Index of content:
Volume 83, Issue 3, March 1988

Speech understanding and aging
View Description Hide DescriptionThe increasing age of the population forecasts a corresponding increase in the number of people suffering from hearing loss and who therefore have difficulty with speech communication. This article, prepared by the Working Group on Speech Understanding and Aging for the Committee on Hearing,Bioacoustics, and Biomechanics, discusses a number of the factors that act on the elderly listener’s ability to understand speech, including physiological aging, changes in cognitive ability, noisy signals, and sensory aids. Both sensory and perceptual processes are considered.

Wave propagation in media with time‐dependent spatial inhomogeneities
View Description Hide DescriptionThe propagation of waves in a medium with time‐dependent spatial inhomogeneities in its velocity profile is given a rigorous integral equation formulation for source and incident field descriptions. This is in the spirit of Rayleigh, whose aim was to bypass complications arising from boundary conditions. A perturbation expansion, correct to all orders, is then obtained with the aid of a simple identity, for the two cases: (i) weak scatterers and (ii) strong scatterers. It is shown that for case (i) a correction term has to be added to previous results already in second order—this seems to have been overlooked until now. For case (ii), the expansion obtained here is new—the reason for this gap in the existing literature is discussed. With these results, expressions are derived for the wavefunctions when the inhomogeneity in the medium is due to distributions of moving particulates. These new closed‐form time‐dependent approximations exhibit explicitly the appropriate Doppler behavior. The application of this formulation to other cases, such as media with random inhomogeneities, is discussed.

Transmission of guided precursor curvilinear waves in layered media
View Description Hide DescriptionA closed‐form solution is obtained for the deformation along a guided impulsive precursor wave that propagates in layered media bounded, transversely, by a free surface. Specifically, this article deals with the diffraction of an ideal elastic longitudinal wave, generated by stress boundary conditions, as it impinges at grazing incidence on the free surface of an array of layers arranged at a right angle to the free surface. Two examples of boundary‐value problems relevant to this configuration are solved. One concerns an impulsive load applied uniformly and radially to the entire cylindrical surface of an infinite cavity drilled into a half‐space made of layers running in the radial direction. The other concerns an impulsive load applied uniformly to one of the two boundaries of a Cartesian quarter‐space made of layers running at a right angle to the free boundary of the quarter‐space. Basic concepts employed in the determination of the material response along the leading wave are based on geometrical strong discontinuity formulas for computational wave motions and multi‐dimensional wavecharacteristics formulations for solids. Refraction, reflection, and diffraction phenomena associated with the curvilinear guided precursor wave as it interacts with the interfaces of the layers are revealed explicitly by the proposed method of solution. For the cases considered here, criteria are established in order to predict stress amplification or attenuation at an interface—the usual prediction criterion based on the uniaxial strain plane wave is not valid here. Mathematical avenues used in this article can be extended to materials with nonelastic and nonlinear behavior.

Validity of linear acoustics for prediction of waveforms caused by sonically moving laser beams
View Description Hide DescriptionThe question is raised as to whether the analysis of the generation of sound by a laser beam moving over a water surface at the sound speedc for an interminable time period requires consideration of nonlinear effects. A principal consideration in this regard is whether the linear acousticstheory predicts a pressure waveform that is bounded in the asymptotic limit when the laser irradiation time is arbitrarily large. It is shown that a bounded asymptotic limit exists when the upper boundary condition corresponds (as is more nearly appropriate) to that of a pressure release surface, but not when it corresponds to that of a rigid surface. The asymptotic solution to the appropriate inhomogeneous wave equation is given exactly for the former case, and it is shown that the highest asymptotic amplitudes, given specified laser power and beam radius a, occur in the limit of a very small light absorption coefficient μ. In this limit, the peak amplitude is independent of μ and occurs at a depth of 0.88/μ. An approximate solution for the pressure waveform at intermediate times establishes that the characteristic time for buildup to the asymptotic limit is of the order of 2.5/(cμ^{2} a). If this time is substantially shorter than the time that a plane‐wave pulse with the asymptotic waveform would take to develop a shock wave, then accumulative nonlinear effects are of minor importance.

