Index of content:
Volume 75, Issue 5, May 1984

Basic and applied research on tactile aids for deaf people: Progress and prospects
View Description Hide DescriptionA brief introduction describes the alternative methods for replacement of the sense of hearing, including the educational procedures of sign language and lipreading, the medical procedure of cochlear implants, and the sensory substitution procedures of visual or tactual displays. For the tactual displays, which are most commonly electronically activated, a listing of desirable objectives is discussed in some detail. Among these are a better understanding of the processing capabilities of the skin, the form an efficient transducer may take, and what features of the speech stream may most profitably be extracted for processing and display to the sense of touch. Because the technology for device design and production in this area is seriously retarded, a great amount of space is devoted to the precise specification of a transducer for the tactile display; included is a discussion of direct electrocutaneous stimulation as a realistic alternative. A number of multichannel displays exist, and several of these may be workable systems if their transducer elements can be kept small and use little energy. What is of current, even urgent, importance is the early and widespread deployment of a single‐channel tactile aid to permit the general assessment of the effectiveness of a simple sensory adjuvant for a deaf person who has lipreading skills.

Acoustic ray‐path fluctuations induced by El Niño
View Description Hide DescriptionThis paper represents a first step in determining the degree to which an El Niño event can be monitored using acoustic tomographic techniques. In tropical waters an acoustic ray entering the near‐surface region from below usually is strongly refracted because of the steep gradient in the sound speed and therefore turns over very rapidly. Since the temperature perturbation associated with an El Niño event is restricted to this near‐surface region, there has been some concern that ray‐path travel‐time fluctuations would be too small to be easily detected. In this note we address this concern using data measured during the 1982–1983 event. We conclude that the travel‐time fluctuations are large enough to be easily measured for almost all ray‐path configurations of interest. We also discuss the direction future efforts might take.

Optical measurement of the reflection coefficient for bounded acoustic waves
View Description Hide DescriptionTwo alternative methods for optical measurement of reflection effects of bounded ultrasonicwaves are suggested. Corresponding reflection coefficients are defined and theoretical results for the special case of Gaussian ultrasonic beams prove consistency with the plane‐wave reflection coefficient. Calculated values of both newly defined reflection coefficients should be directly comparable to experimental data even when bounded beams are incident at critical angles where beam shift and phase reversal occur.

A uniform theory of diffraction for elastic solids
View Description Hide DescriptionWe present a new method for approximating the scattering by cracks in elastic solids in which we reduce the normal surface integral over the crack surface to a line integral along the crack edge. The resultant approximation is spatially uniform and valid for high frequencies (ωa/c _{ L } large). It recovers the geometrical theory of diffraction in the limit as ωa/c _{ L } → ∞, and as such may be considered an extension of this theory. Comparison is made with exact results for circular cracks, with excellent agreement found.

Reflection of finite acoustic beams from loaded and stiffened half‐spaces
View Description Hide DescriptionResults of theoretical calculations and experimental measurements on the reflection of finite acoustic beams from a fluid–solid interace in the presence of a loading or stiffening layer on the solid are presented. Measurements with Gaussian‐profile acoustic beams are reported on wave‐speed dispersion and reflected‐beam amplitude distribution for stiffening layers of chromium on either brass or stainless steel. Good agreement is generally observed. Detailed results of calculations of the reflection coefficient to delineate the behavior of cutoff modes for both stiffened and loaded half‐spaces are given. A straightforward method for deducing the complex Rayleigh wavenumber directly from the reflection coefficient is discussed. Comparisons between direct numerical integration of the reflected beam distribution and results of an extended analytical model demonstrate decreasing accuracy of the latter as one nears a mode cutoff.

Studies in reverberation III. Perturbation theory of scattering of sound by convection
View Description Hide DescriptionA perturbation method is developed for treating scattering of sound by convection. When applied to the problem of scattering of a plane sound wave by a cylindrical vortex, treated previously, good agreement was obtained for a value of the ratio of the frequency of rotation ω to the frequency σ of sound equal to 0.01. As the wavelength of sound diminishes to values smaller than the circumference of the cylinder, the waves which are scattered in directions lying on the side of the source become increasingly weaker than those scattered in directions on the side away from the source.

