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Volume 83, Issue 1, January 1988

Analysis of acoustic scattering from fluid cylinders using a multifilament source model
View Description Hide DescriptionA solution is presented for the problem of two‐dimensional acoustic scattering from homogeneous fluid cylinders. The solution uses fictitious filamentary isotropic sources to simulate both the field scattered by the cylinder and the field inside the cylinder and, in turn, point‐matches the continuity conditions for the normal component of the velocity and for the pressure across the cylinder surface. The procedure is simple to execute and is general in that cylinders of arbitrary shape can be handled effectively. Perfectly rigid cylinders are treated as reduced cases of the general procedure. Results are given and compared with available analytic solutions, which demonstrate the very good performance of the procedure.

Comparison of walleye pollock target strength estimates determined from i n s i t u measurements and calculations based on swimbladder form
View Description Hide DescriptionThe target strength of walleye pollock (T h e r a g r a c h a l c o g r a m m a) at 38 kHz has been determined in each of two ways: (1) i n s i t umeasurement with dual‐beam and split‐beam echosounders, and (2) theoretical calculation based on the swimbladder form. Respective probability density functions of target strength are compared. The several estimates of mean target strength (T̄S̄) determine the relation T̄S̄=20 log l−66.0, where l is the fish fork length in centimeters.

On the nonspecular reflection of bounded acoustic beams
View Description Hide DescriptionIn this article, a comprehensive study of the reflection phenomenon of bounded acoustic beams by uniform and layered half‐spaces and plates is carried out. The incident beam strength is assumed to have a Gaussian variation with different widths and frequencies. The Thomson–Haskell matrix method with delta matrix modification is adopted to solve this problem. Different types of reflectors only change the boundary and continuity conditions but the basic formulation remains unchanged. Several interesting and new features of reflected beam profiles are observed.

GTD for backscattering from elastic spheres and cylinders in water and the coupling of surface elastic waves with the acoustic field
View Description Hide DescriptionThe geometrical theory of diffraction(GTD) has been extended to describe surface elastic wave (SEW) contributions to backscattering from spheres and cylinders in water at high frequencies. The coupling (described by a coefficient G _{ l } ) of the lth class of SEW with the acoustic field and the resulting contribution f _{ l } to the form function for solid spheres were previously derived [K. L. Williams and P. L. Marston, J. Acoust. Soc. Am. 7 9, 1702–1708 (1986)] via a Sommerfeld–Watson transformation (SWT). That work gave a Fabry–Perot representation of f _{ l } . A similar representation was postulated by applying the principles of GTD to the Lamb wave contributions to backscattering from empty cylindrical shells [V. Borovikov and N. Veksler, Wave Motion 7, 143–152 (1985)]. In either case, ‖ f _{ l } ‖=‖G _{ l } exp[−2β_{ l } ×(π−θ_{ l } )]/[1+j exp(−2πβ_{ l } +i2πk a c/c _{ l } )]‖ ,where j=1 for spheres and j=−1 for cylinders, each of radius a. The SEW phase velocity and attenuation coefficient are c _{ l } and β_{ l } , sin θ_{ l } =c/c _{ l } , and c and k are the velocity and wavenumber in water. High‐frequency resonances of the elastic response were shown to be described by the f _{ l } of the relevant SEW. The present work gives approximations for ‖G _{ l } ‖ for spheres and cylinders in terms of β_{ l } , c/c _{ l }, and k a. These are confirmed by comparison with numerical data for ‖G _{ l } ‖ from Borovikov e t a l. for cylinders and from SWT results for Rayleigh and whispering gallery waves on spheres. The ratio of the approximate ‖G _{ l } ‖ is confirmed by geometric considerations. The analysis is applicable to other supersonic surface guided waves. The derivation uses results of resonance scattering theory and the identification of a nonresonant SEW ‘‘background.’’

Reflection and transmission by an infinite array of randomly oriented cracks
View Description Hide DescriptionReflection and transmission of an antiplane shear wave by an infinite array of randomly oriented cracks in an isotropic elastic medium are investigated. The problem has been formulated for an averaged scattered field, and a ‘‘periodization’’ technique has been developed to derive the governing singular integral equation for the conditionally averaged crack‐opening displacement. The singular integral equation has been solved by splitting the kernel into a singular and a regular part. A point scatterer approximation was introduced for the part containing the regular kernel. The approximation has been checked by comparison with exact results for a deterministic periodic system. By using this approximation, the coherent part of the averaged reflection and transmission coefficients of zeroth order has been calculated for normal incidence, a completely random crack orientation, and various values of the wavenumber and the ratio of crack length and crack‐center spacing. The problem was formulated in the context of antiplane shear waves. The results are, however, also applicable to reflection and transmission of acoustic or electromagnetic waves by an array of screens.

