Index of content:
Volume 79, Issue 4, April 1986

Wave equations in linear viscoelastic materials
View Description Hide DescriptionConditions for writing wave equations in linear viscoelasticmaterials are investigated. The study is restricted to the infinitesimal theory and an application is suggested in modeling ultrasound propagation in soft biological tissues. First, a general wave equation is obtained for the displacement field in an inhomogeneous medium. Second, the propagation of ‘‘the mean principal stress’’ (i.e., minus the arithmetical mean of the principal stresses) is examined. That quantity is particularly relevant when the force per unit area is detected at the surface of a nondissipative coupling medium. If the material is homogeneous, a wave equation is always obtained for the mean principal stress. Otherwise, supplementary conditions have to be assumed on the material and possibly on the motion. Results are illustrated by examples which present linearly elastic perfect fluids and linearly elastic Newtonian viscous fluids as particular viscoelastic materials.

K‐space scattering formulation of the absorptive full fluid elastic scalar wave equation in the time domain
View Description Hide DescriptionThe absorptive full fluid elastic scalar wave equation is developed by deriving the full fluid elastic scalar wave equation from the first principles and adding an absorptive term to the result. The time domain solution to the initial value forward scattering problem is developed for this equation. The solution algorithm is an exact numerical solution and is useful in pressure wave modeling for media with spatially varying velocity, density, and attenuation profiles. The number of operations per time step is of the order of N log_{2} N, where N is the number of spatial points into which the model has been discretized.

Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media
View Description Hide DescriptionA unified approach to the study of reflection and refraction of elastic waves in general anisotropic media is presented. Christoffel equations and boundary conditions for both anisotropic media in coordinate systems formed by incident and interface planes, rather than in crystallographic coordinates, are considered. Consideration of wave propagation in an acoustic‐axis direction is included in the general algorithm, so results can be obtained both generally and for planes of symmetry, including planes of isotropy. General features of the numerical results are discussed. Energy conversion coefficients are shown to satisfy reciprocity relations which are formulated. It is much more natural to consider intensity–conversion ratios, rather than amplitude–conversion ratios, showing the important role of ray (rather than wave‐vector) directions in describing phenomena such as grazing angles. In particular, it is shown that the incident wave vector for grazing incidence may be greater or less than 90°: The domain of incident wave‐vector angles can actually split into disjoint pieces. The reflection coefficient at grazing incidence is shown to be unity, as in the isotropic case. Critical‐angle phenomena are described naturally by this approach.

Laboratory studies of diffuse waves in plates
View Description Hide DescriptionMeasurements were conducted on the reverberant diffuse elastodynamic field in a 30‐ ×30‐ ×1.21‐cm aluminum plate, the disturbances being generated by simulated acoustic emission concentrated step loads. The acoustic response in the 50‐ to 500‐kHz range was monitored over periods of 16 ms, long compared to the 100‐μs acoustic transit time across the width or length of the plate. Accurate power spectra estimates were found to require the collection of large amounts of data and to require correction of this data for the effects of absorption, or internal friction. Comparison of the frequency, time, and spatially averaged power spectra with theoretical predictions shows substantial agreement.

Wave propagation through a thin bubbly layer
View Description Hide DescriptionThe shielding effects of a thin bubbly layer submerged in pure liquid on the propagation of acoustic waves are analyzed. By using the method of matched asymptotics, conditions across the bubbly layer are derived. They are: (1) that the pressure is continuous and (2) that the jump of normal velocity is related to the temporal derivative of pressure times a parameter representing the bulk property of the bubbly layer. This parameter is the product of a small number and a large number. The former is the wavenumber times the integral of the gas volume fraction β across the layer and the latter is the ratio of the density times the square of the speed of sound for the liquid phase to that for the gas phase. When the thin bubbly layer is adjacent to a rigid surface, their combined effect is described by an impedance boundary condition.

A new expansion for the velocity potential of a circular concave piston
View Description Hide DescriptionThis paper presents a new method for calculating the velocity potential in the nearfield of a circular concave piston source in an infinite plane baffle for both the case where the vibration is normal to the piston surface and where it is parallel to the axis. The solution is given in the form of an infinite series of spherical surface harmonics in the spherical coordinate system, taking the origin at the center of curvature. The theoretical framework has the advantage that it includes neither approximations nor numerical integrations.

