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Journal of the Acoustical Society of America

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Apr 1994

Volume 95, Issue 4, pp. 1711-2305

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The asymptotic computational ansatz: Application to critical angle beam transmission boundary integral equation solution

R. A. Roberts

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1711-1725 (1994); (15 pages)

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Surface wave generation arising from critical angle beam transmission at a smooth but arbitrarily curved fluid–solid interface is studied using a numerical boundary integral equation (BIE) technique that incorporates a priori field information to significantly reduce computation. The technique substitutes a GTD‐type computational ansatz into the BIE, where the phase factors of the ansatz are prescribed via asymptotic analysis, thus transforming the unknown variables to slowly varying amplitude factors. In situations where the asymptotic evaluation of these amplitude factors becomes intractable or inaccurate, common numerical integral equation methods are employed to determine the amplitude factors. The technique yields exact (in the numerically convergent sense) results for high‐frequency scattering problems unsolvable by prevalent analytic or numeric techniques. Numerical implementation of the technique for critical angle beam transmission is demonstrated.
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43.20.Fn Scattering of acoustic waves

Sound scattering by slender bodies of arbitrary shape

Michel Tran Van Nhieu and Frédérique Ywanne

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1726-1733 (1994); (8 pages) | Cited 3 times

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Scattering of a spherical wave from a perfectly rigid slender body of arbitrary shape is considered. The point source is assumed to be located in the far field of each body cross section but may be placed in the near field of the target. The problem is investigated theoretically with the matched asymptotic expansions method and an approximate solution is derived for the scattered pressure, which takes into account the curvature of the incident wave front. The presented formalism combines the so‐called slender‐body approximation and the two‐dimensional Kirchhoff theory. It allows a great simplification in the geometrical description of the body surface and leads to a practical method even for bodies of complex shape. In the monostatic case, it is theoretically shown that the obtained solution is asymptotically equivalent to that provided by geometrical optics for a large class of finite scatterers. Lastly, monostatic and bistatic angular distributions are computed for a prolate spheroid in the near and far fields to support the present theory.
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43.20.Fn Scattering of acoustic waves

Stop bands for elastic waves in periodic composite materials

E. N. Economou and M. Sigalas

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1734-1740 (1994); (7 pages) | Cited 34 times

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The frequency ω versus wave vector k of elastic waves propagating in periodic binary composites consisting of solid inclusions placed periodically in a host matrix was calculated. Attention was focused on the possibility of stop bands (spectral gaps) for all directions of propagation in such composites. It was found that gold or lead inclusions of about 10% volume fraction in a Si or Be matrix give rise to stop bands.
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43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.20.Jr Velocity and attenuation of elastic and poroelastic waves
43.20.Mv Waveguides, wave propagation in tubes and ducts
62.30.+d Mechanical and elastic waves; vibrations

Spherical wave functions and tensor Green’s functions in transversely isotropic saturated poroelastic media

Wei Ren

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1741-1747 (1994); (7 pages)

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This paper is an outgrowth of the method of angular spectrum expansions studied recently in electromagnetics. A spherical wave function theory for bounded homogeneous transversely isotropic saturated poroelastic media (TISPM) is developed. Series forms, integral representations, and addition theorems of the spherical wave functions of the first, second, third, and fourth kind for homogeneous TISPM are presented. Weyl’s method of deriving the scalar Green’s functions in isotropic media is generalized so as to study tensor Green’s functions in TISPM. The series representations of Green’s functions are of the form of separation variables. These representations are well suited to imposing the boundary conditions in dealing with fields and waves in spherically layered TISPM.
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43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.20.Jr Velocity and attenuation of elastic and poroelastic waves
43.20.Bi Mathematical theory of wave propagation

Elastic waves in homogeneous and layered transversely isotropic media: Plane waves and Gaussian wave packets. A general approach

M. Spies

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1748-1760 (1994); (13 pages) | Cited 7 times

