Modal model prediction of surface waves and resonant characteristics of rectangular grooved gratings.

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.

Pioneering study of outdoor sound propagation.

The Reflections series takes a look back on historical articles from The Journal of the Acoustical Society of America that have had a significant impact on the science and practice of acoustics.

Approximate impedance models for point-to-point sound propagation over acoustically-hard ground containing rectangular grooves.

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.

Acoustic surface wave generation over rigid cylinder arrays on a rigid plane.

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.

Correspondence between sound propagation in discrete and continuous random media with application to forest acoustics.

Although sound propagation in a forest is important in several applications, there are currently no rigorous yet computationally tractable prediction methods. Due to the complexity of sound scattering in a forest, it is natural to formulate the problem stochastically. In this paper, it is demonstrated that the equations for the statistical moments of the sound field propagating in a forest have the same form as those for sound propagation in a turbulent atmosphere if the scattering properties of the two media are expressed in terms of the differential scattering and total cross sections. Using the existing theories for sound propagation in a turbulent atmosphere, this analogy enables the derivation of several results for predicting forest acoustics. In particular, the second-moment parabolic equation is formulated for the spatial correlation function of the sound field propagating above an impedance ground in a forest with micrometeorology. Effective numerical techniques for solving this equation have been developed in atmospheric acoustics. In another example, formulas are obtained that describe the effect of a forest on the interference between the direct and ground-reflected waves. The formulated correspondence between wave propagation in discrete and continuous random media can also be used in other fields of physics.

On the inadvisability of using single parameter impedance models for representing the acoustical properties of ground surfaces.

Although semi-empirical one parameter models are used widely for representing outdoor ground impedance, they are not physically admissible. Even when corrected to satisfy a passivity condition in respect of surface impedance they do not satisfy the condition that the real part of complex density must be greater than zero. Comparison of predictions with frequency-domain data for short range propagation have indicated that physically admissible models provide superior overall agreement. A two parameter variable porosity model yields better agreement for many grassland surfaces and a two parameter version of the slit pore microstructural impedance model yields better agreement with data obtained over low flow resistivity surfaces such as forest floors and gravel. Impedance models and conditions for physical admissibility are summarised. In addition to those examined previously, the slit pore model is shown to be physically admissible. After providing further examples of the better agreement with short range data that can be achieved using two parameter models, it is shown that differences between frequency domain predictions at longer ranges using physically admissible models rather than one parameter models are significantly greater than those resulting from short range spatial variability and comparable with seasonal variability over grassland.

Sound propagation over soft ground without and with crops and potential for surface transport noise attenuation.

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.

Comparisons of two effective medium approaches for predicting sound scattering by periodic arrays of elastic shells.

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.

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.

Analytical approximations for low frequency band gaps in periodic arrays of elastic shells.

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.

Surface waves over periodically-spaced rectangular strips.

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.

Aperiodicity effects on sound transmission through arrays of identical cylinders perpendicular to the ground.

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.

Mathematics summer schools for acoustics research training.

Mathematical methods are important for research in many aspects of acoustics. Most researchers in acoustics in the United Kingdom do not have access to master level courses to broaden their postgraduate study, so they advance their fundamental mathematical methodologies taught at undergraduate level through independent learning. They develop their mathematical skills as appropriate rather than being made aware of the potential of advanced mathematical tools at the onset of their research career. Attempts to improve this situation were made through summer schools held in 2003 and 2005 at Southampton University and in 2007 at Salford University. The background to these Summer Schools, their content and structure, recruitment figures and student feedback are reported together with conclusions about their performance and role particularly in respect of PhD completion.

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.

Deduction of static surface roughness from complex excess attenuation.

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.

Acoustic insertion loss due to two dimensional periodic arrays of circular cylinders parallel to a nearby surface.

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.

Ultrasonic wave propagation in stereo-lithographical bone replicas.

Predictions of a modified anisotropic Biot-Allard theory are compared with measurements of pulses centered on 100 kHz and 1 MHz transmitted through water-saturated stereo-lithographical bone replicas. The replicas are 13 times larger than the original bone samples. Despite the expected effects of scattering, which is neglected in the theory, at 100 kHz the predicted and measured transmitted waveforms are similar. However, the magnitude of the leading negative edge of the waveform is overpredicted, and the trailing parts of the waveforms are not predicted well. At 1 MHz, although there are differences in amplitudes, the theory predicts that the transmitted waveform is almost a scaled version of that incident in conformity with the data.

Predictions and measurements of sound transmission through a periodic array of elastic shells in air.

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.

Predictions of angle dependent tortuosity and elasticity effects on sound propagation in cancellous bone.

The anisotropic pore structure and elasticity of cancellous bone cause wave speeds and attenuation in cancellous bone to vary with angle. Previously published predictions of the variation in wave speed with angle are reviewed. Predictions that allow tortuosity to be angle dependent but assume isotropic elasticity compare well with available data on wave speeds at large angles but less well for small angles near the normal to the trabeculae. Claims for predictions that only include angle-dependence in elasticity are found to be misleading. Audio-frequency data obtained at audio-frequencies in air-filled bone replicas are used to derive an empirical expression for the angle-and porosity-dependence of tortuosity. Predictions that allow for either angle dependent tortuosity or angle dependent elasticity or both are compared with existing data for all angles and porosities.

Laboratory studies of near-grazing impulsive sound propagating over rough water.

Acoustic impulses due to an electrical spark source (main acoustic energy near 15 kHz) have been measured after propagating near to the water surface in a shallow container resting on a vibrating platform. Control of the platform vibration enabled control of water wave amplitudes. Analysis of the results reveals systematic variations in the received acoustic waveforms as the mean trough-to-crest water wave amplitude is increased up to 7 mm. The amplitudes of the peaks corresponding to specular reflections are reduced and the variability in the tails of the waveforms is increased.