High‐frequency scattering from rigid prolate spheroids
View Description Hide DescriptionThe scattering of an acoustic plane wave by a rigid, immovable prolate spheroid is investigated over a broad frequency range (0<k L/2≤300). An unexpectedly large, off‐axis radiation lobe dominates the bistatic beam pattern for axial incidence and aspect ratios larger than unity, over the entire frequency range considered. This lobe is found to be due to an amplitude‐modulated creeping wave. A new asymptotic expansion of the spheroidal radial functions is introduced that gives an improved estimate of the functions for moderate values of the azimuthal index at high frequency.

Sound scattering by cylinders of finite length. I. Fluid cylinders
View Description Hide DescriptionThere are many different finite length scatterers in the ocean such as marine biota in the water column and protuberances (or ‘‘bosses’’) on the seafloor, sea surface, and underside of sea ice. Since it is impossible to describe scattering from the exact shape of most objects, one must use simple geometrical objects such as spheres, spheroids, or finite cylinders as the approximate shape. In this article, the scattering of an incident plane wave by a fluid finite circular cylinder is described for all frequencies. By neglecting end effects, the volume flow per unit length of the scattered field of the finite cylinder is approximated by that of the infinite cylinder. The solution is obtained by integrating this volume flow along the length of the cylinder. This approximation restricts the solution to geometries where the incident waves are normal or near normal to the axis of the cylinder. The solution is adapted to describe the scattering of sound by shrimp, which are elongated fluid‐saturated marine organisms. There was excellent agreement between the adapted solution and shrimp backscatter data.

Sound scattering by cylinders of finite length. II. Elastic cylinders
View Description Hide DescriptionThe theoretical results of the preceding article describing scattering from finite length fluid cylinders [T. K. Stanton, J. Acoust. Soc. Am. 8 3, 55–63 (1988)] are extended to the case of the elastic cylinder. The same method is used: The volume flow per unit length of the scattered field of an infinitely long cylinder is integrated over a finite interval to estimate the scattered field due to a cylinder of finite length. In this article, Faran’s solution for the infinitely long elastic cylinder [J. J. Faran, Jr., J. Acoust. Soc. Am. 2 3, 405–418 (1951)] is used to derive the scattering from the finite elastic cylinder at angles of incidence normal and nearly normal to the axis. This rigorously derived analytical solution compares very well with backscatter data from Dural cylinders and a scattering model derived by qualitative arguments, both from Andreeva and Samovol’kin [I. B. Andreeva and V. G. Samovol’kin, Akust. Zh. 2 2, 637–643 (1976) and Sov. Phys. Acoust. 2 2 (5), 361–364 (1976)]. The conclusions of this work and from Andreeva and Samovol’kin are the same: The acoustic or effective length of a cylinder, whether it be infinitely long or of finite length, is the smaller of L or the radius of the first Fresnel zone (rλ)^{1/2}, where L is the length of the cylinder or of the insonified ‘‘spot’’ of a longer cylinder, r is the distance from the cylinder to the field point or receiver, and λ is the acoustic wavelength.

A singular perturbation problem: Scattering by a slender body
View Description Hide DescriptionThe scattering of sound waves by rigid slender bodies of revolution are investigated by an approach based on the matched asymptotic method. The reduced wavenumber K a is assumed to be of the order of unity. The scattered field is represented at the scale of the body length by a superposition of sectorial spherical harmonics whose distributions are determined by matching them with the solution of the local problem characterized by a typical length scale of the order of the maximum body cross‐section radius. Asymptotic expressions are obtained for the scattered pressures. Comparison of the scattered farfield is made with other methods and numerical computations of the directivity functions of a slender prolate spheroid are presented for several values of angles of plane wave incidence.

On the coefficient of nonlinearity β in nonlinear acoustics
View Description Hide DescriptionAn analysis valid to second order in the acoustic variables is used to investigate the origin and form of the coefficient of nonlinearity β. Two cases are considered. First, for progressive plane waves, the well‐known formula is β=1+B/2A, where B/2A is the coefficient of the quadratic term in the isentropic pressure–density relation. It is shown that the component 1, which is associated with convection, comes solely from nonlinear terms in the equation of continuity. The second component comes from a quadratic term in the equation of state. The momentum equation is linear for this type of wave motion and therefore contributes nothing to the expression for β. Second, for noncollinear interaction of two plane waves, quasilinear analysis shows that the expression for β appropriate for the sum and difference frequency waves has three components. In this case, the momentum equation does contribute to the formula. For most practical problems the three‐component formula reduces to β=cos θ +B/2A, where θ is the angle of interaction. The factor cos θ represents the combination of contributions cos^{2}(θ/2) and −sin^{2}(θ/2) from the continuity and momentum equations, respectively.