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Solutions to the equation of motion are derived for transversely isotropic media such as fiber composites, ideally fiber‐textured austenitic steels, or extruded metal‐matrix composites. The approach is most general in that the orientation of the materials’ axis of rotational symmetry is arbitrary. Thus the results obtained using a coordinate‐free representation are particularly convenient in view of layered structures, where for the materials of interest the fiber axis is perpendicular to the surface normal, but variable in orientation. Plane elastic waves are characterized by the corresponding wave vectors, making especially possible a quantitative evaluation of the deviation of wave propagation direction and energy flux, which is characteristic for anisotropic materials. Reflection and refraction of plane waves at an interface between two arbitrarily oriented transversely isotropic media is examined yielding an algorithm that provides the respective reflection and transmission coefficients. The propagation of elastic waves of finite spatial and temporal extent is modeled using the concept of Gaussian wave packets. The relations given in the literature for general anisotropic media are specialized to the homogeneous and layered transversely isotropic cases. Numerical evaluation of the analytical results is included.
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43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.20.Jr Velocity and attenuation of elastic and poroelastic waves
43.20.Bi Mathematical theory of wave propagation
62.30.+d Mechanical and elastic waves; vibrations

On the determination of the elastic moduli of anisotropic media from limited acoustical data

John J. Ditri

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1761-1767 (1994); (7 pages) | Cited 5 times

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The determination of the elastic moduli of generally anisotropic media from acoustic information has a long history. It is known that, given measurements of the three wave speeds and corresponding polarization vectors in various directions n̂∊R3, all 21 elastic moduli can be determined [A. N. Norris, Q. J. Mech. Appl. Math. 42, 413 (1989)]. However, in some practical cases, depending upon the type of loading a structure will see, not all 21 elastic moduli are needed, and it is therefore of interest to know how many of the constants can be determined from a less robust data set. In this paper, upper bounds are placed on the number of elastic constants that can be determined from acoustic data, which is limited to one or two planes. It is shown that for generally anisotropic media, 15 elastic constants can be uniquely obtained from data taken in one plane, and 20 of the 21 elastic constants can be uniquely obtained from data taken in two planes. Specific examples are given to illustrate the general results.
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43.20.Hq Velocity and attenuation of acoustic waves
43.20.Ye Measurement methods and instrumentation
43.20.Jr Velocity and attenuation of elastic and poroelastic waves
62.20.D- Elasticity

Generalized basic equations for bending motions of piezoelectric bars formulated from Hamilton’s principle

Haruo Tanaka

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1768-1772 (1994); (5 pages) | Cited 3 times

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For the bending motion of piezoelectric bars, the basic equations have generally been formulated from Hamilton’s principle. Using these equations, the bending motions of bars can be analyzed more easily, and the equivalent circuits for the bending vibrators of the bars also can be derived more systematically.
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43.20.Ks Standing waves, resonance, normal modes
43.40.At Experimental and theoretical studies of vibrating systems
43.40.Dx Vibrations of membranes and plates
43.38.Fx Piezoelectric and ferroelectric transducers

Calculation of transient tube‐wave signals in cross‐borehole acoustics

Adrianus T. de Hoop, Bastiaan P. de Hon, and Andrew L. Kurkjian

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1773-1789 (1994); (17 pages) | Cited 1 time

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Closed‐form expressions are obtained for the transient acoustic pressure in a borehole, due to the action of a volume injection (acoustic monopole) source in another borehole in a typical cross‐well seismic setting with a homogeneous isotropic solid formation. At the relatively low frequencies involved the acoustic wave motion inside a fluid‐filled borehole, which may be surrounded by a structure of perfectly bonded circularly cylindrical solid shells, is dominated by tube waves. The excitation and propagation properties of the tube wave are modeled by regarding the borehole as an acoustic waveguide with a compliant inner wall. The corresponding elastic wave‐field quantities at the outer borehole wall are evaluated through a plane‐strain elastostatic transfer of the stress and the elastic displacement across the shell structure. For the radiation of the wave‐field quantities into the formation, the elastodynamic Kirchhoff–Huygens integral representation is used. The acoustic pressure on the axis of the receiving borehole is evaluated with the aid of the fluid/solid acoustic reciprocity theorem. Various physical phenomena are described by the resulting expressions, including pre‐ and postcritical phenomena (conical waves) for slow formations, and tunnelinglike phenomena for proximate boreholes in fast formations.
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43.20.Mv Waveguides, wave propagation in tubes and ducts
43.20.Jr Velocity and attenuation of elastic and poroelastic waves
43.20.Gp Reflection, refraction, diffraction, interference, and scattering of elastic and poroelastic waves
43.40.Ph Seismology and geophysical prospecting; seismographs

