Ray-tracing prediction of optimal conditions for speech in realistic classrooms

Recent papers have discussed the optimal reverberation times in classrooms for speech intelligibility, based on the assumption of a diffuse sound field. Here this question was investigated for more ‘typical’ classrooms with non-diffuse sound fields. A ray-tracing model was modified to predict speech-intelligibility metric U₅₀. It was used to predict U₅₀ in various classroom configurations for various values of the room absorption, allowing the optimal absorption (that predicting the highest U₅₀)—and the corresponding optimal reverberation time—to be identified in each case. The range of absorptions and reverberation times corresponding to high speech intelligibility were also predicted in each case. Optimal reverberation times were also predicted from the optimal surface-absorption coefficients using Sabine and Eyring versions of diffuse-field theory, and using the diffuse-field expression of Hodgson and Nosal. In order to validate the ray-tracing model, predictions were made for three classrooms with highly diffuse sound fields; these were compared to values obtained by the diffuse-field models, with good agreement. The methods were then applied to three ‘typical’ classrooms with non-diffuse fields. Optimal reverberation times increased with room volume and noise level to over 1 s. The accuracy of the Hodgson and Nosal expression varied with classroom size and noise level. The optimal average surface-absorption coefficients varied from 0.19 to 0.83 in the different classroom configurations tested. High speech intelligibility was, in general, predicted for a wide range of coefficients, but could not be obtained in a large, noisy classroom.     

Normal modes of a poroelastic plate and their relation to the reflection and transmission coefficients

A poroelastic plate that obeys the Biot theory is considered. Compact new forms of its reflection and transmission coefficients, similar to those of the resonance scattering theory for an elastic plate, are derived. A numerical comparison of the reflection coefficient modulus with the plate normal modes, at low frequency, shows that a study of the reflection or transmission coefficient does not provide the same kind of information on the poroelastic plate than an investigation of guided leaky waves propagation.     

Numerical modelling of the radiation efficiency of asymmetrical structures

The radiation efficiency of a structural element is required by some models in order to predict its sound insulation. A common assumption is that the radiation on both sides of the element is the same. This is not true for asymmetrical structural elements like lightweight floors consisting of a beam-supported flat board. The radiation efficiency is larger on the beam side, because the beams act as exciters and increase the pressure level in the room. These different radiation efficiencies are calculated here for a two-dimensional cross-section by using finite elements and boundary elements. The obtained preliminary results illustrate that considering a single radiation efficiency can be a source of errors and that further investigation is required in order to improve predictions.     

Double-leaf microperforated panel space absorbers: A revised theory and detailed analysis

A double-leaf microperforated panel space absorber (DLMPP) is composed of two microperforated panels (MPPs) placed in parallel with an air-cavity in-between, without a back wall or any backing structure. This was proposed as a space sound absorber, which can be used for a sound absorbing screen or partition. A conventional MPP absorber with a rigid back wall is effective only around its resonance frequency, which is usually at middle frequencies, and not effective at low frequencies. However, a DLMPP can be effective also at low frequencies, because an additional sound absorption is produced by its acoustic flow resistance. In the authors’ previous work, theoretical analyses on the acoustic properties of a DLMPP were carried out using a simplified electro-acoustical equivalent circuit model. However, the equivalent circuit model includes an approximation, and more sophisticated theory is required for a better prediction and detailed discussion. In this paper, a revised theory for a DLMPP is presented: A Helmholtz integral formulation is employed to obtain a rigorous solution for more precise prediction of the absorptivity of a DLMPP. The result of the present revised theory is compared with that of the equivalent circuit model, and the difference between them is discussed. A parametric survey is made through numerical examples by the present revised theory to discuss its acoustic properties.     

