Index of content:
Volume 77, Issue 2, February 1985

A fast‐field program for sound propagation in a layered atmosphere above an impedance ground
View Description Hide DescriptionThis paper studies sound propagation in a layered atmosphere bounded by a ground, whose impedance is described by the Delany–Bazley–Chessell’s empirical model. The problem is formulated in terms of a Green’s function integral in the spectral domain, and is numerically evaluated by a Fast Field Program (FFP). Numerical results are included to show that (i) in simple test cases, the FFP solution is in excellent agreement with existing asymptotic solutions; (ii) numerical overflow arises when the number of layers is large and/or the frequency is high, and a method to circumvent this difficulty is described; and (iii) the FFP is a most powerful tool in solving propagation problems in layered media bounded by complex impedances.

Calculation of the acoustic material signature of a layered solid
View Description Hide DescriptionA theory is presented for the calculation of the acoustic material signature of a multilayered elastic half‐space overlain by a fluid. The solid layers are composed of homogeneous isotropic linearly elastic materials and are firmly bonded at the interfaces. The calculation procedure is valid at an arbitrarily high frequency of excitation. Results are presented for a uniform, a single layered and a four layered model of the half‐space at two frequencies of excitation; one moderate (35 MHz) and the other relatively high (370 MHz). Several new features of the material signatures and their possible use in the material characterization of layered specimen are indicated.

An advanced computational method for radiation and scattering of acoustic waves in three dimensions
View Description Hide DescriptionThe method proposed in this paper provides a computational method for implementing the Helmholtz integral formula for acoustic radiation and scattering problems associated with arbitrary shaped three‐dimensional bodies. In particular an isoparametric element formulation is used in which both the surface geometry and the acoustic variables on the surface of the body are represented by second‐order shape functions within the local coordinate system. A general formula for the surface velocity potential and the exterior field is derived. This result is applicable to nonsmooth bodies, i.e., it includes the case where the surface may have a nonunique normal (e.g., at the edge of a cube). Test cases are shown involving spherical, cylindrical, and cubical geometry.

Comparison of the T‐matrix and Helmholtz integral equation methods for wave scattering calculations
View Description Hide DescriptionCalculations of the scattering of acoustic waves by rigid prolate spheroids of various aspect ratios were performed with both the T‐matrix method (TMM) and the Helmholtz integral equation method (HIEM) on the same computer to compare the numerical stability of the two methods. For spherical targets the TMM converged more rapidly than the HIEM, but with increasing aspect ratio the rate of convergence of the TMM deteriorated rapidly while that of the HIEM was only slightly reduced. Moreover, roundoff error quickly became a serious problem for the TMM with increasing aspect ratio while for the HIEM it posed no problem at all in the cases considered. The numerical difficulties of the TMM were exacerbated by the fact that the matrices which had to be inverted became increasingly more ill conditioned as the number of partial waves was increased. For the HIEM, on the other hand, the matrices to be inverted became increasingly better‐conditioned as their dimension increased with the order of the calculation.

A multiple scattering theory for elastic wave propagation in discrete random media
View Description Hide DescriptionA multiple scatteringtheory for elastic wave propagation in a discrete random medium is presented. A self‐consistent multiple scattering formalism using the T matrix of a single scatterer in conjunction with the quasicrystalline approximation (QCA) and a self‐consistent pair correlation function is employed to study the phase velocity and coherent attenuation of elastic waves by a random distribution of cavities and elastic inclusions embedded in an elastic matrix. Both uniform and Gaussian size distributions are assumed. The theoretical results obtained in this study are shown to be in excellent agreement with experimental observations.

Spatial variation of phase in ducts and the measurement of acoustic energy reflection coefficients
View Description Hide DescriptionThe sound pressure in a one‐dimensional duct contains amplitude and phase components, both of which vary with position. The spatial variation of phase is examined in this paper and is shown to be closely related to the relative flow of incident and reflected acoustic energy. A technique that determines the acoustic reflection coefficient of the duct termination by measuring the maximum rate change of phase with position is discussed. For the measurements of phase variation a single moveable probe microphone is used with a phasemeter. Good agreement has been obtained between this method and the more usual impedance tube method, which considers the amplitude component of sound pressure. The phase measurements, though, can be applied equally well to ducts of conical, rather than uniform, cross section, and require a relatively small length of duct in which to translate the probe (as little as 1/20 wavelength, for moderate reflectivities). Some preliminary measurements have been made in human ear canals. The eardrum reflection coefficients obtained in the 10‐ to 15‐kHz range are between 0.6 and 0.85, somewhat higher than those obtained by other methods.