Impulse‐response method to predict echo responses from targets of complex geometry. Part II. Computer implementation and experimental validation

Alain Lhémery and Raphaële Raillon

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1790-1800 (1994); (11 pages) | Cited 1 time

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A theoretical model has been proposed for the complete solution of the problem of the radiation of transient ultrasonic pulses, their scattering by targets of complex shape and arbitrary acoustic impedance, and their reception [A. Lhémery, ‘‘Impulse‐response method to predict echo responses from targets of complex geometry. Part I: Theory,’’ J. Acoust. Soc. Am. 90, 2799–2807 (1991)]. Here, its computer implementation and its experimental validation are considered. First, the theoretical formulation is derived in a discrete form and an algorithm is explicitly given to allow its computer implementation. Precautions to be taken to ensure good precision of numerical results are discussed in detail. Then, predicted waveforms are compared with existing measurements (scattering by planar targets) and new measurements (scattering by nonplanar targets). The model is shown accurately to predict measured echoes, both qualitatively and quantitatively. However, some discrepancies are observed and explained as resulting from the lack of precision in the Kirchhoff‐like approximation made in the model’s derivation.
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43.20.Px Transient radiation and scattering
43.35.Yb Ultrasonic instrumentation and measurement techniques
43.58.Ta Computers and computer programs in acoustics

Impulse‐response method to predict echo responses from targets of complex geometry. Part III. Application to nondestructive testing

Alain Lhémery and Raphaële Raillon

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1801-1808 (1994); (8 pages) | Cited 1 time

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A theoretical model has been proposed for predicting the radiation of transient ultrasonic pulses, their scattering by targets of complex shape, and their reception. [A. Lhémery, ‘‘Impulse‐response method to predict echo responses from targets of complex geometry. Part I. Theory,’’ J. Acoust. Soc. Am. 90, 2799–2807 (1991)]. Its computer implementation and experimental validation have also been considered [A. Lhémery and R. Raillon, ‘‘Impulse‐response method to predict echo responses from targets of complex geometry. Part II. Computer implementation and experimental validation,’’ J. Acoust. Soc. Am. 95, 1790–1800 (1994)]. The accuracy of the model allows its application to a problem arising in classical NDT pulse‐echo methods, namely, the discrimination of small defects and misoriented cracks. The echo‐response from these two types of defects can produce the same B‐ or C‐scan images in certain circumstances, leading to the possibility of serious misinterpretations. First, the relative importance of both the geometric and the electroacoustical parameters involved in the echo‐forming mechanism is determined by a computer study conducted with our model’s implementation. Simple relations are found between the echo responses of the two kinds of defects. Insight gained from modeling such responses has led to the development of a new signal processing method to identify the defect. An example of its efficiency on measured waveforms is given.
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43.20.Px Transient radiation and scattering
43.35.Yb Ultrasonic instrumentation and measurement techniques
43.35.Zc Use of ultrasonics in nondestructive testing, industrial processes, and industrial products
43.60.Qv Signal processing instrumentation, integrated systems, smart transducers, devices and architectures, displays and interfaces for acoustic systems

Acoustic coupling to membrane waves on elastic shells

Andrew N. Norris and Douglas A. Rebinsky

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1809-1829 (1994); (21 pages) | Cited 14 times

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The interaction of an acoustic field with a smooth thin shell in a fluid is described by the superposition of a background field plus membrane waves on the shell. The former is defined by a local impedance condition, which accounts for the inertia of the shell, but takes no account of the in‐surface, membrane effects. The shell’s flexural stiffness turns out to be of secondary importance. The bulk of the paper deals with the coupling mechanism between the acoustic field and the supersonic membrane waves, both longitudinal and shear. The coupling is mediated by the shell curvature, and vanishes when the curvature vanishes. Ray methods are used to express the membrane waves by curved wave fronts with amplitudes subject to a transport equation over the curved shell surface. The coupling, and decoupling or launching, then reduces to solving an ordinary differential equation for the unknown ray amplitude. In essence, the transport equation is forced, or ‘‘beaten’’ by the locally phase‐matched background field. Explicit expressions are obtained for the coupling and detachment coefficients on arbitrarily curved regions. These are combined, using ray theory for the propagation over the shell, to give the scattered field due to rays traveling over the shell. The general results are explicitly tested on the cylinder and sphere, for which the ensemble of surface rays can be summed into a resonance form, and numerical comparisons are made with the exact results for these canonical geometries.
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43.20.Dk Ray acoustics
43.20.Fn Scattering of acoustic waves
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.40.Yq Instrumentation and techniques for tests and measurement relating to shock and vibration, including vibration pickups, indicators, and generators, mechanical impedance