Reconstruction of one‐dimensional inhomogeneities in elastic modulus and density using acoustic dimensional resonances
View Description Hide DescriptionA method is described for quantitatively reconstructing a spatial inhomogeneity along a one‐dimensional structure from measurements of its resonant frequencies (fundamental and higher modes). A relationship between the shifts in the resonant frequencies of the structure due to a material inhomogeneity (computed relative to the frequencies of the homogeneous state) and the coefficients in a Fourier expansion of the inhomogeneity, which holds to the first order in the material perturbation, is derived. If a number of successive resonant frequencies are excited and measured, the unknown inhomogeneity may then be reconstructed by Fourier summation. The material inhomogeneity recovered by this technique is the sum of the fractional changes in elastic modulus and density. For simplicity, the analysis is carried out in one dimension in the absence of damping. Compared to pulse‐echo methods, the advantages of the dimensional resonance method are that it can image slowly varying impedance variations, can utilize narrow bandwidth detection, has its signal enhanced by the resonantQ, and generally utilizes lower frequencies where problems of attenuation and scattering are less serious.

Transient and multiple frequency sound transmission through perforated plates at high amplitude
View Description Hide DescriptionThe transmission of complex periodic and transient acoustic signals through orifice plates at high amplitude, and in the absence of mean fluid flow, is discussed. A simple fluid dynamical model, involving a time‐varying mass end correction, is the basis of the theory. The equation of motion for the air in the orifice is solved numerically in the time domain. For a specific instance, an analytical solution in the frequency domain is possible. Good agreement is noted between experimental and theoretical results in both time and frequency domains.

Diffractive corrections to the high‐frequency Kirchhoff approximation
View Description Hide DescriptionDiffractive corrections to the physical optics solution for the scattering of high‐frequency sound by a random rough pressure release surface are derived. The correction terms are obtained by applying the composite‐roughness theory to an expansion of the scattering integral. Results are presented for a three‐dimensional rough surface and are compared with those obtained using a conventional composite‐roughness approach.

Source range information loss in waveguides
View Description Hide DescriptionIn a previous study [E. C. Shang, C. S. Clay, and Y. Y. Wang, J. Acoust. Soc. Am. 7 8, 172 (1985)] a new method of passive source ranging in a layered waveguide was proposed. This paper investigates the reduction (loss) in range information due to phase fluctuations and to an inaccurate description of the environment (waveguide mismatch). The effects of phase fluctuations are investigated using a two‐dimensional Gaussian distribution function. A numerical normal mode code is used to study the effects of waveguide mismatching. The loss in range information caused by incorrect descriptions of both the bottom sediment type and the sound speed profile in the water column is calculated. Examples are given for a water depth of 100 m and frequencies in the range from 100–500 Hz.

Surface‐generated noise under low wind speed at kilohertz frequencies
View Description Hide DescriptionSome experimental observations of the oceansurface under low wind speed conditions, carried out with the high gain acoustic distribution array, ADA, indicate that bubbles may play an important role in the noisegenerating mechanism in this wind speed regime. One of the mechanisms discussed in the theory is that of bubble collapse in the surfaceturbulence layer as first proposed by Furduev [Atmos. Ocean. Phys. 2, 314 (1966)]. Under typical ocean conditions, low wind speeds, and the available bubble population data, the calculated noise level agrees well with experimental results, both in magnitude and in the shape of the spectrum. The spectrum has a peak in the frequency range of 100 to 1000 Hz and an ω^{−} ^{2} behavior at high frequencies. Several geophysical parameters could influence the noise generation. Local wind speed probably controls the population of bubbles, and swell‐induced static pressure variations could play an important role in the critical turbulencepressure for bubble collapse. There seems to be further evidence that additional structure within the water, perhaps bubble density associated with different water masses,generates a patch type of distribution on the sea surface in the low wind speed situation.

