Index of content:
Volume 81, Issue 1, January 1987

Resonance theory of elastic waves ultrasonically scattered from an elastic sphere
View Description Hide DescriptionThe interaction of elastic waves incident on an elastic spherical inhomogeneity is studied in detail, particularly in the resonancescattering regime. Incident and scattered compression and shear waves in lossless elastic media separate into three modes: a p mode for the compression wave, and s and t modes for the shear wave. A description of how the acoustic energy redistributes among these modes during the scattering process is contained in the scattering matrix that we separate here into background and resonance portions for the two extreme cases of a nearly soft and a nearly rigid elastic sphere. This produces farfield scattering amplitudes which are a superposition of a background contribution felt to contain reflected and Franz‐type circumferential waves and a resonance contribution that seems to contain refracted, Rayleigh, and whispering gallery waves. Limiting cases (a fluid sphere in an elastic medium, an elastic sphere in a liquid medium, and a fluid sphere in a fluid medium) are extracted from these results to show agreement with previous work. Plots show the background and resonance portions of the scattered amplitudes and their connections with the poles of the scattering amplitude in the complex frequency plane. The methodology of the resonancescattering theory (RST) is summarized with a very general yet basic example of importance in acoustic/ultrasonics and elastodynamics/NDE, which contains all earlier situations.

Geometrical strong discontinuity formulas for computational wave motions
View Description Hide DescriptionGeometrical, strong discontinuity formulas are obtained here in order to accommodate multidimensional wavecharacteristicequations which are the interior differential equations on wave surfaces. As they stand, the multidimensional wavecharacteristicequations are integrable only in a weak material motion where discontinuities across waves are allowed in first partial derivatives of continuous dependent variables. This paper deals with the extension of these equations in order to make them also compatible with strong material motion where the dependent variables are themselves discontinuous across the wave surfaces. In particular, the discontinuity formulas are obtained for the characteristics computational scheme on Huygen’s wavelets. For this purpose, strong discontinuity formulas are derived which do not depend on the motion of a surface. The derivation is guided by the intrinsic properties of the wavecharacteristicequations and is based on concepts of differential geometry in conjunction with Hadamard’s basic proposition of a jump across a surface of discontinuity. The known concepts of differential geometry needed for the analysis are obtained directly from the propagation derivative of the two‐point parallel propagator tensor by a unified approach in non‐Riemannian geometry.

Torsional dispersion relations in a radially dual elastic medium
View Description Hide DescriptionExact dispersion relations for torsional waves are derived for a system consisting of an elastic cylindrical core embedded in an elastic medium having different material properties. Dispersion curves are presented as a function of an aspect ratio and ratios of material properties. Cutoff wavelengths dependent on material properties are established. The results are compared with a previous solution obtained using a simplified approximate model. While the approximate model is seen to yield the correct range of phase velocities, the resulting dispersion relations are shown to be inaccurate for relatively short wavelengths in systems for which the surrounding material is markedly stiffer or denser than the core. The approximate model is also shown to be overly restrictive in predicting cutoff wavelengths.

Radiation from S H‐wave line sources embedded in layered media having rough interfaces
View Description Hide DescriptionA method for determining the radiation characteristics of an S H‐wave line source embedded in a layered medium having rough interfaces is herein described. The presented technique utilizes the plane‐wave spectral decomposition of the relevant fields in the framework of the extended boundary condition method. It is also shown how the equations derived for the general case reduce considerably when the interfaces are periodically rough. Extensions of the problem solved here have been briefly mentioned, and the presented solution technique should find application in several areas involving the propagation of elastic waves.

Phase gradient method of measuring the acoustic impedance of materials
View Description Hide DescriptionA free‐field method using a point source has been developed to measure the normal specific impedance of porous materials. The phase gradient is measured as a function of distance along the normal to the materials passing through the point source. The phase gradient is obtained from a two‐microphone probe. The phase and amplitude of the complex reflection coefficient are used as constants adjusted for the best fit to experimental results using a standard optimization technique. Results are obtained on layers of fiberglass and polyurethane foam in the frequency range between 250 and 400 Hz. Good agreement is found when the measured results are compared to the predictions of Delany and Bazley [Appl. Acoust.3, 105–116 (1970)]. The method has the advantages of requiring a minimum of instrumentation and is particularly adapted to measurements at low frequencies.