A slow‐waveguide filter as an acoustic interference controlling device
View Description Hide DescriptionUsing the fact that low‐frequency sound waves are diffracted by any kind of obstacle, a ‘‘sound velocity reducer’’ waveguide has been designed so as to create a 180° phase lag between the diffracted part of the incident noise and that transmitted through the duct of the guide. Further, this waveguide, being a low‐pass filter, insures that the acoustic pressure amplitudes diffracted and transmitted are of the same order of magnitude. For a low‐frequency band of noise, this results in the formation of coherent dipole line sources and, thus, of destructive interferences, at a distance from the acoustically transparent obstacle. The goal of this paper is to show how we can calculate this phase lag and the relative amplitudes of the components, and how they compare to the actual measurements. The results for the model investigated show good agreement between calculation and measurement, within the precision expected.

Experimental determination of the variation of specific heat ratio in air with humidity
View Description Hide DescriptionThis paper describes a precise and direct acoustical method for experimental verification of the variation of γ in air with humidity. The experimental results are within 100 to 250 ppm of the theoretical predictions. The experimental arrangement may be used to assess the specific heat ratio of other gases or gas mixtures by a comparison method.

Sensitivity of total field and array performance to profile‐model selection in the deep ocean
View Description Hide DescriptionThe sensitivity of total‐field receptions to sound‐speed profile choice is analyzed using ray theory. The profiles are depth dependent, and may be used to describe a deep‐ocean sound channel. A variety of locations of a fixed source and receiver, separated by less than about 50 km, is considered. Given a specified profile and a second, simpler profile constructed by procedures previously described [J. Acoust. Soc. Am. 7 5, 112–124 (1984)], it is demonstrated that the acoustic fields associated with the profiles are negligibly different. Approximations for total‐field phase and amplitude differences are presented, which facilitate the determination of those ranges where the total fields match closely. In addition, the sensitivity of performance measures for horizontal linear receiving arrays to profile selection is studied. Expressions for normalized power pattern are developed which incorporate certain nonplane‐wave effects associated with an assumed dominant ray arrival. Conditions are presented for which a simpler profile may replace a specified profile and still maintain nearly equivalent array performance.

Some representations of the integrals of Cron and Sherman for surface‐generated ocean noise
View Description Hide DescriptionTwo integrals of Cron and Sherman which arise in modeling of ocean‐generated surface noise are given several representations, the most notable of which is obtained from the Laplace transformation of a mild generalization of the given integrals. It is also found that the complex sum, with weights 1 and i, of the integrals reduces to a sum of simpler integrals plus an expression which is representable as a multiple partial derivative of a spherical Hankel function of the first kind, with respect to the normalized vertically projected baseline length of the two relevant sensors. This latter expression is the homolog for the correlation function, of the pressure field of a distant vertical axial multipole of order m being proportional to the m‐fold derivative, in a vertical direction, of the Green’s function of a monopole, which is proportional to a spherical Hankel function of the first kind of order zero.

Speed of sound in saturated pure water
View Description Hide DescriptionThe speed of sound in saturated pure water has been measured between 273.16 and 534.69 K at 7.5 MHz using the pulse‐echo‐overlap method. An equation was fitted to our data within the experimental uncertainties of 0.05%. This equation predicts the values of speed of sound over the whole vapor pressure curve with an assigned zero value at the critical point. Our data were combined with available density data to obtain the isentropic compressibilities.