Rainfall measurements using underwater ambient noise
View Description Hide DescriptionObservations are made which show that the underwater ambient noise spectrumgenerated by rain has a unique spectral shape which can be distinguished from other noise sources. Furthermore, the relationship between spectral level and rainfall is quantifiable. The spectral shape is dominated by a broad peak at 15 kHz, but also depends on the drop size distribution in the rain. A numerical study of the acoustic physics of a drop splash is used to explain the observed spectra. There are two contributions to underwater sound from the impact. The first contribution is from an initial acoustic water hammer pulse. The magnitude of this pulse depends on drop size, shape, and impact velocity. The contribution to the underwater sound spectrum is white and is very large for large drops. The second contribution occurs because at impact the incompressible continuity equation is not satisfied. Once this equation is satisfied, the splash is no longer an acoustic source. Numerically, the time required to closely satisfy this equation is roughly constant for all drop sizes at their terminal velocity. This time interval causes a low‐frequency rolloff at roughly 15 kHz in the sound spectrum.

Acoustic microscopy applied to measurements of sound absorption in liquid propane
View Description Hide DescriptionAn acoustic lens has been used to study the relative change in sound attenuation for frequencies in the range 90–300 MHz between the normal freezing and boiling points of liquid propane. These are the first results for the lower part of this temperature range and they confirm the predominance of the viscous contribution to the attenuation.

An ultrasonic power meter
View Description Hide DescriptionA new ultrasonic power meter has been developed to measure the acoustic power flow of longitudinal vibration in a metallic rod as the product of particle velocity and vibration force. The technological difficulty that should be faced in measuring the vibration force by electrically obtaining the spatial differential coefficient of particle velocity has been overcome. The theory used here and the experimental verification of this method are also described.

A distribution based definition of impulse noise
View Description Hide DescriptionDetermining when a worksite exposure should be considered impulsive is a problem which has complicated both research into mechanisms of auditory pathology and protection of the exposed worker. An ideal solution requires that a definition of impulsive noise be developed which is independent of specific characteristics such as duration and amplitude. As an alternative to duration independence, a fixed time window over which a statistic is calculated may also serve as a basis for classification. Additionally, selecting this window on the basis of TTS production in the ear provides a biological basis for the definition of impulsiveness. Classification of impulsiveness based on the sample kurtosis meets the requirements of a generally applicable impulse definition.

Super‐resolution imaging of finite extent objects by estimating the hologram outside an aperture
View Description Hide DescriptionA super‐resolution imaging method is proposed which utilizes the finite extent of the object to estimate the hologram data outside the limited aperture from the hologram data detected at a small number of the points in the aperture by using the regularized singular value decomposition algorithm. The characteristics of this method are made clear by computer simulations, and the experiments show the usefulness of the method.

Standing wave patterns in the human ear canal used for estimation of acoustic energy reflectance at the eardrum
View Description Hide DescriptionStanding wavepatterns were measured in the unoccluded ear canals of 13 human subjects, for applied pure tones of 3 to 13 kHz. Measurements were made, using a probe microphone technique, over a region which could be approximated as a duct of constant cross‐sectional area. Analysis of the patterns allowed the reflective properties of the middle ear to be determined in terms of an acoustic energy reflection coefficient, or reflectance, at the eardrum. Over all subjects the trend of the results was for the energy reflection coefficient to rise from about 0.3 at 4 kHz up to 0.8 at 8 kHz, and continue at this value to 13 kHz. There was, however, significant intersubject variation, especially at frequencies greater than 7 kHz.