The input power of distributed sources
View Description Hide DescriptionAn alternative to the conventional method of calculation of net power radiated by flux integration is presented. This method allows power radiated by distributed sources to be calculated by an integral only over the source region. Furthermore, the method is applicable to calculation of radiation from distributed sources in flow. Examples of power radiation, for the geometry of the finite cylinder, are given for both stationary and moving media. Analytic results are presented for the long wavelength approximation.

Combined integral equation formulation and null‐field method for the exterior acoustic problem
View Description Hide DescriptionThe numerical implementation of a combined integral equation and null‐field method used to solve the exterior Neumann problem [D. S. Jones, Q. J. Mech. Appl. Math. X X V I I, 129 (1974)] is presented here. The exterior Helmholtz integral equation is solved on the radiating or scattering surface, and the irregular frequencies are eliminated up to a given irregular frequency f _{ M } through the use of M additional null‐field equations. An impedance matrix, defined on the object surface, is then obtained that can be used as an exact radiation condition in a finite‐element code. The program and the numerical examples presented here are specialized to axisymmetrical problems. A purely null‐field method is implemented and simple rules are defined that display its failure when applied to high aspect‐ratio objects and (or) in the high‐frequency range. Similar, but less restricting rules are used to specify the numerical limitations of Jones’ technique. Besides, a few theoretical considerations clarify the role played by the additional null‐field equations in the elimination of the irregular frequencies and help in performing accurate high‐frequency computations for surfaces such as the circular cone and the finite circular cylinder.

Generation and detection of high‐order harmonics in liquids using a scanning acoustic microscope
View Description Hide DescriptionThe nonlinear generation of harmonics by high‐power focused acoustic beams in liquids has been investigated. A transmission mode acoustic microscope using focal planedetection has been used for high‐harmonic signal sensitivity. Detection of up to the 14th harmonic in ethanol has been achieved at an emission frequency of 15 MHz. Measurements show that signal in all harmonics tends to saturate at a very high emitted power. At lower power, harmonics varied as P ^{ n } _{1}, where P _{1} is the emitted power and n the harmonic number. Resolution improvement of the acoustic microscope by receiving at harmonic signals has also been demonstrated. The resolution has been shown to increase as (n)^{1/2} for reception at the nth harmonic, in good agreement with focused Gaussian beam theory. A nonlinear resolution improvement by a factor of 3 has been obtained.

Hybrid (ray)‐(parabolic equation) analysis of propagation in ocean acoustic guiding environments
View Description Hide DescriptionAcoustic ray theory provides an effective means for predicting propagation in general environments. Ray theory fails in the vicinity of caustics and must there be augmented by uniform asymptotic treatment. However, even such corrections are inadequate at long ranges in a ducting channel, where the caustics due to multiple reflected and/or refracted rays accumulate at locations near the duct axis. To repair this deficiency of ray acoustics, the caustic forming ray spectra have previously been replaced by guided modes in a self‐consistent ray‐mode scheme. It is now shown that the troublesome ray spectra at long ranges can be replaced as well by a narrow‐angle parabolic equation (PE) approximation to the full pressure field. Taken together, the hybrid ray‐PE form can be regarded either as correcting via PE the failure of ray acoustics near the guiding axis or as removing the narrow‐angle restriction from PE by filling the wide angle spectra with rays. The theory is developed first for a range‐independent surface duct, and then for a range‐dependent guiding‐to‐antiguiding transition. Unlike the adiabatic modes, the numerical PE algorithm can accommodate changes from guiding to antiguiding. The analogous problem of propagation along a circular concave boundary and along a boundary with concave–convex transition is treated briefly in the Appendix.