Sound field fluctuations in a shallow water waveguide
View Description Hide DescriptionExperimental measurements of sound transmissions in a laboratory waveguide are analyzed. The transmissions were from a single source to a vertical array of receivers that operated as a mode filter. Water waves on the surface caused the sound fields to fluctuate at the receiver. We used theories of coherent mode transmission to describe the experiments. Within a mode, sound field fluctuations have three components: (1) phase fluctuations due to fluctuations of the horizontal component of the wave number, (2) fluctuations of depth‐dependent eigenfunctions at source and receiver positions, and (3) mismatch of the mode filter to the local eigenfunction. Analysis showed that most of the fluctuations of the mode filtered signals were due to components (2) and (3).

Applicability of the Biot theory. I. Low‐porosity materials
View Description Hide DescriptionThe Biot theory of wave propagation in porous, saturated materials contains 13 parameters. We discuss empirical and theoretical ways to predict values of these parameters for natural materials. The self‐consistent theory of composites is used to predict the elastic moduli of the skeletal frame assuming that the inclusions (pore fluid, sediment grains) are needle‐shaped at low concentrations. The Biot theory is then used to predict compressional and shear wave speeds in consolidated materials. In a man‐made material (porous sintered glass), the predictions agree with experimental data to within 3% (experimental uncertainty is also 3%); these samples were distilled‐water‐saturated. The predictions agree with data to within 1% for Berea sandstone, and to within 5% for Bedford limestone; all of these samples were brine‐saturated. The predictions agree with data to within 8% for distilled‐water‐saturated Bedford limestone. In the natural sedimentary rocks, the experimental uncertainty in measuredwave speeds is estimated at 5%, and the comparisons apply at high effective pressures (>0.3 kbar), where the experimentally determined wave speeds approach ‘‘limiting velocities.’’ In distilled‐water‐saturated Massilon sandstone, predicted shear wave speeds are about 25% to 35% higher than measured speeds; this may indicate a reduction of the frame shear modulus due to interaction of the pore fluid with the minerals of the rock.

Applicability of the Biot theory. II. Suspensions
View Description Hide DescriptionThe Biot theory is used to compute compressional wave speeds and attenuation in fluid–solid suspensions. The frame moduli are estimated from the self‐consistent theory of composites, assuming needle‐shaped pores and spherical or ellipsoidal grains of uniform size. The permeability is computed from the Kozeny–Carman equation. The attenuation data are matched by assuming that all losses are caused by viscousabsorption in the fluid.For suspensions of kaolinite, polystyrene beads, and glass beads in various fluids, the Biot model agrees with experimental sound speed data at least as well as do other models. For aqueous suspensions of kaolinite, of attapulgite, and of hydrousaluminum silicate pigments, the Biot model generally is in better agreement with attenuation data than are other models.

Applicability of the Biot theory. III. Wave speeds versus depth in marine sediments
View Description Hide DescriptionEmpirical and theoretical methods are used to estimate the elastic moduli of the skeletal frame in sedimentary materials. The Biot model is then used to estimate compressional wave speeds as a function of depth. These estimates are compared to laboratory data and to field measurements. Using the empirical method to estimate the frame moduli, the measured wave speeds are matched within 3% for Ottawa sand pack and within 10% for glass bead pack at pressures corresponding to depths of about 500 m or less. A new method for estimating the frame moduli of partially consolidated materials is used to quantify the effects of grain packing and cementation. Velocity gradients are estimated for shear and compressional waves in terrigenous sand and calcareous clay. Predicted gradients for compressional waves, when corrected for the effect of temperature, lie within the range of published values. Predicted gradients for shear waves fall within a range of shear‐wave gradients determined from i n s i t u measurements of saturated terrestrial and marine materials. Using a constant porosity of 0.40 to simulate conditions in pure sands, predicted compressional wave gradients agree with laboratory results.