Diffraction on locally reacting surface—Schroeder’s diffusor
View Description Hide DescriptionIn the process of sound scattering, we treat the scattering surface as a radiating source yielding the scattered sound wave. On the basis of this idea, the scattering problems of a locally reacting surface (the one‐ and two‐dimensional Schroeder’s diffusor) are investigated when the incident wave is a plane wave or a pulse signal. A Schroeder’s diffusor with complex impedance is suggested.

Multiple modal resonances of thin cylindrical shells vibrating in an acoustic medium
View Description Hide DescriptionStructural modes of a thin cylindrical shell can display as many as three natural frequencies when immersed in an acoustic medium, all lower than the corresponding i n v a c u o natural frequency. This phenomenon results from the marked peak displayed by the inertial radiation loading of a slender cylindrical shell when the structural wavenumber of a modal configuration lies close to the acoustic wavenumber. This is illustrated for the axisymmetric ‘‘breathing mode’’ in the limiting case of an infinitely periodic cylindrical shell. For the parameters of metal shells in water, three natural frequencies are anticipated for modes whose axial wavelength exceeds the radius by at least one order of magnitude. For submerged shells of less stiff material or smaller modal wavelength‐to‐radius ratio, one or two natural frequencies are predicted.

Nearfield of a large acoustic transducer. Part IV: Second harmonic and sum frequency radiation
View Description Hide DescriptionThe theory presented in two previous papers [J. Acoust. Soc. Am. 7 4, 1013–1020 (1983) and J. Acoust. Soc. Am. 7 5, 769–779 (1984)] is generalized to the second harmonic and sum frequency components in the acoustic beam from a moderate amplitude parametric radiator. The theory also applies to the second harmonic component in the acoustic field from a moderate amplitude monochromatic transducer. Asymptotic formulas are presented, showing the development of the second harmonic and sum frequency sound from the source (transducer) into the farfield. Numerical results for the axisymmetric case are given. The results are compared with earlier theories and observations.

Sound field of a parametric focusing source
View Description Hide DescriptionAn analytical description of the sound field of a parametric focusing source was given in a previous paper by Lucas, Naze Tjo/tta, and Muir [J. Acoust. Soc. Am. 7 3, 1966–1971 (1983)]. Results of an experimental investigation were also presented and compared with the theory. The results of new numerical computations are shown in the present paper. They lead to a more accurate evaluation of the parametric field in planes perpendicular to the axis of symmetry and to a better agreement with the observations.

Expanding sound created by a time‐varying acoustic source in an arbitrarily oriented subsonic passage above a finite impedance reflecting ground surface
View Description Hide DescriptionAn arbitrarily time‐varying concentrated real source travels above a finite impedance (nonrigid) ground surface in an arbitrary direction. Sound transmission commences at zero instant. The impedance‐modified reflected sound field is posed as a derivative of an intermediary field induced by the acoustic potential of an ‘‘underground’’ traveling image source. A general solution is then established in closed form for a subsonic source passage. The known impedance‐independent acoustic potential of the image source together with an impedance‐dependent transform of the temporal source factor constitute the reflected field. Superposed reflected and direct sounds expand inside a growing reflected front which, for an aerial source position at zero instant, trails above‐ground behind a growing radiated front. The latter advances into a receding expanse of silence. Only direct sound evolves between both fronts. The reflected front must overtake the subsonic source; this, in turn, lags permanently behind the radiated front. Explicit results are deduced for time‐invariant transmission. The sound field of a vertically ascending time‐varying source is next investigated; it turns out to be axisymmetric. A large‐time approximation discloses, for a time‐invariant stationary source, an impedance supported transient superposed upon an impedance independent static field which ultimately survives in the steady state. Finally, if the traveling source emits a sequence of singular impulses, then reflection produces a sequential nonconcentric expansion of reflected fronts, each (i) conveying a singular but temporally attenuated distinct echo that is partially impedance influenced and (ii) enclosing an impedance‐sustained nonsingular elongated reflected sound.

