Volume 83, Issue 6, June 1988
Index of content:

High‐frequency reflection and scattering of sound by ellipsoidally embossed surfaces
View Description Hide DescriptionEarlier results for coherent reflection and incoherent scattering by embossed rigid or free surfaces [V. Twersky, J. Acoust. Soc. Am. 2 9, 209–225 (1957); 7 3, 85–94 (1983)] are applied to ellipsoidal bosses with axes large compared to wavelength. The asymptotic procedures used originally for circular cylinders and spheres, and, subsequently, for elliptic cylinders [J. E. Burke and V. Twersky, J. Acoust. Soc. Am. 4 0, 883–895 (1966)], are generalized to triaxial ellipsoids, and results for the corresponding bosses are obtained by the image method. Illustrative curves for both isotropic and anisotropic surfaces exhibit the influences of boss shape and orientation on the coherent reflection coefficients and incoherent differential scattering cross sections per unit area with emphasis on forward‐(specular) and backscatteredeffects.

Generalized Doppler effect: Coherent and incoherent spectra
View Description Hide DescriptionThe generalized Doppler effect spectrum produced by particles moving on arbitrary trajectories is analyzed.Scattering by a single particle moving in the farfield of a transmitter and a receiver is considered. It is shown that the Doppler spectrum exciting the particle is due to two factors: The longitudinal (or radial) component of the motion produces a spectrum similar to the conventional Doppler effect, by affecting the phase of the excitation wave. In addition, spectral effects are produced by the particle moving transversely (or angularly) through the spatially modulated radiation pattern of the transmitter. By virtue of the reciprocity properties of transmitters and receivers, each spectral component of the excitation signal again gives rise to spectra induced by the longitudinal and the transversal components of the motion relative to the receiver. The combined Doppler spectrum observed at the receiving transducer or antenna output is a convolution of all four spectra. The behavior of an ensemble of scattering particles is analyzed. The statistics are found by defining the particle and/or the trajectory parameters as random variables. Presently, it is assumed that the particles are identical, their positions are uncorrelated, and multiple scattering is ignored. It is shown that the interference of scattered waves from various particles, manifested in the coherent radiation, gives rise to a spectrum that might be different from that of a single particle. In special cases, the combined spectrum degenerates into a single frequency, and when this is the transmitter’s frequency, the Doppler effect completely disappears. This explains the fact that when we have moving media, but the boundary surfaces are at rest, there is no Doppler effect. The results of the present analysis contribute to our understanding of Doppler velocimetry methods using ultrasound or laser radiation in medical and industrial instrumentation.

Wave propagation in laminated composite plates
View Description Hide DescriptionA stiffness method has been used in this article to study dispersive wave propagation in a laminated anisotropic plate. The advantage of this method is in its usefulness in obtaining numerical results for the dispersion characteristics of waves propagating in a plate with an arbitrary number of arbitrarily anisotropic laminae. This method has been applied here, as a way of illustration, to a plate made up of transversely isotropic laminae with the axis of isotropy of each lamina lying in the plane of the lamina. Results thus obtained are shown to agree well with the exact solutions for isotropic and transversely isotropic single layered plates. Numerical results are presented for cross‐ply (0°/90°/0°) laminated composite plates and show that the frequency spectrum in this case differs considerably from that for a single layered (0°) plate.

Wideband acoustic response of fluid‐saturated porous rocks: Theory and preliminary results using waveguided samples
View Description Hide DescriptionThe complex dilatational (C ^{*} _{12}) and shear (C ^{*} _{44}) frequency‐dependent elastic constants of nonporous and porous solids are measured in a frequency range 5kHz to 1 MHz. The measurements are performed in a continuous wave acoustic transmission bridge using cylindrical samples. Using samples with free external surfaces produces waveguided modes, enabling experiments to be conducted circumventing problems of diffraction and wavefront spreading, which are difficult to correct over broad frequency ranges. The theory of waveguided elasticwave propagation in isotropic media with complex elastic constants [generalization of the Pochammer–Cree solution, Pochammer, J. Math. (Crelle) 8 1, 324 (1876)] is presented. For solids with frequency‐independent complex elastic constants (constant Q), solution of the resulting dispersion relations reveals the appearance of specific dissipation peaks associated with waveguide geometry. The dispersion relations are utilized in the inversion of torsional shear and extensional experimental results from nonporous and porous solids, thus obtaining their complex frequency‐dependent effective elastic constants. A great variation in the elastic constants of Plexiglas with frequency is demonstrated. Evidence of the effects of pore scattering and the reduction of matrix moduli due to water adsorption is shown for porous glass. The effects of adsorption on the effective elastic moduli of porous solids are quantified utilizing the concept of surface elastic constants [M. E. Gurtin and I. A. Murdoch, Arch. Rat. Mech. Anal. 5 7, 291 (1975)]. The resulting equation reveals the importance of the surface to volume ratio in determining the effective elastic constants.