Comparison of perturbation theories for rough‐surface scattering
View Description Hide DescriptionRayleigh–Rice perturbation theory is compared with the more rigorously derived perturbation theory based on the extinctiontheorem (or extended boundary condition) for the case of Dirichlet boundary conditions. Numerical calculations for a sinusoidal surface profile show that the two theories give identical results when carried out to high order. This is true even when the two series do not seem to converge numerically. Numerical convergence of the two series is found in several cases, including some cases in which the Rayleigh hypothesis is invalid. For surfaces of arbitrary shape, the two perturbation series appear superficially to differ at third and higher order. It is shown, however, that a reciprocity transformation of one series makes it identical to the other through fifth order. Finally, it is shown that reciprocity holds in both perturbation theories, establishing analytically the equivalence of the two theories at least through fifth order. These results are surprising given the limited regime of validity for the Rayleigh hypothesis compared with the extinctiontheorem. They are useful in that they justify the use of perturbation formulas obtained from the Rayleigh hypothesis in lieu of the more complicated formulas obtained from the extinctiontheorem. While these results do not establish the identity of the two perturbation methods to all orders or settle questions as to their convergence, they do provide some theoretical clues to the nature of these problems.

Optical levitation of bubbles in water by the radiation pressure of a laser beam: An acoustically quiet levitator
View Description Hide DescriptionThis article demonstrates the stable levitation of single small gas bubbles in water in a downward directed visible laser beam. The natural upward buoyancy of the bubbles was counteracted by the optical radiationpressure of the light beam, whose optical power ranged from 1–3.5 W. The sizes of the levitated bubbles ranged from 10–30 μm in radius. (The term ‘‘levitation’’ is synonymous to ‘‘trapping’’ even though the radiation force must be directed downward on the bubble.) For horizontal stability of the levitated bubble, the laser was operated in a mode giving an irradiance minimum at the center of the laser beam. An approximation is derived for the force on the bubble in the direction of the beam axis; it includes only the contribution to the radiation pressure due to the total‐reflection region of the bubble’s surface (which appears to be the major contribution). The resulting estimate of the power required to levitate is consistent with observations. Optical levitation is a quiet alternative to acoustical levitation that could facilitate the measurement of weak acoustic emissions from isolated bubbles.

Quantitative evaluation of microfracture due to disbonding by waveform analysis of acoustic emission
View Description Hide DescriptionSurface motions due to a disbonding of a stainless overlay welded on base metal of a pressure vessel have been measured by the use of a commercially available flat‐frequency displacement transducer. The experimental result showed that a buried tensile crack (penny‐shaped crack) can be generated by hydrogen‐induced disbonding of stainless weld overlay from base metal.Acoustic emission(AE) was found to be very sensitive and effective to monitor the disbonding. Some tens of AE events could be located by using two meaningful Δt values. The detected waveforms due to the disbonding exhibited interesting variation as a function of the distance between the source epicenter and the transducer location. On the basis of the theory of elastodynamics and dislocation models, simulation analysis was made for surface motions due to a penny‐shaped crack parallel to the stress‐free surface in a half‐space. Simulated waveforms were obtained as a function of the distance between the epicenter and the observation position. Comparison of the detected and simulated waveforms indicated remarkable agreement in the early time response. This agreement demonstrates the applicability of the transducer and the present simulation analysis to quantitative waveform analysis relating to fundamental AE work. It is shown that quantitative analysis of microfracture due to the disbonding can be readily made by comparison of experimentally measured surface displacements and theoretically calculated surface motions.

Evaluation of vertical vibration given to the human foot
View Description Hide DescriptionThe effects of acceleration amplitudes and frequencies of vertical foot vibration on mechanical and sensation responses were studied in two sets of experiments. The first experiments determined the mechanical characteristics of the foot in three seated subjects at frequencies between 5 and 1000 Hz, in terms of the driving point mechanical impedances and acceleration transmission ratios between the foot and lower leg. In the second set of experiments, sensation scales for foot vibrations were determined in ten seated subjects at octave center frequencies between 8 and 400 Hz, which involved equal sensations of continuous and impulsive motions, sensation magnitudes, and rating of five successive categories of sinusoidal motion. Contours of mechanical and sensational responses are presented. Using the results obtained, a foot response meter was made and used in a field survey to evaluate foot vibration.

