Shahram Taherzadeh

Outdoor ground impedance models

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.

Ground effect over hard rough surfaces

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.

Deduction of ground impedance from measurements of excess attenuation spectra

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.

Propagation from a point source over a rough finite impedance boundary

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.

Sound propagation from a dipole source near an impedance plane

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 an...

Sound propagation in a refracting fluid above a layered fluid‐saturated porous elastic material

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.

Scattering by coupled resonating elements in air

Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of these scatterers in air has been investigated analytically and through laboratory experiments. The composite scatterer forms a system of coupled resonators and gives rise to multiple low-frequency resonances. The corresponding analytical model employs polar angle dependent boundary conditions on the surface of the N-slit cylinder. The solution inside the slits assumes plane waves. It is shown also that in the low-frequency range the N-slit rigid cylinder can be replaced by an equivalent fluid layer. Further approximations suggest a simple square root dependence of the resonant frequencies on the number of slits and this is confirmed by data. The observed resonant phenomena are associated with Helmholtz-like behaviour of the resonator for which the radius and width of the openings are much smaller than the wavelength. The problem of scattering by a finite periodic array of such coupled resonators in air is solved using multiple scattering techniques. The resulting model predicts band-gap effects resulting from the resonances of the individual composite scatterers below the first Bragg frequency. Predictions and data confirm that use of coupled resonators results in substantial insertion loss peaks related to the resonances within the concentric configuration. In addition, for both scattering problems experimental data, predictions of the analytical approach and predictions of the equivalent fluid layer approximations are compared in the low-frequency interval.

The sound field of an arbitrarily oriented quadrupole near ground surfaces

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.

Diffraction assisted rough ground effect: models and data

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.

An improved ray-tracing algorithm for predicting sound propagation outdoors

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.