Propagation of vertical shock waves in the atmosphere

Christophe Besset and Elisabeth Blanc

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1830-1839 (1994); (10 pages) | Cited 2 times

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Modeling the propagation of shock waves is a major problem for studies of wave propagation in the atmosphere because of the exponential amplification of the wave amplitude during the vertical propagation. The waves generated by pulse sources at the ground can have shock wave characteristics upon reaching the upper layers of the atmosphere. This paper proposes a new computation method based on studies of shock propagation in ray tubes for laboratory experiments and attempts to adapt this method to atmospheric propagation. This nonlinear approach shows reflections from the stratospheric temperature increase that were not predicted by the linear acoustic theory for the same atmospheric model. The nonlinear computations also predicts focusing of the rays at mesospheric altitudes.
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43.28.Bj Mechanisms affecting sound propagation in air, sound speed in the air
43.28.Mw Shock and blast waves, sonic boom
92.60.Gn Winds and their effects

A high‐frequency approximation of sound propagation in a stratified moving atmosphere above a porous ground surface

Kai Ming Li

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1840-1852 (1994); (13 pages) | Cited 4 times

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This paper examines the sound propagation in a moving stratified atmosphere above a porous ground surface. A generalized expression is derived for the sound field above a porous half‐space and the existence of an asymptotic behavior is demonstrated. The leading term of the solution is not only consistent with ray theory but mathematically rigorous. The analysis starts from the fundamental hydrodynamic equations of pressure and particle velocity, etc., and the assumption that the atmosphere is vertically stratified. These hydrodynamic equations are reduced to a one‐dimensional Helmholtz equation by applying the Fourier transform method. The solution for the simplified Helmholtz equation is approximated in the high‐frequency limit and then the sound pressure is represented by a Fourier integral. The method of stationary phase is used to evaluate the Fourier integral in order to give an asymptotic expression for the sound pressure. It should be emphasized that the Weyl–Van der Pol formula has been generalized to give the field due to a point source in a moving stratified medium above an extended reaction boundary. The total sound field is derived as the sum of three components: a direct contribution from the source, a geometrically reflected component, and a ground wave term, respectively. The ground wave gives a significant contribution to the total sound field especially at low frequencies and at the ground effect dip.
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43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.20.Bi Mathematical theory of wave propagation
43.50.Vt Topographical and meteorological factors in noise propagation

Oscillation modes of underexpanded jets issuing from square and equilateral triangular nozzles

Y. Umeda and R. Ishii

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1853-1857 (1994); (5 pages) | Cited 2 times

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The oscillation modes of underexpanded jets exhausted from square and equilateral triangular nozzles were investigated experimentally. Two stages were observed for both jets. The oscillation modes corresponding to these stages were identified by using optical and acoustical methods. The experimental results show that oscillation modes for both jets are first axisymmetric and then sinuous with increasing jet pressure ratio. The helical oscillation mode, which appeared for the circular jet, was not observed in these jets. The hysteresis phenomenon found for the circular jet cannot be seen in these jets.
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43.28.Ra Generation of sound by fluid flow, aerodynamic sound and turbulence
43.25.Gf Standing waves; resonance
43.50.Nm Aerodynamic and jet noise

A small‐slope theory of rough surface scattering

Suzanne T. McDaniel

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1858-1864 (1994); (7 pages) | Cited 1 time

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A method due to Urusovskii [Sov. Phys. Acoust. 5, 362–369 (1959)] is applied to predict the field scattered by rough pressure release surfaces. Comparison of the predictions of this theory for scattering from a sinusoidal surface shows that his method yields results closer to an exact solution than do other approximations. When applied to predict the coherent field scattered by a random rough surface, the predictions agree well with those of the Kirchhoff approximation provided that the horizontal wave‐number component of the incident field is much greater than the wave numbers at which the spectral decomposition of the surface irregularities attains its maximum value. For high‐frequency scatter near the forward direction, Urusovskii’s theory yields a new result that provides a significant improvement to the Kirchhoff approximation.
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43.30.Hw Rough interface scattering
43.20.Fn Scattering of acoustic waves