Community response to noise: A review of factors influencing the relationship between noise exposure and reaction
View Description Hide DescriptionSocial surveys of the relationship between noise exposure and the subjective reactions to it were reviewed. This review indicated that remarkably similar results have been obtained across different nationalities with different measurement techniques. Only a small percentage (typically less than 20%) of the variation in individual reaction is accounted for by noise exposure. Analysis of potential errors in both measurement of noise and reaction suggests that elimination of errors would only slightly increase the observed correlations. Variables, such as attitude to the noise source and sensitivity to noise, account for more variation in reaction than does noise exposure. The weaker relationship between noise exposure and attitude than between reaction and attitude suggests that the attitude/reaction relationship is not entirely due to noise exposure causing a change in attitude itself. Noise/reaction correlations based on individual data are significantly lower in studies of impulsive noise than nonimpulsive noise. This may be caused, in part, by the restricted range of noise exposure studied in some socioacoustic investigations of impulsive noise. However, the significantly higher correlations of attitude and reaction in impulsive noise studies suggest that attitude plays an even larger part, while noise exposure plays a lesser part in determining reaction to impulsive noise, relative to nonimpulsive noise.

Design charts for sound absorber layers
View Description Hide DescriptionBased on the experience that the acoustic characteristic variables Γ_{ a n }, Z _{ a n } of fibrous absorber materials can be expressed by one nondimensional variable E=fρ_{0}/Ξ with sufficient accuracy for survey calculations, the sound absorption of absorber layers has been calculated and plotted in a way that permits at the same time the reconstruction of the frequency curve of sound absorption for individual absorbers, as well as quantitative answers on questions of general interest, which up to now have been discussed in literature mostly in qualitative manner only. The sound field was assumed to consist of plane waves, with either normal, oblique, or diffuse incidence. The absorber layers could be either locally reacting or bulk reacting. The same holds for air cavities that could exist between the absorber layer and the rigid wall. A general recurrence calculus for computation of the input impedance or the reflection factor and absorption of multilayer arrangements was presented. Some numerical examples of its application were shown, in conclusion.

Probability density functions of sums of sinusoidal waves having nonuniform random phases and random numbers of multipaths
View Description Hide DescriptionThe purpose of this article is to study the first‐order statistics (i.e., probability density functions and moments) of finite sums of cosines and of sines, each having nonuniformly distributed random phases governed by a von Mises probability density function. The number of sinusoids N is, first, taken to be deterministic, but arbitrary, and, second, taken to be a discrete random variable governed by a negative binomial distribution (which includes the Poisson distribution as a special case). Since the phase probability density functions are nonuniform, the probability density functions of the cosine sum and the sine sum are different. The probability density functions of these cosine and sine sums are evaluated using Fourier series expansions whose Fourier coefficients are sampled values of the corresponding characteristic functions. Representative numerical calculations have been carried out to illustrate the general features. The corresponding moments have also been evaluated. Finally, the behavior of the probability density functions and moments when N approaches infinity in the deterministic situation and 〈N〉 approaches infinity in the random situation is investigated, the former involving the theory of stable probability density functions, the latter involving the theory of infinitely divisible probability density functions.

Underwater noises: Statistical modeling, detection, and normalization
View Description Hide DescriptionKnowledge of the noiseprobability density function (PDF) is central in signal detection problems, not only for optimum receiver structures, but also for processing procedures such as power normalization. Unfortunately, the statistical knowledge must be acquired since the classical assumption of a Gaussian noise PDF is often not valid in underwater acoustics. In this article, statistical modeling is studied using a Gaussian–Gaussian mixture (GGM) for three different underwater noisedata sets. It is shown that one of them can be adequately described by a Gaussian–Gaussian mixture, one is very close to a Gaussian model and is described by a mixture with a very small perturbating term, whereas the third one seems closer to a nonstationary version of the Middleton class‐A model. The first noise sample is also studied with emphasis on the normalization needed in the receiver in order to achieve a constant false alarm probability and on the optimal receiver structure for the detection of a deterministic signal. It is also shown that the classical noise power estimate, calculating the L ^{2} norm of the observation vector, is a good approximation of the square of the maximum likelihood estimator of the noise amplitude for the Gaussian–Gaussian mixture. The notion of noise alone reference is investigated and the performances of normalized test functions using different power estimates are studied. The principal result of our preliminary study is that the use of the receiver associated with the mixture model can lead to improvements with respect to the classical matched filter, this improvement being measured in terms of receiver operating characteristics (ROC) curves.