A simple empirical model of polyester fibre materials for acoustical applications

A new empirical model has been developed by the authors to predict the flow resistivity, acoustic impedance and sound absorption coefficient of polyester fibre materials. The parameters of the model have been adjusted to best fit the values of airflow resistivity and sound absorption coefficient measured over a set of 38 samples. Calculated results are compared with normal incidence measurements carried out using two different techniques: the transfer-function method in an impedance tube (ISO 10534-2) and the free-field impulse response method (ISO 13472-1). Measurements performed on polyester fibre materials with different density and thickness values, and diameter ranging from 18 to 48 μm, are in good agreement with the predictions of the new model. It is concluded that the new model can predict the basic acoustic properties of common polyester fibre materials with any practical combination of thickness and density².     

A theoretical study of ultrasonic wave transmission through a fluid-solid interface

This article develops a model for the study of the transient ultrasonic waves radiated by a transducer in a liquid and transmitted into a solid through a plane interface. The method is an extension to the transient case, of the angular spectrum method previously developed for the monochromatic case. It is based on the decomposition of the ultrasonic field, in impulse plane waves. The radiated waveform is calculated at any point in the field by a simple summation of these impulse plane waves, where the propagation delay and the refraction have been taken into account. These plane waves are, first of all, delayed by an amount of time corresponding to the travel time up to the considered field point. The transmission through the plane interface is taken into account by using Snell refraction laws and transmission coefficients. In the obtained results all the waves previously described by other authors are highlighted: direct wave, edge waves, head waves as well as subsurface waves with a clear resolution between compression and shear waves.     

The acoustical properties of consolidated expanded clay granulates

The paper presents a systematic study of acoustic and non-acoustic properties of consolidated porous samples of expanded clay granulates. The effect of the particle size on the acoustic performance of consolidated expanded clays is investigated experimentally and theoretically. This work involves a comparison of the measured and predicted values of the absorption coefficient and normalised acoustic surface impedance data. It is demonstrated that the values of tortuosity and standard deviation in the pore size distribution do not depend significantly on the size of the material aggregate. An empirical expression which links the flow resistivity of the consolidated granular mix has been derived from the measured data. These results pave the way for the development of a simple practical model which will be able to link the acoustic properties of a consolidated granular mix with the characteristic particle dimension and the porosity data. These materials are structurally robust and easy to integrate in buildings and highway structures to control the levels of environmental noise and improve the acoustic quality of spaces.     

Guided wave dispersion curves for a bar with an arbitrary cross-section,a rod and rail example

Theoretical and experimental issues of acquiring dispersion curves for bars of arbitrary cross-section are discussed. Since a guided wave can propagate over long distances in a structure, guided waves have great potential for being applied to the rapid non-destructive evaluation of large structures such as rails in the railroad industry. Such fundamental data as phase velocity, group velocity, and wave structure for each guided wave mode is presented for structures with complicated cross-sectional geometries as rail. Phase velocity and group velocity dispersion curves are obtained for bars with an arbitrary cross-section using a semi-analytical finite element method. Since a large number of propagating modes with close phase velocities exist, dispersion curves consisting of only dominant modes are obtained by calculating the displacement at a received point for each mode. These theoretical dispersion curves agree in characteristic parts with the experimental dispersion curves obtained by a two-dimensional Fourier transform technique.     

The detectability of kissing bonds in adhesive joints using ultrasonic techniques

This paper concerns a study of the detectability of dry contact kissing bonds in adhesive joints using three ultrasonic inspection techniques. Conventional normal incidence longitudinal and shear wave inspection were conducted on dry contact kissing bonds using a standard damped ultrasonic transducer and an electro-magnetic acoustic transducer (EMAT) respectively. The detectability of the dry contact kissing bonds was assessed by calculating the reflection coefficient of the imperfect interface at varying loads for a number of surface roughnesses. A high power ultrasonic method was also employed to determine the non-linear behavior of the adhesive interface. The non-linearity of the interface was determined by the ratio of the amplitudes of the first harmonic and fundamental frequencies of the transmitted waveform. It was found that the high power technique showed the greatest sensitivity to these kissing bonds at low contact pressures, however at high loads conventional longitudinal wave testing was more sensitive. It was also noted that a combination of two or more techniques could provide enhanced information about the kissing bond compared to a single technique alone.     