High‐frequency acoustic variability in the Arctic
View Description Hide DescriptionFluctuations in acoustic intensity have been studied for two locations in the Arctic—the Chukchi Sea (1974) and the Kane Basin (1979)—using the same measurement and analysis techniques. A five‐frequency transducer covering the range 10–75 kHz was moved continuously in the vertical direction from 10–70 m. The results were used to determine the vertical correlation length and the coefficient of variation (rms variance) for the intensity at the five frequencies simultaneously. Conductivity and temperature versus depth were measured continuously before and after each set of acoustic runs. These profiles were used to construct sound ray diagrams and to compute the refractive index variance. For direct‐path propagation in both locations, it was found that when the acoustic intensity variance at low spatial wavenumbers is filtered out, remaining variance depends on the first power of the frequency and approximately the square of the range. This internal‐wavelike behavior is supported by additional evidence. The vertical correlation lengths observed for the direct‐path intensity indicate that the scattering features have lifetimes longer than a few seconds and less than a few minutes. The study suggests that the scattering structures are related to anisotropiceddies that tend toward isotropy as they cascade to smaller sizes. Plots of a strength parameter versus a diffraction parameter show that after deterministic variations are removed from the measurements, the remaining variations lie in the unsaturated direct‐path region.

Rough surface boundary wave attenuation due to incoherent scatter
View Description Hide DescriptionCalculation of the energy scattered out of an advancing wave front allows one to derive an attenuation coefficient δ for the low‐frequency boundary mode carried by a rough interface between two media. For a point source of sound on or near the interface this leads to a farfield boundary wave pressure p _{ B }∝r ^{−} ^{1} ^{/} ^{2} f ^{3} ^{/} ^{2} e ^{−δr } with δ=A f ^{6}, where r is the range, f is the frequency, and A is a parameter which depends upon the form and size of roughness (for close packing it is proportional to the fifth power of the roughness height). For given r, then, p _{ B } must exhibit a maximum in the frequency domain at f=(4A r)^{−} ^{1} ^{/} ^{6} and falls off sharply for higher frequencies. This paper gives a simple procedure for calculating A for bossy roughness models of two fluid interfaces. In the particular case of a hard rough boundary the theory predicts results in reasonable agreement with reported experimental results, at least insofar as the magnitude and shape of the p _{ B }(f) curve is concerned.

Theory of ultrasonic resonances in a viscoelastic layer
View Description Hide DescriptionWe present a resonancetheory for the acoustic transmission and reflection coefficients of an elastic plate imbedded in a fluid medium, which includes the effects of plate viscosity. This formulation provides a direct means for determining the material parameters of the plate from the measured acoustic resonances of the Rayleigh and Lamb waves in the plate (i.e., their positions in frequency or angle, their widths, and their heights) which are given in our formalism by explicit analytic expressions that depend on the material parameters. Viscosity is seen to manifest itself in a decrease of the resonance peaks and in a broadening and frequency dependence of the resonance widths, which may be used to determine the frequency‐dependent loss factor of the plate.

The influence of the physical properties of ice on reflectivity
View Description Hide DescriptionA model for the plane‐wave reflection coefficient from a layered elastic solid bounded on either side by a fluid half‐space is developed and applied to study environmental factors affecting the reflectivity of smooth arctic ice. Experimental measurements of the internal friction in ice and snow are reviewed and applied to compute realistic attenuation profiles. An examination of the effect of ice layers conforming with measuredtemperature profiles in floe ice shows that the use of average values for sound speed and attenuation is an acceptable approximation for modeling purposes. A study of the reflectivity due to the absorption of shear and compressional waves demonstrates that shear wave attenuation is the most important loss mechanism from 20° to 60° incidence. The effect of an additional snow layer is to produce more attenuation without shifting the pattern of reflection nulls. Major results are presented for a frequency of 2 kHz. Data comparisons are performed from 0.5–3 kHz that show a limited qualitative agreement with the model.

A biological chorus in deep water northwest of Australia
View Description Hide DescriptionThis paper is a summary of observations of a biological chorus in deep waters northwest of Australia. The data were collected from underwater noise recordings made in the course of sonar performance trials at sites in the eastern Indian Ocean.Measurements are made for frequencies between 20 and 800 Hz. Chorusnoise at 500 Hz, consisting of continual drumming sounds, was evident for 9–10 h in the evening, with the peak noise level occurring soon after sunset. The noise spectrum level at this peak frequency rose to 72 dB r e: 1 μPa^{2}/Hz, approximately 12 dB above the background noise level. Typical spectra and time waveforms for individual noise bursts are presented. The source of the noise is believed to be fish of the family Sciaenidae, commonly known as croakers.