Stochastic propagation of the mutual coherence function in the deep ocean
View Description Hide DescriptionWe present a computer‐implemented algorithm for underwater acoustic propagation based upon a theoretical formulation which simultaneously incorporates probabilistic random volume scattering and deterministic refraction and diffraction. The model, called the Combined EffectsModel, adds the vertical scattering caused by the random inhomogeneities in the ocean to the multipath features produced by the mean sound‐speed structure. The analysis is based on the two‐point coherence function which describes the acoustic field in terms of position and the direction of energy flux, and as such is directly related to the field as seen by an acoustic array. Basic to the theoretical formulation is a locally quadratic approximation on the index of refraction. Although multipath interference effects (which are apparent when the coherence function is calculated directly from a propagation algorithm) are lost with this assumption, estimates for the output of a vertical array are not significantly affected. The incorporation of random volume scatter with realistic background sound‐speed structure results in the distribution of arriving energy being smoothed over vertical arrival angles. This effect depends on the magnitude of the strength of the fluctuating field. The multipath structure can still exist for over 100 km, for signals below a few hundred Hz, in the presence of a typical scattering field or can deteriorate in the first few kilometers in the presence of strong scatter.

PERUSE: A numerical treatment of rough surface scattering for the parabolic wave equation
View Description Hide DescriptionScattering of underwater acoustic signals from real ocean surfaces often does not fit into any of the classical theoretical approaches to the problem. Thus the need for a numerical approach is clear. A novel method is presented that uses a sequence of c o n f o r m a l m a p p i n g s to locally flatten successive segments of the surface, which is assumed piecewise linear and frozen in time. Each conformal mapping preserves the elliptic form of the reduced wave equation, so that in each transformed space the parabolic approximation can be made and the solution advanced one range step using the split‐step Fourier algorithm. This PERUSE (P E RoUgh SurfacE) numerical method is validated by exhibiting classically predicted Bragg angle peaks for single scatter of a plane wave from a sinusoidal surface. For multiple rough surfacescattering in surface ducts, PERUSE results are analyzed by resolution in depth into the virtual modes of Labianca [J. Acoust. Soc. Am. 5 3, 1137–1147 (1973)]. The resulting modal intensities are then plotted as functions of range, and decay rates are estimated for each mode. Comparison with a classical ray‐based scattering theory shows no obvious correlation; it appears that there is significant mode coupling due to the rough surface.

Application of two‐variable Taylor series to the ray theory of propagation in an unbound medium
View Description Hide DescriptionThe Taylor series method is applied to the ray theory solution for the acoustic field near the initial caustic of the first convergence zone. This field is formed by a pair of rays that are heading downward at the source and upward at the receiver. The ray parameter (namely the phase velocity) of each ray is expressed as a two‐variable Taylor series in horizontal range and depth relative to a fixed expansion point. The terms of the series are calculated for derivatives up to fifth order. The method is applied to a typical oceanic example modeled by a bilinear sound‐speed profile in which the caustic of the rays passes the expansion point at vertical distances of 15–60 m and at horizontal distances of 200–1200 m, respectively. The Taylor‐series phase velocities are inserted into the usual ray theory expressions for relative energy and travel time. It is found in some cases that satisfactory accuracy is obtained over a region of the ocean that is sufficiently large for sonar application. The advantage of this new approach is that, to calculate the sound field at a grid of points within a region, the (relatively expensive) iterative method of determining ray parameters need be applied to only one expansion point.