Theoretical description of a focused Gaussian ultrasonic beam in a nonlinear medium
View Description Hide DescriptionThe focusing of an ultrasonic beam is described by beginning with a nondimensional form of the nonlinear waveequation. The method of successive approximations is used to arrive at analytical expressions for the fundamental and the second harmonic of an initially sinusoidal wave with a Gaussian amplitude distribution. The results show that both the fundamental and the second harmonic retain the Gaussian distribution even through the focus. Plots are given of the fundamental and second harmonic Gaussian coefficients, their radial amplitude distributions, their beamwidths, and their pressure amplitudes as a function of distance from a focusing transducer. Acoustic power in the second harmonic as a function of propagation distance in a lossless medium also is evaluated.

A simple model of a vapor bubble
View Description Hide DescriptionA simple yet reasonably accurate vapor bubble model based on switching between an empty bubble and a gas bubble is introduced. The switching bubble wall velocity is determined by adjusting the theoretical model to experimental data. A comparison with gas bubble models is given.

Impedance of grass‐covered ground at low frequencies measured using a phase difference technique
View Description Hide DescriptionAlthough the impedance of natural outdoor ground surfaces has been measured extensively at frequencies above about 200 Hz, measurements at lower frequencies are scarce and have been inaccurate. To overcome some of the difficulties at low frequencies, a two‐microphone, phase difference technique to obtain the ground impedance has been adapted. A point source is suspended above the ground and the sound field is measured with two microphones along the vertical line below the source. The magnitude and phase of the reflection coefficient, and hence the impedance, is inferred from the variation of the phase difference between microphones as a function of height above the ground surface. Measurements were made in the range 25–300 Hz on flat, grass‐covered ground, free of reflecting objects. The results obtained are consistent with recent seismic/acoustic coupling experiments and theoretical calculations based on layered poroelastic frame models for the ground. In particular, the measured results show evidence for fine structure expected from the layered nature of the ground.

Estimating horizontal coherence in the ocean
View Description Hide DescriptionThe horizontal and vertical coherence that results from scattering of acoustic waves in the ocean cannot, in general, be treated separately. The governing equation couples the two effects. If, however, changes in horizontal and vertical coherence occur on widely different range scales, approximate decoupling is possible. Here we shall show what conditions are necessary for this decoupling and, using a two‐scale embedding procedure, derive an equation governing the horizontal coherence in terms of effective horizontal scattering functions. Several special cases will be considered.

Underwater noise due to rain, hail, and snow
View Description Hide DescriptionThe spectra of underwater noise generated by rain,hail, and snow have been measured in a lake at a depth of 35 m, for a variety of atmospheric conditions. Rainnoise spectra, for light winds (<1.2 m s^{−} ^{1}), have a sharp peak at 13.5 kHz with a steep falloff (∼60 dB/oct) on the low‐frequency side and a more gradual falloff (9 dB/oct) on the high‐frequency side. A quasi‐flat spectral regime exists in the frequency interval 2–10 kHz. Wind, for speeds increasing above 1.2 m s^{−} ^{1}, progressively rounds the peak. The spectral level at 15 kHz (i.e., near the peak) shows a linear dependence on the log of the rain rate with wind speed as a parameter. Correlation of the rainnoise spectra with raindrop‐size distributions suggests that low frequencies are generated by the larger drops, although this aspect of the problem needs further work. Hailnoise spectra have rounded maxima appearing between 2 and 5 kHz with an approximately 10‐dB falloff on each side. The spectrum of underwater soundgenerated by gently falling snow shows a linear increase in level, averaging 5 dB/oct, when plotted against the log of frequency.

Propagation of sound in vibrationally excited N_{2}/H_{2} mixtures
View Description Hide DescriptionMeasurements of the resonant reverberation of sound in a closed tube have shown an amplification of the sound following the rapid excitation of the gas by an electrical discharge. The measurements have been corrected for tube losses due to viscosity and thermal conductivity and the corrected amplification studied as a function of energy in the electrical discharge, sound frequency, gas pressure, and percentage of H_{2} in the mixture. The translational temperature during the relaxation process is monitored by measuring the sound speed in the tube. Amplification is attributed to the relaxation of the vibrational temperature which is left elevated to several thousand degrees following the electrical discharge. Experimentally measured gains have been compared to values previously predicted.

On the acoustic slow wave in air‐filled granular media
View Description Hide DescriptionThe relationship between the slow wave predicted by the rigid‐frame limit of the Biot theory propagation in a fluid‐saturated poroelastic solid and the modified‐fluid wave predicted by classical theory for propagation in a rigid porous solid is examined. An anomalous difference between the two formulations of the viscodynamic operator for noncylindrical pores is exposed and explored. The pore shape factor ratio previously introduced in an extension of the classical approach is redefined. The classical rigid‐frame formulation is shown to give good agreement with measured data on air‐filled spherical lead shot and sands in the audio‐frequency range. Modifications to the Biot viscodynamic operator, and the associated low‐frequency/low‐permeability approximations, that ensure consistency with the classical formulation, are proposed.