Long‐range backscatter from the Mid‐Atlantic Ridge

Nicholas C. Makris and Jonathan M. Berkson

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1865-1881 (1994); (17 pages) | Cited 9 times

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Acoustic backscatter returns measured with a vertical source and horizontal receiving array are beamformed and charted to respective scattering sites on the western flank of the Mid‐Atlantic Ridge (MAR). Well‐defined patterns of high‐level backscatter resembling bottom morphology occur within the direct path and at convergence zone ranges. Measured backscatter is compared with modeled two‐way transmission loss using the wide‐angle parabolic equation (PE) and high‐resolution supporting bathymetry. The level of backscatter is found to be strongly dependent upon two‐way transmission loss (TL). Specifically, TL selects prominent bathymetric features from which high backscatter is returned, with backscatter maxima corresponding to TL minima. Scattering strength estimated for the wide area surveyed shows low variance and relatively minimal spatial variation. Apparently, distinct scattering contributions are so well mixed in long‐range backscatter, that dominant variations are generally due to propagation. These results indicate that it is possible to forecast the range and azimuth of prominent MAR backscatter returns simply by propagation modeling if high‐resolution bathymetry is available. They also have led to the development of a new technique for ambiguity removal in reverberation data measured with a horizontal line array. The method takes advantage of environmental asymmetry provided by TL in highly range‐dependent environments and does not require multiple measurements as do other existing methods.
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43.30.Bp Normal mode propagation of sound in water
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.30.Vh Active sonar systems

Oceanographic–topographic interactions in acoustic propagation in the Iceland–Faeroes front region

Jessie C. Carman and Allan R. Robinson

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1882-1894 (1994); (13 pages)

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Effects of oceanographic variation with distance on long‐range, low‐frequency acoustic propagation in the Iceland–Faeroes front region of the ocean are considered in the presence of realistic topographic variations. A numerical model using a parabolic approximation to the Helmholtz equation, a fluid sediment parametrization and variable topography, is used to calculate acoustic propagation. Oceanographic sound‐speed fields output from the Harvard Open Ocean Model, supplemented by climatology in deep regions, provide input sound‐speed profiles. Two different propagation transects are considered, both running from shallow to deep water across a developing eddy and across the front. Source depths near the surface, middle, and bottom of the shallow starting profile are studied. Some cases of near invariance to oceanographic changes are found, as are other cases of locally large oceanographic effects (≳30 dB).
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43.30.Bp Normal mode propagation of sound in water
43.30.Pc Ocean parameter estimation by acoustical methods; remote sensing; imaging, inversion, acoustic tomography

A theoretical study of low‐frequency oceanic ambient noise

H. N. Og̃uz

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1895-1912 (1994); (18 pages) | Cited 10 times

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This paper describes a theoretical model that predicts the wind‐dependent ambient noise level in the ocean. Wave breaking and subsequent formation of whitecaps are assumed to be the sole source of sound at the sea surface and their contributions are computed by the use of a simple model for the bubble cloud generated by this process. Inverted hemispherical shapes for which an analytical solution to the wave equation is given are employed to describe the cloud geometry. The input physical parameters to the model are the bubble‐size distribution, the dipole strength of the entrained bubbles, the cloud size distribution and growth rate, and the void fraction of the bubble cloud. By using an empirical relation between the whitecap coverage ratio and the wind speed, the underwater ambient noise and surface source levels are computed as a function of frequency and wind speed. Calculated noise levels are in good agreement with the field measurements.
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43.30.Ft Volume scattering
43.30.Nb Noise in water; generation mechanisms and characteristics of the field
43.30.Jx Radiation from objects vibrating under water, acoustic and mechanical impedance

Bubble production by capillary‐gravity waves

Ali R. Kolaini, Lawrence A. Crum, and Ronald A. Roy

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1913-1921 (1994); (9 pages) | Cited 7 times

