance that differs from the impedance of the surrounding plane, is found to give better agreement with data for propagation over rough finite impedance surfaces. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A fast Fourier method of solution of wave equations is applied to sound propagation in a system composed of a horizontally stratified fluid overlying a horizontally stratified porous and elastic solid. A Biot model is used for the porous elastic material. Predictions are made of sound-pressure level in the fluid and vertical displacement in the solid. These are validated by comparison to analytic approximations, and results from another numerical model for propagation in a layered, nonporous viscoelastic material system. The validated code predicts the possibility of significant ground elasticity effects on above-ground propagation. [ABSTRACT FROM AUTHOR]

A numerical procedure for computing sound propagation from a point source in an environment consisting of a stratified fluid half-space above a layered poro-elastic ground is described. The wave amplitudes are computed from depth-separated wave equation by forming a system of linear equations arising from the boundary conditions at each and every interface between layers and solving the resulting global matrix. The inverse Hankel transform is then performed by fast Fourier method (FFP) to obtain the pressure and particle velocity at any elevation as a function of range. Wave propagation within the porous elastic layers is calculated according to the modified Biot-Stoll theory which predicts two compressional and one shear wave types in the medium. Six boundary conditions are therefore required at each ground intefaces and four at the fluid-ground interface, while only two are needed at the fluid-fluid interfaces. Using this code the role of the ground elasticity on above-ground propagation and in acoustically induced seismic excitation are explored. It is predicted that on certain ground types, characterized by a thin layer with small compressional and shear velocities, and at frequencies that coincide with a peak in the seimic-to-acoustic coupling ratio spectrum there is an extra sound attenuation. [ABSTRACT FROM AUTHOR]

An airborne sound wave striking the ground surface can produce seismic excitation in the ground. The acoustic-to-seismic coupling spectra show distinctive structure. The structure is mainly attributed to wave resonances within the ground layers. This phenomenon has been studied extensively in the past. Here the extent to which certain parameters influence the position of maxima of acoustic-to-seismic coupling are investigated. The ground has been modeled as a vertically layered porous-elastic medium using the modified Biot-Stoll theory. Predictions based on this theory and also some previously derived expressions are compared with data. It is shown that for some typical ground types, only the full Biot-Stoll theory rather than a low velocity elastic layer model is required to predict the acoustic-to-seismic coupling spectra adequately. [ABSTRACT FROM AUTHOR]

Previous studies of the boundary wave associated with near-grazing propagation over randomly rough surfaces have been concerned with high-frequency (2.5-30 kHz) pulses and acoustically rigid surfaces [see, for example, Medwin et al., J. Acoust. Soc. Am. 66, 1131-1134 (1979)]. Continuous wave measurements of the excess attenuation spectrum by means of maximum length sequence signal analysis have been carried out. These have enabled study of roughness effects in the frequency range 500 to 2500 Hz. Data have been obtained over rough wooden surfaces and over a thin polymer foam layer to which rectangular 3 cm by 0.5 cm strips have been attached. These data have been compared with predictions due to Howe [J. Sound Vib. 98, 83-94 (1985)] modified for effects of roughness shape according to Tolstoy [J. Acoust. Soc. Am. 66, 1135-1143 (1989)]. [Work supported by S.E.R.C. (UK).] [ABSTRACT FROM AUTHOR]

At large ranges or at higher frequencies, it is necessary to incorporate a large number of isovelocity layers to achieve tolerable accuracy in fast field calculations. This has a predictable effect on computation time. There is a standard solution in terms of Airy functions that allows for a linear gradient within each layer. This paper presents a preliminary investigation of an alternative form of solution that involves Hankel functions of complex order. These arise from a transformation of the depth-separated wave equation into a form of Bessel's differential equation. Results have been obtained for a low-frequency case and are compared with results from the standard form in terms of Airy functions. [ABSTRACT FROM AUTHOR]

Data for complex excess attenuation have been used to determine the effective surface admittance and hence characteristic roughness size of a surface comprising a random distribution of semi-cylindrical rods on an acoustically hard plane. The inversion for roughness size is based on a simplified boss model. The technique is shown to be effective to within 4%, up to a threshold roughness packing density of 32%, above which the interaction between scattering elements appears to exceed that allowed by the model., (© 2011 Acoustical Society of America)