Prediction of the nonlinearity parameter of a liquid from the Percus–Yevick equation
View Description Hide DescriptionUsing the compressibility of the Percus–Yevick equation, where a liquid is regarded as a hard sphere molecule, a nonlinearity parameter B/A of the liquid was calculated. The ratio B/A is in fair agreement with the experimental value. The expression of B/A has revealed information on the importance of geometrical packing effect on B/A.

Controlled experiments of the diffraction of sound by a curved surface
View Description Hide DescriptionControlled measurements of the sound field from a point source above a curved surface are described. The measurements were made in the frequency range between 0.3 and 10 kHz, in the case of a rigid boundary and a surface of finite impedance. Receiver positions include all of the area within, and above, the shadow zone and for various source heights. Particular attention is given to the region across the shadow boundary. The measurements are compared to diffraction theory expressed in terms of a residue series, or creeping wave solution. The calculation is extended by removing restrictive approximations and by carrying the computation to higher‐order terms. A numerical algorithm allows the extension to the general case of a finite impedance. Above the shadow boundary, the sound field is calculated using geometrical theory that accounts for reflections from a curved surface. Deep within the shadow, theory and measurements agree to, typically, 0.5 dB. The same agreement is obtained between measurements and the geometrical theory well above the shadow boundary. In the vicinity of the shadow boundary, both theories agree to within 0.5 dB but differ from the measured results by 2 to 5 dB. Finally, the theory is compared to measurements obtained outdoors above a grass covered curved ground with no refraction and above flat ground with refraction.

Numerical ray tracing in the atmospheric surface layer
View Description Hide DescriptionA numerical ray‐tracing model, including calculation of the sound pressure, was developed. It is valid for propagation from a point source in a moving, stratified atmosphere. Numerical integration of the ray equations was performed, and all rays reaching a specific point were found. Several expressions for the height dependency of the wind speed and the temperature were used, e.g., Monin–Obukhov similarity theory functions, the parameters of which were determined by use of a least‐squares method. Measurements of sound propagation from a point source over finite impedance ground were made. Meteorological parameters were monitored simultaneously, wind direction and relative humidity at a single height, wind speed and temperature at five elevations. Comparison with the model was made out to a distance of 150 m. The agreement between the model values and those measured was good. The influence of the directional characteristics of the source was studied, and found to be very important.

A generalized approach to acoustic intensity
View Description Hide DescriptionAn approach to acoustic energy considerations by employing the general theory of mechanics of continua is the topic of this article. A description of power flow is developed from the first law of thermodynamics instead of utilizing combinations of the linearized governing equations describing a continuous medium. The main aim is the derivation of energy equations when a mean background flow is present. The actual energy flux in moving media is first considered. After this, the appropriate energy equations to consider in moving media are taken up. In the first case, an accurate interpretation of energy flux is essential to determine the power output and location of a sound source. For the second topic, acoustic energy equations can describe conservation principles. These, in turn, can be used to determine regions where dissipation is occurring.