The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum
View Description Hide DescriptionThe validity of the Kirchhoff approximation for rough surfacescattering is examined by comparison with exact results obtained by solving an integral equation. The pressure release boundary condition is assumed. The field quantity calculated is the bistatic scattering cross section, which is obtained with a Monte Carlo technique. The accuracy of correcting the Kirchhoff scattering cross section for shadowing is also addressed. The surface realizations used are randomly rough with a Gaussian roughness spectrum and have height variations in only one direction. The surface correlation length is found to be the most important parameter in defining the valid region of the Kirchhoff approximation away from the low grazing angle region. A procedure is given that provides a quantitative measure of the accuracy of the shadow‐corrected approximation when the root‐mean‐square (rms) slope angle of the surface γ is ≲20° and when the incident grazing angle θ is ≳2γ. Examples with θ≲2γ are also discussed.

Shallow seismic experiments using shear waves
View Description Hide DescriptionDuring the summer of 1986, a series of seismo‐acousticexperiments was carried out in shallow water off the New Jersey shore. The purpose of these experiments was to measure the geoacoustic properties of the ocean sediments that comprise the upper few hundred meters of the sediment column. Seismic sources and receivers were deployed at or very near the bottom in order to excite shear waves in the sediment and minimize the effects of interference from waterborne propagation. The experiments were performed at several sites where prior field work had established physical properties and a detailed profile of the sediments. By using conventional air guns deployed in an unconventional way, strong interface and diving shear waves were generated; these data were inverted to obtain shear wave velocity as a function of depth. The inversion results were then compared with the predictions of a geoacoustic model that accounts for the effects of voids ratio, overburden pressure, and other physical parameters. The i n s i t umeasurements from experiments and the gradients predicted by the model were in good agreement, suggesting a strong dependence of velocity on overburden pressure near the water–sediment interface.

Waveguide characterization and source localization in shallow water waveguides using the Prony method
View Description Hide DescriptionHorizontal samples of a point source in a shallow water waveguide are processed by the Prony method. First, when the source position is known, a high resolution estimation of the normal mode parameter K _{ m } (the horizontal component of mode wavenumber) can be obtained. Owing to the weak damping process, β_{ m }, the modal attenuation coefficient, can be obtained by using a modified Prony method. In this article, an ‘‘interval average and iterative’’ approach is proposed. Numerical examples illustrate that a 10^{−} ^{4} resolution of K _{ m } (150‐Hz frequency) is provided by a 500‐m data length, roughly an order of magnitude smaller than the data length required by the linear spectrum analysis technique. Second, when the source position is unknown but the waveguide characters (K _{ m }, β_{ m }) are known, the same procedure can be used for source position estimation. Some numerical examples in typical shallow water are presented.

A new method for determining acoustoelastic constants and plane stresses in textured thin plates
View Description Hide DescriptionThe texture of the material is taken into account in the present analysis of polycrystalline structures, which means that at least the third‐order terms must be considered in the elastic strain energy density function. An original method is discussed that determines the acoustoelastic constants directly so that the third‐order elastic constants can be included without having to determine them explicitly. A special type of test specimen is used to simulate a perfectly plane stress state with a uniaxial tensile load. A texture is introduced by cold rolling the specimen and then annealing it to eliminate the residual stresses due to manufacturing. The plane stresses are then estimated from the propagation times of bulk ultrasonic waves polarized in three orthogonal directions. The small rotation induced by the texture is measured along with the stress of the shear wave polarization plane. A more in‐depth characterization of the material is deemed necessary if the theory is to be applied i n e x t e n s o to the plastic domain.

On Green’s functions for elastic waves in anisotropic media
View Description Hide DescriptionThe Green’s function, as a temporal Fourier transform of the point‐source solution of the wave equation in an infinite medium, is obtained for the homogeneous, transversely isotropic solids, such as fiber composites or directionally solidificated steels of the columnar‐grained polycrystalline structure. The surface integrals, representing the exact point‐source solutions for the quasilongitudinal, quasitransverse, and purely transverse horizontally polarized shear waves, are approximated in terms of elementary functions, given that the elastic parameters characterizing the deviation of the solid from the isotropic medium are relatively small (weak anisotropy approximation). A brief discussion of the main features of the solution and a comparison to well‐known eikonal (ray) approximations are presented.