Measurement of tortuosity in aluminum foams using airborne ultrasound

The slow compressional wave in air-saturated aluminum foams was studied by means of ultrasonic transverse transmission method over a frequency range from 0.2 MHz to 0.8 MHz. The samples investigated have three different cell sizes or pores per inch (5, 10 and 20 ppi) and each size has three aluminum volume fractions (5%, 8% and 12% AVF). Phase velocities show minor dispersion at low frequencies but remain constant after 0.7 MHz. Pulse broadening and amplitude attenuation are obvious and increase with increasing ppi. Attenuation increases considerably with AVF for 20 ppi foams. Tortuosity ranges from 1.003 to 1.032 and increases with AVF and ppi. However, the increase of tortuosity with AVF is very small for 10 and 20 ppi samples.     

Wave structure analysis of guided waves in a bar with an arbitrary cross-section

Both dispersion curves and wave structures, which are displacement distributions on a bar cross-section, are essential for guided wave NDEs. Theoretical dispersion curves and wave structures for a bar with an arbitrary cross-section are derived in this paper using a special modeling technique called the semi-analytical finite element method (SAFEM). The guidelines for guided wave NDEs of bar-like structures are also shown based on wave structure and modal analysis. First, the relationship between the dispersion curves and their corresponding wave structures were obtained for a square rod. Modes with longitudinal vibration have higher group velocities and torsional modes have constant phase and group velocities. Next, the relationship between the dispersion curves and wave structures for a rail are detailed. The rail is used to represent a bar with a complex cross-section. Similar to the square rod results, the rail's longitudinal modes have higher group velocities. However, the rail contains modes with local vibration. Finally, single mode detection and excitation techniques are introduced. A single mode can be obtained by detecting and exciting with a weighted function that corresponds to a specific mode's wave structure.     

Locating point of impact in anisotropic fiber reinforced composite plates

The conventional triangulation technique cannot predict the point of impact in an anisotropic composite plate because the triangulation technique assumes that the wave speed is independent of the direction of propagation which is not the case for anisotropic plates. An alternative method based on the optimization scheme was proposed by Kundu et al. [T. Kundu, S. Das, K.V. Jata, Point of impact prediction in isotropic and anistropic plates from the acoustic emission data, J. Acoust. Soc. Am. 122, 2007, 2057-2066] to locate the point of impact in plates by analyzing the time of arrival of the ultrasonic signals received by the passive sensors attached to the plate. In this paper, that objective function is modified further to overcome the inherent difficulties associated with multiple singularities and to maximize the efficiency of the acoustic emission data for multiple receiving sensors. With this modified objective function the impact point on an anisotropic composite plate is predicted from the acoustic emission data. Experiments are carried out by dropping steel and ping pong balls on a graphite-epoxy composite plate and recording acoustic signals by passive transducers adhesively bonded to the plate at three different locations. The impact point is predicted by the proposed method and compared with the actual location of impact.     

Numerical and experimental studies on the effects of stage risers

The acoustic effects of stage risers, especially on the sound of lower string instruments, are numerically and experimentally analyzed. To discuss the effects of the vibration of riser’s boards due to the mechanical force from an instrument, a structural-acoustical coupling approach is applied based on the mode expansion and the boundary element technique. Measurement results of the mechanical force from real instruments are used in the numerical study. The vibration of the top board of a riser affects the sound field only around the natural frequencies of the board and the cavity of the riser. In contrast, the acoustic diffraction due to the riser affects the sound field in a wide frequency range. The riser’s sideboard that faces to receiving points increases the sound pressure levels because it reflects waves diffracted at the riser’s edge to the front. To verify the numerical results, the effects of acoustic diffraction due to risers are especially investigated in detail through a scale model experiment.     