Calculations pertaining to the dipole nature of the edgetone
View Description Hide DescriptionCalculations are performed to verify the dipole nature of the edgetone in which the flow consists of an incompressible two‐dimensional jet issuing from a nozzle and impinging on a fixed rigid wedge‐shaped body. The wedge body is abruptly removed from a previously computed, laboratory‐verified, multifrequency edgetone flow at a Reynolds number of 450 and replaced by an oscillating dipole. The dipole strength is treated as unknown and part of the solution process but is such that the combination of the dipole flow and jet flow yields a transverse jet velocity time trace near the the dipole identical to that from the previously computed edgetone flow. The resultant flow field is numerically computed for a Reynolds number of 450 and, after initial start‐up effects, the flow field for the latest cycle computed strongly resembles that of the previously computed edgetone flow. Results for the jet–dipole flow are given in the form of stream function and equivorticity contour plots and jet spectra. In addition, sound‐pressure radiation due to a fluctuating pressure distribution at the surface of the wedge‐shaped body is computed using data from the previously calculated edgetone flow. The moduli of the computed sound‐pressure components corresponding to various time frequencies reveal on polar plots a figure eight pattern in the farfield with the largest component or tone associated with the frequency of jet impingement. According to theory, this is the farfield sound pattern due to a fluctuating dipole centered at the wedge tip with axis transverse to the wedge tip.

Superresonant systems of scatterers. II
View Description Hide DescriptionS y s t e m s of identical monopole scatterers interacting through multiple scatter will, under certain conditions, develop normal modes, i.e., b o n a f i d eresonant behavior at certain frequencies (corresponding to poles of the multiple scatter coefficients). This occurs when the monopole scattering cross sections are large enough to give significant interaction; this happens for highly tuned scatterers, e.g., gas‐filled bubbles/balloons/shells in water, insonified at frequencies near their characteristic resonant frequencies. This phenomenon has been called s u p e r r e s o n a n c e (SR) and has been discussed mostly in the case when the primary energy transport mechanism between scatterers is a cylindrically spreading boundary wave, like the flexure mode of a thin elastic plate [I. Tolstoy, J. Acoust. Soc. Am. 8 0, 282–294 (1986)]. The singularity of the field at the scatterer is removed by introducing the finite radius of the scatterers. The present article investigates the effect of the plate material on the SR phenomenon, showing that for a steel plate and a pair of bubbles/balloons (doublet) the acoustic amplitudes on the scatterer surfaces may be 3×10^{3} times the free‐field value, i.e., one has an amplitude amplification factor μ≊3×10^{3}, where μ decreases as the plate rigidity decreases. On the other hand, in a homogeneous acoustic full space SR does not, strictly speaking, occur:
The scatterer system does not become fully resonant (the theory does not indicate the existence of poles) since spherically spreading acoustic modes are less efficient transporters of energy between scatterers than the cylindrically spreading boundary modes. Nevertheless, simple symmetrical systems of bubbles/balloons/shells can still demonstrate a tendency to resonate, i.e., produce sharp peaks on the μ curve. Plane and polyhedral configurations may still yield μ≊10^{2} at each scatterer. To distinguish this from b o n a f i d e SRs near a plate, we call these q u a s i r e s o n a n c e s (QRs). It is shown, however, that partial shielding between selected pairs of scatterers in such configurations affects the phase relationships in the system in such a way as to allow the appearance of true SRs.

Random‐bottom structural effects on shallow‐water sound transmission using a modified ray theory
View Description Hide DescriptionA modified ray theory is used to study the effects on acoustic intensity of randomness in bottom structure. A shallow isospeed ocean channel with horizontal boundaries is assumed. The randomness is produced by stochastic variations in the bottom density and sound speed in the horizontal direction beneath the water–bottom interface. Beam and time displacements at the ocean bottom are incorporated into each acoustic ray. Ray geometry, spreading loss, and bottom loss are analyzed in order to obtain expressions for the mean and variance of intensity at a point receiver for a transmitted cw signal. Formulas are sufficiently general to permit their use with different bottom‐acoustic models of sound reflection. In order to incorporate bottom attenuation simply, Mackenzie theory is employed here. The distinctive acoustic consequences of bottoms of different density mean and horizontal correlation are discussed. In addition, comparisons of results using the modified ray theory and standard ray theory are provided. Also, intensity moments are described for differing source–receiver range, water depth, and acoustic frequency.

Wideband ambiguity function of broadband signals
View Description Hide DescriptionBroadband signal analysis and design for radar and sonar systems require the use of a wideband ambiguity function (WAF) to estimate their performance. The properties of WAF for FM signals are studied and the results of numerical computation are compared with the theoretical expressions. The main findings presented here include the following. (a) A broadband LFM signal is not a Doppler tolerant one. At high velocity, the magnitude of WAF is similar to the signal envelope, and its range resolution decreases obviously. (b) an LPM signal exhibits a fairly good range resolution, even at very high velocity. The performances of Doppler tolerant signals for three models are described and compared. The different envelopes for the LPM case have little influence on the behavior of WAF. (c) The unbiased delay estimation for both LFM and LPM signals, with bandwidth B= f _{max}− f _{min} and duration T, can be obtained by a special shift in time, which is such that t ∈ ( f _{min} T/B, f _{max} T/B). An approximate method for derivation of WAF, based on the Doppler cross‐power spectrum and the stationary phase principle, is proposed. Such an analysis is applied to a bat’s sonar signal.