Investigation of Lamb waves having a negative group velocity
View Description Hide DescriptionThe propagation characteristics of Lamb waves in a solid plate are typically represented by a set of dispersion curves, which describe the Lamb‐wave phase velocity as a function of the product f d, where f is the acoustic frequency and d is the plate thickness. For certain modes, within a range of phase velocity and f d, it has been theoretically predicted that the associated group velocity could be negative, i.e., the energy transport is in the opposite direction to the phase velocity. In the present study, Lamb waves are generated via mode conversion from a water‐borne sound beam incident onto a flat brass plate. Measurement of the phase and group velocities of the Lamb waves of the S _{1} mode is performed for the f d range of 2.0–2.3 MHz‐mm. Comparison of the measured and computed values of phase and group velocities shows good agreement and clearly demonstrates that S _{1}‐mode Lamb waves have a negative group velocity for f d=2.08–2.24 MHz‐mm.

Ultrasonic losses at cryogenic temperatures in a Roraima (Venezuela) tuff
View Description Hide DescriptionMeasurements in a local tuff of the attenuation of ultrasonicwaves in the range from 10–60 MHz are reported as a function of temperature from 4–365 K. The relative attenuation in the material is low corresponding to Q’s in excess of 1000 and, except for negligible scattering losses below 150 K, it displays temperature‐ and frequency‐dependent contributions that are sensitive to vacuum outgassing at moderate and high temperatures. Stress relaxations at low temperatures attributed to viscous losses in adsorbed supercooled water films produce an attenuation peak centered around 250 K. A fast rising loss above room temperature is analyzed in terms of thermally activated motions of physisorbed fluid molecules.

The eigenvalue problem for −Δu=λu with Dirichlet boundary conditions for two‐dimensional regions. II. T‐shaped, cross‐shaped, and H‐shaped regions
View Description Hide DescriptionThis article deals with the calculation of the eigenvalues and eigenfunctions of the two‐dimensional Laplacian with Dirichlet boundary condition for T‐shaped, cross‐shaped, and H‐shaped regions. The method used is the Weinstein method (the intermediate method). The suitable base problem can be obtained through dividing the given region into rectangles and replacing Dirichlet boundary conditions by Neumann boundary conditions on a part of the boundaries. The intermediate problems can be determined by appropriate trial functions, and by the eigenvalues and eigenfunctions for each decomposed rectangle. The numerical results are considered to be reasonably precise. Special attention is paid to the dependence of the eigenvalues and eigenfunctions on parameters of the region. Some consideration is also given to the curve‐veering phenomena observed frequently in the numerical results.

Vowel processing by a model of the auditory periphery: A comparison to eighth‐nerve responses
View Description Hide DescriptionA model of peripheral auditory processing that incorporates processing steps describing the conversion from the acoustic pressure‐wave signal at the eardrum to the time course activity in auditory neurons has been developed. It can process arbitrary time domain waveforms and yield the probability of neural firing. The model consists of a concatenation of modules, one for each anatomical section of the periphery. All modules are based on published algorithms and current experimental data, except that the basilar membrane is assumed to be linear. The responses of this model to vowels alone and vowels in noise are compared to neural population responses, as determined by the temporal and average rate response measures of Sachs and Young [J. Acoust. Soc. Am. 6 6, 470–479, (1979)] and Young and Sachs [J. Acoust. Soc. Am. 6 6, 1381–1403, (1979)]. Despite the exclusion of nonlinear membrane mechanics, the model accurately predicts the vowelformant representations in the average localized synchronized rate (ALSR) responses and the saturating characteristics of the normalized average rate responses in quiet. When vowels are presented in background noise, the modeled ALSR responses are less robust than the neural data.

Interpreting measures of frequency selectivity: Is forward masking special?
View Description Hide DescriptionIn a previous article [Lutfi, J. Acoust. Soc. Am. 7 6, 1045–1050 (1984)], the following relation was used to predict measures of frequency selectivity obtained in forward masking from measures obtained in simultaneous masking: F(g)=G+H(g)−H(0), where, for a given masker level, F is the amount of forward masking (in dB) as a function of signal‐masker frequency separation (g), H is the amount of simultaneous masking, and G is the amount of forward masking for g=0. In the present study, the relation was tested for a wider range of signal and masker frequencies, masker levels, and signal delays. The relation described thresholds from all conditions well with the inclusion of one free parameter λ corresponding to a constant frequency increment, F(g)=G+H(g+λ)−H(λ). The parameter λ was required to account for observed shifts in the frequency of maximum forward masking. It is argued that a single tuning mechanism can account for commonly observed differences between simultaneous‐ and forward‐masked measures of frequency selectivity.