Frequency selectivity of single cochlear‐nerve fibers based on the temporal response pattern to two‐tone signals
View Description Hide DescriptionThe physiological basis of auditory frequency selectivity was investigated by recording the temporal response patterns of single cochlear‐nerve fibers in the cat. The characteristic frequency and sharpness of tuning was determined for low‐frequency cochlear‐nerve fibers with two‐tone signals whose frequency components were of equal amplitude and starting phase. The measures were compared with those obtained with sinusoidal signals. The two‐tone characteristic frequency (2TCF) is defined as the arithmetic‐center frequency at which the fiber is synchronized to both signal frequencies in equal measure.
The 2TCF closely corresponds to the characteristic frequency as determined by the frequency threshold curve. Moreover, the 2TCF changes relatively little (2%–12%) over a 60‐dB intensity range. The 2TCF generally shifts upward with increasing intensity for cochlear‐nerve fibers tuned to frequencies below 1 kHz and shifts downward as a function of intensity for units with characteristic frequencies (CF’s) above 1 kHz. The shifts in the 2TCF are considerably smaller than those observed with sinusoidal signals. Filter functions were derived from the synchronization pattern to the two‐tone signal by varying the frequency of one of the components over the fiber’s response area while maintaining the other component at the 2TCF. The frequency selectivity of the two‐tone filter function was determined by dividing the vector strength to the variable frequency signal by the vector strength to the CF tone. The filter function was measured 10 dB down from the peak (2T Q _{10 dB}) and compared with the Q _{10 dB} of the frequency threshold curve. The correlation between the two measures of frequency selectivity was 0.72. The 2T Q _{10 dB} does change as a function of intensity. The magnitude and direction of the change is dependent on the sharpness of tuning at low and moderate sound‐pressure levels (SPL’s). The selectivity of the more sharply tuned fibers (2T Q _{10 dB}>3) diminishes at intensities above 60 dB SPL. However, the broadening of selectivity is relatively small in comparison to discharge rate‐based measures of selectivity. The selectivity of the more broadly tuned units remains unchanged or improves slightly at similar intensity levels. The present data indicate that the frequency selectivity and tuning of low‐frequency cochlear‐nerve fibers are relatively stable over a 60‐dB range of SPL’s when measured in terms of their temporal discharge properties.

Auditory filter shapes in subjects with unilateral and bilateral cochlear impairments
View Description Hide DescriptionThe shape of the auditory filter was estimated at three center frequencies, 0.5, 1.0, and 2.0 kHz, for five subjects with unilateral cochlear impairments. Additional measurements were made at 1.0 kHz using one subject with a unilateral impairment and six subjects with bilateral impairments. Subjects were chosen who had thresholds in the impaired ears which were relatively flat as a function of frequency and ranged from 15 to 70 dB HL. The filter shapes were estimated by measuring thresholds for sinusoidal signals (frequency f ) in the presence of two bands of noise, 0.4 f wide, one above and one below f . The spectrum level of the noise was 50 dB (r e: 20 μPa) and the noise bands were placed both symmetrically and asymmetrically about the signal frequency. The deviation of the nearer edge of each noise band from f varied from 0.0 to 0.8 f. For the normal ears, the filters were markedly asymmetric for center frequencies of 1.0 and 2.0 kHz, the high‐frequency branch being steeper. At 0.5 kHz, the filters were more symmetric. For the impaired ears, the filter shapes varied considerably from one subject to another. For most subjects, the lower branch of the filter was much less steep than normal. The upper branch was often less steep than normal, but a few subjects showed a near normal upper branch. For the subjects with unilateral impairments, the equivalent rectangular bandwidth of the filter was always greater for the impaired ear than for the normal ear at each center frequency. For three subjects at 0.5 kHz and one subject at 1.0 kHz, the filter had too little selectivity for its shape to be determined.

Frequency discrimination as a function of tonal duration and excitation‐pattern slopes in normal and hearing‐impaired listeners
View Description Hide DescriptionFrequency difference limens were determined as a function of stimulus duration in five normal‐hearing and seven hearing‐impaired subjects. The frequency DL duration functions obtained from normal‐hearing subjects were similar to those reported by Liang and Chistovich [Sov. Phys. Acoust. 6, 75–80 (1961)]. As duration increased, the DL’s improved rapidly over a range of short durations, improved more gradually over a middle range of durations, and reached an asymptote around 200 ms. The functions obtained from the hearing‐impaired subjects were similar to those from normal subjects over the middle and longer durations, but did not display the rapid changes at short durations. The paper examines the ability of a variation of Zwicker’s excitation‐pattern model of frequency discrimination to explain these duration effects. Most, although not all, of the effects can be adequately explained by the model.