Minimization of finite beam effects in the determination of reflection and transmission coefficients of an elastic layer

A special data acquisition technique was applied to determine the acoustic plane-wave reflection and transmission properties of a plane-parallel aluminum plate. In this technique, the reflected and transmitted wavefield along a plane or line normal to the reflected or transmitted wave vector is recorded at equidistant receiver positions. The obtained traces are subsequently added up in the temporal domain to satisfy plane-wave conditions, thus effectively removing the effect of the limited beam of commonly used transducers. The agreement between plane-wave theory and experiment was found to be excellent, both in the temporal and in the frequency domain.     

Resonant acoustic scattering by a finite linear grating of elastic shells

Theoretical and experimental studies of the acoustic scattering by a finite linear grating of elastic cylindrical shells are performed. It is observed that a resonant interaction takes place at low frequency when the shells are very close to each other. This phenomenon can be clearly associated to the Scholte-Stoneley wave that propagates around a single shell. It is shown that each resonance of the Scholte-Stoneley wave is split up into N resonances when N shells compose the grating.     

Simultaneous determination of the ultrasound velocity and the thickness of solid plates from the analysis of thickness resonances using air-coupled ultrasound

A method that combines transmission of air-coupled ultrasound pulses through solid plates and amplitude and phase spectral analysis is presented. In particular, the method analyzes the first thickness resonance of the plates. The purpose is to determine, simultaneously, velocity and attenuation coefficient of the ultrasounds in the material and the thickness of the plate. This is especially useful when thickness can not be measured independently. The method is successfully applied to soft membranes, biological samples and FRP composites.     

Generalized eigenproblem of hybrid matrix for Floquet wave propagation in one-dimensional phononic crystals with solids and fluids

A method based on the solution to a generalized eigenproblem of hybrid matrix is presented for stable analysis of Floquet wave propagation in one-dimensional phononic crystals with solids and fluids. The method overcomes the numerical instability in the standard eigenproblem of transfer matrix, thus enabling Floquet waves to be determined reliably. The recursion relations of hybrid matrix for periodic multilayered structure of various solid and/or fluid phases are formulated. Dispersion relation and omnidirectional reflection for one-dimensional phononic crystals with solids and fluids are discussed. The frequency-thickness range of phononic bandgap is determined conveniently based on the Floquet wavenumbers.     

The use of an orthogonality relation for reducing the size of finite element models for 3D guided waves scattering problems

The scattering of guided waves by complex shaped defects in three-dimensional (3D) waveguides is considered. For such problems, analytical solutions do not exist, and modal decomposition techniques based on the establishment of the displacement and stress fields in the vicinity of the scatterer are quite heavy and complicated to perform. On the other hand, finite elements (FE)-based methods constitute a powerful way to obtain solutions, but they are known to be very memory consuming. This paper proposes a post-processing technique, based on a 3D orthogonality relation, to decompose a complex acoustic field produced by a scatterer and predicted by a 3D FE model, into plane waves, the amplitudes of which are quantified in the far field. This technique allows important reductions in the size of the FE models to be made. Two applications are presented to demonstrate the potential of this method. The first one concerns the scattering of the S₀ Lamb wave incident on a flat bottom circular hole. In this example, the amplitude of each mode is calculated via the orthogonality relation-based method, and compared to that obtained by simply monitoring the displacements at appropriate through-thickness positions. In the second application, the incident S₀ Lamb mode is converted into five modes scattered by a defect of complex geometry.     

Measurements of velocity and attenuation of leaky waves using an ultrasonic array

A new method of measuring velocity and attenuation of leaky surface waves is presented. A single focused transmitting transducer and linear receiving array in a pitch-catch arrangement are used in the proposed system. The spatial distribution of the acoustic field in the leaky wave is recorded by the array, and the parameters of the leaky wave can be obtained by processing the output waveforms. In comparison with existing material characterization systems, the mechanical scanning of the transducers is not used any more, and the measurement time is only limited by the time of the wave propagation and speed of the electronic data acquisition system.