An iterative perturbation approach for ocean acoustic tomography
View Description Hide DescriptionAn iterative algorithm for the inversion of ocean acoustic tomographic data is introduced. This allows the calculation of ocean environmental acoustic parameters from measured travel times between a distributed system of acoustic sources and receivers. The algorithm does not require expensive (because slowly convergent) nonlinear ray tracing. In each iteration both the modified environmental parameters and the perturbations to the ray paths are calculated from linearized equations. A convergence proof is outlined. It is shown in an example that a single iteration, which corresponds to the classical perturbation solution, can give insufficient accuracy in a realistic ocean. This is accomplished by evaluating the second variation of the travel‐time data with respect to the environmental parameters and demonstrating that in typical, strongly focused sound channels it can be comparable in size to, or larger than the first variation.

Linearized travel time, intensity, and waveform inversions in the ocean sound channel—A comparison
View Description Hide DescriptionLinearized inversion schemes involving waveform (total record), intensity (dephased total record), and travel times (intensity peaks) are used on synthetically generated arrival patterns to solve for the sound speed structure in the upper km of a range‐independent oceanmodel. In all three cases inversions are carried out for a variety of source center frequencies and bandwidths. The results are compared; conditions under which each inversion method performs poorly and well are outlined. The nature of the linearization approximation is discussed for each of the three types of inversion scheme as well as the methods used to solve the general linearized system.

Reflection of parametric radiation from a finite planar target
View Description Hide DescriptionResults are reported of an investigation of the reflection of parametric radiation from a finite planar target. The interference of the difference frequency sound generated after reflection with the reflected difference frequency sound is considered. Amplitude and phase were measured before and after reflection from a polyfoam target. Target size ranged from slightly larger than the beamwidth to smaller than the beamwidth. The results are compared with calculations based on equations describing the linear radiation and the parametric radiation. These equations are derived using the parabolic approximation.

Bubble size measurements using the nonlinear mixing of two frequencies
View Description Hide DescriptionA double frequency method of measuring bubble size which has better spatial resolution than previous techniques, is described. Bubbles are insonified simultaneously by a swept, relatively low, ‘‘pumping’’ frequency near their resonance and a high ‘‘imaging’’ frequency. Theoretical expressions are derived for the sound scattered by a bubble under the influence of these two frequencies. Existence of sharp resonance behavior in the scattered sound at the sum frequency is shown both theoretically and experimentally.

Sound scatter and shadowing at a seamount: Hybrid physical solutions in two and three dimensions
View Description Hide DescriptionLaboratory scale models and wedge diffraction computer models of sound propagation over a seamount have been used to determine the laws and the physical causes of seamount shadowing in terms of diffraction, forward scatter, and multiple reflections from seamount to ocean surface. The model results are ‘‘hybridized’’ with a ray solution (FACT model) for the refractive and attenuative effects away from the seamount and the sum produces excellent agreement with detailed continuous wave and impulse ocean data for Dickins Seamount over the frequency range 50–500 Hz [G. R. Ebbeson and R. G. Turner, J. Acoust. Soc. Am. 7 3, 143–152 (1983) and N. R. Chapman and G. R. Ebbeson, J. Acoust. Soc. Am. 7 3, 1979–1984 (1983)]. It is shown that: depending on the ocean roughness, diffraction over the crest can be the strongest contributor to the sound in the shadow region; the diffracted signal always arrives before the multiply reflected sound; the diffraction loss is proportional to f ^{1} ^{/} ^{2}; a two‐dimensional model produces excessive diffraction and excessive multiple reflection signal compared to a realistic three‐dimensional model.

Rayleigh wave transmission reciprocity past a step change in elevation
View Description Hide DescriptionContradicting experimental, approximate theoretical, and numerical results have been reported in the literature by several authors on Rayleigh wavetransmission coefficient past a step change in elevation. In this paper, reciprocity for wave propagation in both directions across a step is demonstrated experimentally using a new ratio technique eliminating error sources introduced from elastic wave generation, coupling, and detection. Two‐dimensional ultrasonic models were use to obtain the data. The experimental transmission coefficientmeasurements are compared with other published results. The ratio of step height to Rayleigh wavelength tested ranged from 0.159 to 1.33. The effect of step height on the interference of the transmitted wave components is examined. The conversion between Rayleigh and shear waves at the step plays an important role in the transmission coefficient.