Experimental confirmation of horizontal refraction of cw acoustic radiation from a point source in a wedge‐shaped ocean environment
View Description Hide DescriptionAnalysis of experimental data obtained in the region of the East Australian Continental Slope has been found to be consistent with theoretical predictions of energetic horizontal refraction due to multiple reflections from a sloping bottom. The observed azimuthal characteristics are in accordance with both normal mode and ray theoretical solutions. The experiment, conducted with two ships (one towing a source and the other an array), started in water ≊400 to 500 m deep with an initial separation of 34 km and proceeded to deeper water on a diverging but constant line of bearing course. Bearing shifts deduced from beamformed data show changes of tens of degrees in as little as half an hour. These bearing shifts demonstrate the dominance of horizontally refracted arrivals for the geometry. A combination of source–array positions and critical angle effects served to limit both the azimuthal extent of energy received and the total number of modes arriving at any one position.

Numerical computations of time‐domain diffractions from wedges and reflections from facets
View Description Hide DescriptionNumerical computations of time‐domain impulsive functions require a low‐pass‐filter operation to satisfy the Nyquist sampling rule. For example, the exact impulsive solutions for diffraction and reflection from a rigid wedge [M. A. Biot and I. Tolstoy, J. Acoust. Soc. Am. 2 9, 381–391 (1957)] both have singularities at their initial arrival times. These particular solutions can be approximated and low‐pass filtered to satisfy the sampling rule in numerical computations. In evaluating specular reflection from a finite plane facet, a reinterpretation of the physical meanings of the terms resulting from the impulsive solution of the Fresnel–Kirchhoff integral is introduced [M. Born and E. Wolf, P r i n c i p l e s o f O p t i c s (Pergamon, Oxford, 1965), Sec. A.9, and A. W. Trorey, Geophysics 3 5, 762–784 (1970)]. It is believed that the solution contains terms associated only with reflection, and that the interpretation of the Rubinowicz representation of the boundary terms as boundary diffraction waves is physically incorrect. As a consequence, for amplitude calculations of a specular facet reflection, a working hypothesis is proposed, namely that the reflected amplitude is proportional to the incident signal where the constant of proportionality is a function of the geometry, facet width, and the signal waveform. By numerical studies, the constant of proportionality g(v) can be expressed as a polynomial in v, where v=w(λ_{ A } r)^{1} ^{/} ^{2}, w is the facet width, λ_{ A } is the wavelength corresponding to the peak frequency of the signal, and r is the distance from a colocated source and receiver to the facet. The function g(v) depends on the waveform of the signal (i.e., a boxcar, single cycle of a sinewave, etc.). As v tends to zero, the facet reflection tends to zero. For large v (>2 or 3), g(v) tends to one and the facet reflection is effectively that from a full plane.

Shallow‐water high‐frequency bottom scattering off Panama City, Florida
View Description Hide DescriptionA series of bottom backscatteringmeasurements was made in a flat, uniform, and isotropic area 19 miles south of Panama City, FL. Sidescan sonar, underwater television, stereo photography, high‐resolution bathymetry, and sediment core analysis were used to locate and classify the experimental site. A sidescan sonar areal mosaic was contructed detailing the relationship between the experimental area and the surrounding topography. Bottom backscatteringmeasurements were made as a function of frequency (20–180 kHz), grazing angle (5°–30°), azimuthal angle, and environmental conditions. Backscattering strengths were found to follow Lambert’s law with little frequency dependence or measurableanisotropy. For this particular site, scattering strengths at 90 kHz were found to agree with predictions made using the Applied Physics Laboratory—University of Washington (APL—UW) model.