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In the absence of whitecapping, other physical mechanisms may contribute to the generation of high‐frequency ambient noise. It has been suggested [Longuet‐Higgins, in NATO Advanced Research Workshop on Sound Generation Mechanisms at the Open Surface (NATO, Geneva, 1987)] that capillary waves, with surface profiles that are peaked downward in the troughs and are relatively flat at the crests, can inject acoustically active bubbles into the ocean, and thus contribute to the ambient noise background. It has been demonstrated in the laboratory that bubble injection can be generated at the trough of capillary‐gravity, short‐fetched waves by blowing air over water contained in a long, narrow tank. Simultaneous in situ acoustic and high‐speed video monitoring of the capillary‐gravity waves demonstrate that these waves can produce acoustically active bubbles. The generation of capillary waves depends principally upon the surface tension, which can be changed by adding surface‐active agents to the water. The bubble production rate per unit area of these capillary‐gravity waves was measured, as well as the dependence of this rate on wind speed, laboratory wind fetch, and surface tension. It was determined that an increase in water salinity and a reduction in surface tension increases the bubble production rate. The spectra of radiated frequencies ranges from 1 kHz to over 100 kHz with a broadband peak located around 4 kHz. The measured spectral densities were weakly related to wind speed. The wind‐speed threshold value for bubble production was determined to be approximately 8.6 m/s (14.6 m/s at 10‐m level) in fresh water and salt water, which decreased to 8.1 m/s (13.8 m/s at 10‐m level) with a surface tension of 40.5 dyn/cm.
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43.30.Lz Underwater applications of nonlinear acoustics; explosions
43.30.Nb Noise in water; generation mechanisms and characteristics of the field

Acoustical measurements of microbubbles within ship wakes

Mark V. Trevorrow, Svein Vagle, and David M. Farmer

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1922-1930 (1994); (9 pages) | Cited 7 times

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High‐frequency sonar measurements of target strength due to microbubbles were obtained within the wakes of three oceanographic vessels. Two self‐contained, high‐frequency acoustics instruments suspended at 25‐m depth were used to measure the wake acoustic properties during three separate sea trials. The backscatter cross section per unit volume, Mv, as a function of depth and time was calculated from the echo intensity of six upward‐looking, conical beam sonars (28–400 kHz). Four 100‐kHz steerable sidescans allowed measurement of wake locations, widths, and persistence. In the near‐surface core of the wake Mv reached peak values of approximately 0.3 m−1 for the 120‐ and 200‐kHz sonars. The volumetric scattering cross sections were observed to be roughly constant at all frequencies within the top 5–6 m of the wake, suggesting a roughly homogeneous vertical bubble distribution. However, differences in the volumetric backscatter at different acoustical frequencies suggest a higher relative concentration of larger bubbles (≳100 μm) in the center of the wake. The ship wakes were observed to spread to typical widths of up to 66 m (ship speed 10 kn) and to depths of 7–12 m and to persist as strong acoustic scatterers for approximately 7.5 min. Gas diffusion causing bubble dissolution is suggested as the mechanism for decay of the wake bubble clouds.
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43.30.Lz Underwater applications of nonlinear acoustics; explosions
43.30.Nb Noise in water; generation mechanisms and characteristics of the field
43.30.Vh Active sonar systems

Delta operator technique to improve the Thomson–Haskell‐method stability for propagation in multilayered anisotropic absorbing plates

Michel Castaings and Bernard Hosten

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1931-1941 (1994); (11 pages) | Cited 8 times

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A modified version of the transfer‐matrix method that models propagation of heterogeneous plane waves through immersed multilayered plates made of anisotropic absorbing layers is presented. Since this method suffers from numerical instabilities, the so‐called delta matrix operator is applied. As for propagation through isotropic media, the case of propagation in the principal plane of anisotropic media requires us to define sixth‐order delta matrices. This method eliminates numerical difficulties. The same technique is used for propagation out of the principal plane. Fifteenth‐order delta matrices are necessary to get improved results. However, numerical problems persist with computational data corresponding to the usual experimental situations. Then, a modified version of the delta matrix operator is proposed. From the reflection and transmission coefficients expressions, both 15th‐ and 20th‐order delta matrices are necessary to get reliable numerical results, whatever the computational data may be.
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43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.35.Mr Acoustics of viscoelastic materials