Frequency discrimination in the mammalian cochlea: Theory versus experiment
View Description Hide DescriptionA three‐dimensional hydroelastic model for the motion in the cochlea is analyzed for the case of a pure‐tone forcing. It is shown to agree well with experiment, including moderate intensity tuning curves and the frequency map, for a variety of mammals. In doing this, the parameters that are needed for each animal are geometric; thus the theory is easy to apply. The analysis also indicates that the fluid viscosity is the dominant dissipation mechanism, at least for moderate to high frequencies.

Threshold characteristics of the human auditory brain stem response
View Description Hide DescriptionAuditory brain stem responses (ABRs) were recorded from ten normal‐hearing subjects in response to 100‐μs clicks from a TDH 49 earphone at a rate of 48 pps and at levels randomly varied in 2‐dB steps between 34 and 52 dB p.e. SPL. At each level, 10 000 epochs were averaged with use of a weighted concept and a running estimate was made of the signal‐to‐noise ratio (SNR). This quantity was used to detect the presence of the ABR and the median threshold was found at 38 dB p.e. SPL. The mean averaged background noise level was 11.3 nV_{rms}, and the ‘‘true’’ ABR_{rms} amplitude function crossed this value at 35.5 dB p.e. SPL, which indicates the level where the SNR=1. By extrapolation, it was found that the ABR amplitude became zero at 32 dB p.e. SPL. The perceptual thresholds of the click were estimated by means of a modified block up–down procedure, and the median value was found at 33 dB p.e. SPL. The slope of the amplitude function and the magnitude of the averaged background noise are the two factors responsible for the ABR threshold sensitivity, which thus depends on both physiological and technical parameters. Therefore, these have to be considered together with the method of detection when the ABR is used to indicate the hearing sensitivity.

Binaural versus monaural loudness: Supersummation of tone partially masked by noise
View Description Hide DescriptionA series of three experiments used the method of magnitude estimation to examine binaural summation of the loudness of a 1000‐Hz tone heard in the quiet and against various backgrounds of masking noise. In the quiet, binauralloudness as measured in sones, is twice monaural loudness. Two conditions of noise masking acted to increase the ratio of binaural/monaural loudness in sones above 2:1—that is, to produce supersummation. (1) When tone was presented to both ears, but masking noise to just one ear (dichotic stimulation), the loudness of the binaural tone was 30%–35% greater than the sum of the loudnesses of the monaural components. This increase in summation provides a suprathreshold analog to increases in threshold sensitivity observed with dichotic stimulation (masking‐level differences). (2) Supersummation was also evident when tone and noise alike were presented to both ears (diotic stimulation); here, the binaural tone’s loudness was 10%–25% greater than the sum of the monaural components. The increase in summation with diotic stimulation may be related to the characteristics of binaural summation of the noise masker itself.

Comparative learning of pitch and loudness identification
View Description Hide DescriptionThis study investigated possible similarities between the ability to identify pitches and the ability to identify loudnesses. Systematic training of musically naive subjects indicated that frequency identification performance improves at about the same rate as intensity identification performance. Examination of frequency and intensity identification behavior of musically trained subjects showed that their ability to code pitch information efficiently does not generalize to an ability to encode loudness information more efficiently than untrained subjects. Intensity identification training curves of musically trained and untrained subjects are similar, but final performance levels are below frequency identification performance levels exhibited by musically trained subjects, especially those with absolute pitch.

Temporal gap resolution in listeners with high‐frequency sensorineural hearing loss
View Description Hide DescriptionTemporal gap resolution was measured in five normal‐hearing listeners and five cochlear‐impaired listeners, whose sensitivity losses were restricted to the frequency regions above 1000 Hz. The stimuli included a broadband noise and three octave band noises centered at 0.5, 1.0, and 4.0 kHz. Results for the normal‐hearing subjects agree with previous findings and reveal that gap resolution improves progressively with an increase in signal frequency. Gap resolution in the impaired listeners was significantly poorer than normal for all signals including those that stimulated frequency regions with normal pure‐tone sensitivity. Smallest gap thresholds for the impaired listeners were observed with the broadband signal at high levels. This result agrees with data from other experiments and confirms the importance of high‐frequency signal audibility in gap detection. The octave band data reveal that resolution deficits can be quite large within restricted frequency regions, even those with minimal sensitivity loss.