The moving thermoacoustic array: A theoretical study
View Description Hide DescriptionA theoretical study of the moving thermoacoustic array as an underwater sound projector is presented. The movement imparts to the acoustic signal a Doppler shift which is direction dependent. Extremely high Doppler shifts are achievable because it is a noncontact source. While the moving thermoacoustic array has certain interesting features compared to conventional acoustic projectors, notably the noncontact property and the direction‐dependent Doppler shift, its thermoacoustic energy conversion efficiency is found to be no better than that of the stationary thermoacoustic array. It was found that the thermoacoustic conversion was most efficient when the laser energy was delivered as an impulse train. The efficiency is fundamentally limited by the physical properties of the medium, particularly the coefficient of thermal expansion and the specific heat.

The dynamic shear modulus of marine sediments
View Description Hide DescriptionThe dynamic shear modulus of marine sediments (μ) as a function of overburden pressure (p) and voids ratio (e) can be represented approximately by the expression μ=μ_{0}(p/p _{0})^{ n } ×exp(−Γe), where μ_{0}, n, and Γ are constants. Available laboratory results for sands, silts, and clays over a pressure range of 24 to 700 kPa and a voids ratio range of 0.35 to 1.5 lead to the values: n=0.45, Γ=1.50 and, if p _{0} is taken as 1 atm, μ_{0}=2526 atm. For bentonite, an expandable clay with high cation‐exchange capacity, the voids ratio dependence is similar (Γ=1.60) but the pressure has relatively little effect (n=0.08). Secondary effects due to quasistatic stress history and dynamic shear strain amplitude may modify these values somewhat for low‐amplitude acoustic signals in i n s i t u sediments.

An experimental study of acoustic waves in saturated glass beads
View Description Hide DescriptionThe Biot–Stoll theory describes the propagation of acoustic waves in a saturated granular material. Expressions for the phase velocity and attenuation derived from the theory depend explicitly on the viscosity, density, and bulk modulus of the pore fluid. The results of an experiment designed to measure the dependence of the phase velocity and attenuation of compressional waves on these properties of the fluid are reported. The measurements were made in a laboratory tank containing glass beads saturated with a mixture of water and glycerin. To compare theory to data, the parameters of the theory were chosen so that they agreed with the measurements for the case of pure water. The values of the parameters were then kept constant and the theory was compared with the measurements obtained for various proportions of glycerin. It was shown that, within the estimates of the accuracy of the measurements, the Biot–Stoll theory predicts the effect of the fluid properties on the phase velocity and attenuation of compressional waves.

Measurement of the temporal fluctuations of cw tones propagated in the marginal ice zone
View Description Hide DescriptionThe frequency dispersion of hour‐long acoustic tonal signals, stepped in frequency between 25 and 200 Hz, is measured via the covariance method. This method is computationally efficient and relatively unexploited for this purpose. The signals are from MIZEX 84 and have propagated through a partially ice‐covered 100‐km path. Source/receive drift‐induced Doppler shift compares favorably with available navigational data. The dispersion is expressed in terms of the parameter ν, which is a function of a host of possible oceanic processes dynamically perturbing the sound field.

Effects of water‐depth mismatch on matched‐field localization in shallow water
View Description Hide DescriptionThis article discusses the impact of incorrect estimates of the water column depth on matched‐field source localization in a shallow water environment. Computer calculations were performed for the case of a nominal 100‐m depth water column subject to water‐depth variations of up to ±3.5 m, which would be caused by long‐period ocean swell or by tidal changes. The environment was assumed to be range independent (by proper choice of the geometry); thus the question of rough surfacescattering was not an issue. The calculations incorporated source depths of 25, 50, and 75 m, a propagation distance of 4 km, an acoustic frequency of 150 Hz, and a linear vertical receiving array. The array consisted of 21 hydrophones with an interelement spacing of 2.5 m, and it spanned the center one‐half of the water column (25‐ to 75‐m depth). The matched‐field algorithm utilized in this study is the high‐resolution maximum‐likelihood estimator. A primary result of the work is that, as the output of the matched‐field processor degrades due to water‐depth mismatch, the apparent source location varies in a systematic way; i.e., the source appears closer and deeper for increasing water depth and, conversely, the source appears farther and shallower for decreasing water depths. Another significant observation is that, as acoustic modes are stripped from the waveguide due to reduced channel depth, instabilities in the solution of the processor cause random variations in localization estimates.