Focusing of fast transverse modes in (001) silicon at ultrasonic frequencies

Kwang Yul Kim, Arthur G. Every, and Wolfgang Sachse

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1942-1952 (1994); (11 pages) | Cited 3 times

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This paper presents observations of the focusing of fast transverse (FT) ultrasonic waves in a (001) oriented, disk‐shaped silicon single crystal. These modes are almost perfectly shear horizontally (SH) polarized and were absent from earlier reported observations of focusing of ultrasonic waves based on axisymmetric excitation and sensing. In an experiment the FT modes are generated and detected at room temperature by two small [100] polarized PZT piezoelectric shear transducers. The source transducer is fixed on the bottom surface of the specimen and the detector scans the top surface in the [100] direction along lines that intersect the [010] axis at various distances from epicenter. The observed focusing pattern indicates a strong concentration of the FT mode flux in a narrow band about the (100) plane containing the source. Because of the specific way in which the monopolar source acts, the radiated acoustic flux pattern breaks the fourfold symmetry associated with cubic media. While it shows a strong concentration of FT flux toward the (100) plane, it suppresses FT modes propagating very near the (010) plane passing through the source. The spatial variation of the Fourier components of the detected signal at approximately 2, 6, and 8 MHz has been examined, and there is good accountability for this variation on the basis of the computed frequency domain elastodynamic Green’s function for silicon.
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43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.35.Ty Other physical effects of sound
62.65.+k Acoustical properties of solids

Mode theory as a framework for the investigation of the generation of a Stoneley wave at a liquid–solid interface

R. Briers, O. Leroy, G. N. Shkerdin, and Yu. V. Gulyaev

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1953-1966 (1994); (14 pages) | Cited 8 times

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A theoretical model, based on mode theory for acoustic waves, is presented in order to describe the complicated scattering of an ultrasonic volume or surface wave at the boundary between two adjacent liquids abutting a single solid. Analytical expressions for the displacement fields of the scattered and mode‐converted waves are derived. In particular, it is shown that a volume wave incident from the liquid of the first liquid/solid structure can generate a Stoneley wave along the interface of the second liquid/solid structure. The relative amplitude of the displacement of the excited Stoneley wave is calculated for several (liquid–liquid)/solid configurations. The angle of most efficient excitation can be derived from the maximum of the function describing the interaction between a radiation mode and a Stoneley eigenmode in the division plane separating both liquid/solid structures.
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43.35.Pt Surface waves in solids and liquids

A fundamental study of the excitation of a Stoneley wave at a liquid–solid interface: Rayleigh angle and Gaussian beam incidence

R. Briers, O. Leroy, and G. N. Shkerdin

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1967-1976 (1994); (10 pages) | Cited 2 times

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Theoretical calculations show that near the Rayleigh angle the amplitude of the Stoneley wave generated by a homogeneous plane wave incident at the intersection between two liquids overlying a single solid has a local maximum. This maximum is very small compared with the one obtained for almost normal incidence at the mentioned intersection when the most efficient excitation occurs. The paper also presents numerical results for the generation of a Stoneley wave by means of an incident Gaussian beam. Finally, a very simple to interpret expression for the amplitude of the excited Stoneley wave is given.
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43.35.Pt Surface waves in solids and liquids
68.43.-h Chemisorption/physisorption: adsorbates on surfaces

A new concept of a low‐frequency underwater sound source

Dimitri M. Donskoy and Joseph E. Blue

J. Acoust. Soc. Am. Volume 95, Issue 4, pp. 1977-1982 (1994); (6 pages)

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A new concept of a low‐frequency (<1000‐Hz) underwater sound source has been developed and tested. The oscillation of a rigid body and a means for converting the dipole oscillation of the body to monopole radiation are used in this source. The source can be powered with electric or linear motors or hydrodynamic exciters that convert tow or flow to vibration. To prove the concept, a small version of the electric motor powered source has been built and successfully tested. To extend the bandwidth of the source, the variable resonance frequency and multiresonances of the device are discussed. A gas spring with a frequency‐dependent stiffness is employed for the multifrequency resonant source design. The source promises to be reliable, inexpensive, highly efficient, and powerful.
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43.38.Ar Transducing principles, materials, and structures: general
43.30.Yj Transducers and transducer arrays for underwater sound; transducer calibration
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