Direction of arrival estimation by eigenstructure methods with imperfect spatial coherence of wave fronts
View Description Hide DescriptionEigenstructure/subspace methods for direction of arrival estimation are only applicable when each wave front contributes a rank one component to the array covariance. This implies that the wave fronts need to have perfect spatialcoherence. In several practical situations where the wave fronts may only have partial spatialcoherence, eigenstructure algorithms show poor performance such as overestimation of the number of sources, bias, and reduced accuracy and resolution in estimating the directions of arrival. In this article, the performance degradation due to partial spatialcoherence is studied and a new approach is proposed that exploits the underlying coherence model to yield asymptotically exact estimates. For finite data, this method provides improved results only when the number of snapshots exceeds a certain threshold. Results of computer simulations are also presented.

Broadband signal analysis with the smoothed pseudo‐Wigner distribution
View Description Hide DescriptionSeveral nonstationary broadband signals, a voiced speech signal, and flute signals are studied with the short time Fourier transform(STFT) and the smoothed pseudo‐Wigner distribution. The time frequency description of flute signals is more precise with the smoothed pseudo‐Wigner distribution, and the instant of glottal closure can be reached with better precision in the voiced speech signal. The smoothed pseudo‐Wigner distribution is more suitable for these signals than the STFT.

First Born and Rytov approximations: Modeling and inversion conditions in a canonical example
View Description Hide DescriptionFirst Born and, more recently, first Rytov approximations are widely used for solving complex forward and inverse seismic scattering problems. The exact pressure‐field response from a one‐dimensional velocity slab included in an infinite constant velocity medium is expressed analytically. This solution is used for testing these two approximations in modeling and in inversion. Conditions of applicability and parameter estimates lead to the following results: The first Rytov approximation is best suited for modeling and inverting the transmitted, or forward scattered, part of the wave field, whereas the first Born approximation is best suited for modeling and inverting the primary reflected, or backscattered, part of the wave field. If the long wavelength condition holds, linearization of the field with respect to slowness squared is preferable over linearization with respect to slowness, allowing for a very large velocity contrast between the slab and the reference medium. However, if the weak heterogeneity condition holds (i.e., small velocity contrast), the linearization choice is reversed. Numerical examples show and display these differences quantitatively.

Simulation of auditory–neural transduction: Further studies
View Description Hide DescriptionA computational model of mechanical to neural transduction at the hair cell–auditory‐nerve synapse is presented. It produces a stream of events (spikes) that are precisely located in time in response to an arbitrary stimulus and is intended for use as an input to automatic speech recognition systems as well as a contribution to the theory of the origin of auditory‐nerve spike activity. The behavior of the model is compared to data from animal studies in the following tests: (a) rate‐intensity functions for adapted and unadapted responding; (b) two‐component short‐term adaptation; (c) frequency‐limited phase locking of events; (d) additivity of responding following stimulus‐intensity increases and decreases; (e) recovery of spontaneous activity following stimulus offset; and (f) recovery of ability to respond to a second stimulus following offset of a first stimulus. The behavior of the model compares well with empirical data but discrepancies in tests (d) and (f) point to the need for further development. Additional functions that have been successfully simulated in previous tests include realistic interspike‐interval histograms for silence and intense sinusoidal stimuli, realistic poststimulus period histograms at various intensities and nonmonotonic functions relating incremental and decremental responses to background stimulus intensity. The model is computationally convenient and well suited to use in automatic recognition devices that use models of the peripheral auditory system as input devices. It is particularly well suited to devices that require stimulus phase information to be preserved at low frequencies.