An aerodynamic study of Korean stop consonants: Measurements and modeling
View Description Hide DescriptionMeasurements were made of intraoral air pressure and oral flow of ten native speakers uttering word pairs contrasting Korean fortis and lenis voiceless stop consonants in initial position. The production of fortis stops was found to be characterized by a higher intraoral pressure before release, yet a lower oral flow after release, than corresponding lenis stops. Possible reasons for this difference were explored with the use of a computer implemented aerodynamicmodel, giving an output of air pressure and flow. Input parameters were adjusted in accordance with known or hypothesized variations in glottal area function, vocal tract wall tension, respiratory muscle force, and supraglottal cavity volume, as given in the literature. In addition to the previously known differences in glottal area, it is inferred from the results of the modeling experiment that fortis stops are produced with greater vocal tract wall tension than lenis stops. Speaker‐specific production strategies such as larynx lowering and heightened subglottal pressure during fortis stops and differences noted between word pairs are also discussed.

Minimum spectral contrast for vowel identification by normal‐hearing and hearing‐impaired listeners
View Description Hide DescriptionTo determine the minimum difference in amplitude between spectral peaks and troughs sufficient for vowel identification by normal‐hearing and hearing‐impaired listeners, four vowel‐like complex sounds were created by summing the first 30 harmonics of a 100‐Hz tone. The amplitudes of all harmonics were equal, except for two consecutive harmonics located at each of three ‘‘formant’’ locations. The amplitudes of these harmonics were equal and ranged from 1–8 dB more than the remaining components. Normal‐hearing listeners achieved greater than 75% accuracy when peak‐to‐trough differences were 1–2 dB. Normal‐hearing listeners who were tested in a noise background sufficient to raise their thresholds to the level of a flat, moderate hearing loss needed a 4‐dB difference for identification. Listeners with a moderate, flat hearing loss required a 6‐ to 7‐dB difference for identification. The results suggest, for normal‐hearing listeners, that the peak‐to‐trough amplitude difference required for identification of this set of vowels is very near the threshold for detection of a change in the amplitude spectrum of a complex signal. Hearing‐impaired listeners may have difficulty using closely spaced formants for vowel identification due to abnormal smoothing of the internal representation of the spectrum by broadened auditory filters.

A methodology for modeling vowel formant contours in CVC context
View Description Hide DescriptionModels for the formant‐frequency contours of vowels in CVC’ context are presented and illustrated with an American English database comprising isolated syllables with C, C’=/b,d,g/ and V=/i,i,q,æ,a,c,U,u,v,W/. Both established and reinterpreted regularities among context effects are cast in a series of successively elaborated mathematical models. The first model(model I), in common with all its successors, embodies the notion of the superposition of CV and VC’ transitions, according to which a formant trajectory F _{CVC’}(n) is modeled as f _{CV}(n)+T _{V}+g _{VC’}(n), where n is duration‐normalized time, T _{V} is a vowel target, and f _{CV}(n) and g _{VC’}(n) are initial‐ and final‐consonant transition functions. The rms errors for F _{1}, F _{2}, and F _{3} (30, 89, and 111 Hz) against independent test data are near the minimum theoretical values (32, 69, and 100 Hz) predicted from interrepetition variation and its contribution to uncertainty in the model elements. Subsequently, the elements of the additive model are individually characterized by further incorporating per‐consonant transition shape similarity (model II), target‐locus scaling (model III), exponential transition shapes (model IVa), and exponential duration dependence (model IVb).
In model II, the CV and VC’ trajectories are respectively defined as L+k f*(n) and L’+k’g*(n), with contour shape functions f* and g*, scale factors k and k’, and consonant loci L and L’. The loci are herein defined as baselines about which families of formant transitions are scaled. This model fits the data nearly as well as theory allows, except for F _{2} of C/i/C’ and C/ud/. Then, in model III, the scale factors k and k’ are represented by forms proportional to the target‐locus distances T−L and T−L’. The vowel target T is then redefined to best fit these forms. The target‐locus scaling hypothesis fares quite well except for F _{2} of CV sequences. In model IVa, the shape functions f* and g* are fit to exponentials with asymptotes associated with the vowel targets. Target‐locus scaling is a corollary of this vowel target definition. Finally, in model IVb, the exponential model is redefined on a recovered real‐time scale. The resulting context effect follows Lindblom’s [J. Acoust. Soc. Am. 3 5, 1773–1781 (1963)] in decaying exponentially with vowel duration.