Microstructures for lowering the quarter wavelength resonance frequency of a hard-backed rigid-porous layer

The frequency of the quarter wavelength resonance in the sound absorption spectra due to a thin hard-backed rigid-porous layer can be influenced by the design of its microstructure as well as its thickness. Microstructures considered include parallel arrays of identical cylindrical, slit-like or rectangular pores with deep sub-wavelength cross sections inclined to the surface normal, cylindrical annular pores, slits with log-normal width distributions, slits with cross sections that vary in a sinusoidal manner and slits with two distinct widths (dual porosity). Formulae that predict the bulk acoustical properties due to these microstructures are presented and used to explore the extent to which specific microstructures could be used separately or in combination to improve low-frequency absorption. Predicted normal incidence absorption coefficient spectra are compared using microstructural dimensions that would be feasible for 3D printing. The most effective microstructures are predicted to be slits with sinusoidally-varying widths, or with two distinct widths, inclined to the surface normal at 70°. The quarter wavelength layer resonances predicted in absorption coefficient spectra using these microstructures are comparable with those predicted for layers of the same thickness and bulk porosity having cylindrical pores with dead-end branches

Acoustic propagation over periodic and quasi-periodic rough surfaces

Transport noise is an ever present concern in urban areas affecting the quality of life for millions of people. The traditional noise barrier is not always a convenient method of noise control and can divide communities. Deliberate introduction of small scale (0.3 m high or less) periodic roughness on otherwise acoustically-hard ground has been investigated as a way of reducing noise near to a surface transport corridor. The roughness alters the effective surface impedance of the ground and thereby creates a 'soft' ground effect. Moreover the effectiveness if the rough surface is not reduced significantly if there are pathways through it. However the rough ground also creates surface waves that must be absorbed for the noise reduction to be effective. An alternative way of reducing surface waves may be to alter the periodicity. The effects of altering the periodicity of circular rods placed on a hard surface in the laboratory have been investigated. Predictions of multiple scattering theory and a boundary element code have been compared with the experimental data

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

Sound propagation through forests and tree belts

The potential use of forests or narrow belts of trees alongside surface transport corridors to reduce noise is often dismissed. This may be a consequence of conflicting experimental evidence and incomplete understanding of the various attenuation mechanisms involved. Important mechanisms include (a) destructive interference between sound travelling directly between source and receiver and reflected from the ‘acoustically-soft’ ground formed by decaying leaf litter, (b) the influence on this interference of loss of coherence due to the reverberant scattering by trunks and branches and (c) visco-thermal scattering by foliage. First the paper lists experimental evidence of significant attenuation due to forests and tree belts. Subsequently models for predicting the various contributions to overall attenuation are outlined. Predictions of the ‘soft’ ground effect are made using physically admissible ground impedance models. Incoherence due to trunk and branch scattering is modelled as enhanced turbulence. An empirical formula involving leaf area density and mean leaf size is used to predict foliage attenuation. Predictions that sum these contributions are compared with data. Regular or near-regular tree planting can cause ‘sonic crystal’ effects but the relatively sparse distributions of scatterers in realistic tree planting schemes means that the first band gap due to the periodic structure is weak. On the other hand the first pass band may be reduced and the second band gap can be enhanced by perturbing the tree locations with respect to periodic spacing. Finally results of numerical simulations showing the potential for traffic noise reduction by narrow tree belts are outlined

Meteorological effects on the noise shielding by low parallel wall structures

Numerical calculations, scale model experiments and real-life implementations have shown that the insertion of a closely spaced array of low parallel walls beside a road is potentially a valuable road traffic noise abatement technique. However, all previous studies have assumed a non-refracting and non-turbulent atmosphere. This study carries out a numerical assessment of the extent to which the noise reduction is preserved in the presence of wind gradients and turbulence. Several full-wave calculation techniques have been used to model the noise reduction provided by parallel walls subject to moderate and strong winds, and in a turbulent atmosphere. While meteorological effects do not deteriorate the insertion loss of the parallel wall array in the low frequency range, higher sound frequencies are strongly negatively affected. These numerical results are compared to the noise shielding of traditional highway noise walls with different heights including refraction

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

Ground characterization for JAPE

Above-ground propagation modelling at the JAPE (Joint Acoustic Propagation Experiment) site requires a reasonably accurate model for the acoustical properties of the ground. Various models for the JAPE site are offered based on theoretical fits to short range data and to longer range data obtained with random noise and pure tones respectively from a loudspeaker under approximately quiescent isothermal conditions

Analytical Approximations for Sub Wavelength Sound Absorption by Porous Layers with Labyrinthine Slit Perforations

Analytical approximations for the acoustical properties of a rigid-porous matrix perforated by labyrinthine slits are developed using classical theories for sound propagation in tortuous slits and for sound absorption by double porosity materials. Predictions of enhanced low-frequency absorption result from a combination of pressure diffusion and labyrinth tortuosity if there is a high permeability contrast between the matrix and the labyrinthine slit. Additional insight into the predicted influence of the properties of the porous matrix is gained by considering the matrix porosity to be provided by inclined micro-slits. Extra tortuosity can be introduced by alternating the width of the labyrinthine slit. An alternating-width vertical-wall labyrinth perforation is predicted to lead to low-frequency absorption peaks in a relatively low-flow-resistivity and low-porosity matrix. Example predictions, even when using underestimates of labyrinth tortuosity, demonstrate the potential of labyrinthine slit perforations for achieving narrowband deep sub wavelength absorption peaks from thin hard-backed porous layers

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 semicylindrical 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