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Feb 1991

Volume 89, Issue 2, pp. 503-946

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Analysis of boundary conditions for elastic wave interaction with an interface between two solids

S. I. Rokhlin and Y. J. Wang

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 503-515 (1991); (13 pages) | Cited 40 times

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The boundary conditions for an interface between two solids are analyzed to model a thin viscoelastic interface layer. Boundary conditions that relate stresses and displacements on both sides of the interface are obtained as an asymptotic representation of three‐dimensional solutions for an interface layer in the limit of small wavelength to thickness ratio. The interface boundary conditions obtained include interface stiffnesses and inertia and terms involving coupling between normal and tangential stresses and displacements. The applicability of such boundary conditions is analyzed by comparison with exact solutions for ultrasonic wave reflection. Fundamental boundary conditions are introduced where only one transverse or normal mass or stiffness is included. It is shown that the solution for more exact interface boundary conditions which include two inertia elements and two stiffness elements can be decomposed into a sum of fundamental solutions. The transition between welded and slip boundary conditions on an interface with a thin viscous layer is also analyzed as a function of interface thickness, viscous skin depth, and frequency.
Show PACS
43.20.Bi Mathematical theory of wave propagation
43.20.Fn Scattering of acoustic waves
43.20.Mv Waveguides, wave propagation in tubes and ducts
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants

Influence of voids in interface zones on Lamb wave propagation in composite plates

R. Y. Vasudeva and P. Govinda Rao

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 516-522 (1991); (7 pages) | Cited 1 time

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An attempt is made to develop a simple analytical model to study the influence of voids in the interface zones—leading to a weak adhesion—between the constituent laminas of a composite plate treating the thin adhesive layer as a linear elastic material with voids (LEMV) [S. C. Cowin and J. W. Nunziato, J. Elasticity 13, 125–147 (1983)]. The frequency equation for free harmonic wave motion in a sandwich plate with an LEMV adhesive layer at the core is derived and the dispersion curves for Al/adhesive/Al sandwich are compared for a thin adhesive layer core with those obtained from other available imperfect bond model studies.
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43.20.Bi Mathematical theory of wave propagation
43.20.Hq Velocity and attenuation of acoustic waves
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants

A generalized diffraction tomography algorithm

L.‐J. Gelius, I. Johansen, N. Sponheim, and J. J. Stamnes

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 523-528 (1991); (6 pages) | Cited 3 times

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Available diffraction tomography algorithms are based on Fourier transform techniques and require either plane‐wave illumination in a uniform background medium or far‐field illumination combined with paraxial approximations. In this paper a generalized diffraction tomography algorithm is introduced that can handle both irregularly spaced measurement data, nonuniform background models, and general aquisition geometries. Using data from water tank experiments, the method’s ability to yield high‐quality reconstructions of geometry and velocity, as long as the weak‐scattering assumption is satisfied, is demonstrated.
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43.20.Fn Scattering of acoustic waves
43.20.Hq Velocity and attenuation of acoustic waves
43.20.Ye Measurement methods and instrumentation
43.30.Sf Acoustical detection of marine life; passive and active

An improved formalism for wave scattering from rough surfaces

D. Michael Milder

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 529-541 (1991); (13 pages) | Cited 12 times

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The scattered field and its normal gradient obey a mutual linear relation at the scattering surface that is distinct from the physical boundary condition connecting either quantity to the incident radiation. On a moderately rough surface this relation can be represented by an operator whose series expansion in surface slope converges nicely even for large values of the Rayleigh parameter. This allows the Helmholtz integral for scattering amplitude to be written as a series of readily computable terms, one or two of which provide good approximations for surfaces too irregular for the usual Bragg expansion. This formulation reproduces the Bragg series for small surface elevations, and in the limit of low roughness wavenumber gives the Kirchhoff approximation with an explicit correction term in surface curvature. The usual results for a composite surface also emerge naturally. On several test profiles the method produces better overall accuracy than other multiscale approximations, at comparable efficiency.
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43.20.Fn Scattering of acoustic waves
43.30.Hw Rough interface scattering

Elastic wave propagation in fluid‐loaded multiaxial anisotropic media

Adnan H. Nayfeh and D. E. Chimenti

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 542-549 (1991); (8 pages) | Cited 6 times

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Theoretical investigations supported by extensive experimental comparisons are carried out on the interaction of ultrasonic waves with multilayered media. It is assumed that each constituent of the plate can possess up to as low as monoclinic symmetry. The plate is assumed to be immersed in a fluid and subjected to incident acoustic waves at arbitrary angles from the normal as well as at arbitrary azimuthal angles. Reflection and transmission coefficients are derived from which all characteristic behavior of the system is identified. Solutions are obtained for the individual layers that relate the field variables at the upper and lower layer surfaces. The response of the total plate proceeds by satisfying appropriate interfacial conditions across the layers.
Show PACS
43.20.Fn Scattering of acoustic waves
43.20.Mv Waveguides, wave propagation in tubes and ducts
43.35.Cg Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in solids; elastic constants
43.30.Ky Structures and materials for absorbing sound in water; propagation in fluid-filled permeable material

The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross‐sectional shape

Michael R. Stinson

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 550-558 (1991); (9 pages) | Cited 25 times

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The general Kirchhoff theory of sound propagation in a circular tube is shown to take a considerably simpler form in a regime that includes both narrow and wide tubes. For tube radii greater than rw=10−3 cm and sound frequencies f such that rwf3/2<106 cm s−3/2, the Kirchhoff solution reduces to the approximate solution suggested by Zwikker and Kosten. In this regime, viscosity and thermal conductivity effects are treated separately, within complex density and complex compressibility functions. The sound pressure is essentially constant through each cross section, and the excess density and sound pressure (when scaled by the equilibrium density and pressure of air, respectively) are comparable in magnitude. These last two observations are assumed to apply to uniform tubes having arbitrary cross‐sectional shape, and a generalized theory of sound propagation in narrow and wide tubes is derived. The two‐dimensional wave equation that results can be used to describe the variation of either particle velocity or excess temperature over a cross section. Complex density and compressibility functions, propagation constants, and characteristic impedances may then be calculated. As an example, this procedure has been used to determine the propagation characteristics for a tube of rectangular cross section.
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43.20.Mv Waveguides, wave propagation in tubes and ducts

Signal pressure received by a hydrophone placed on a plate backed by a compliant baffle

Sung H. Ko and Howard H. Schloemer

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 559-564 (1991); (6 pages) | Cited 1 time

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An investigation is made of the signal reception of a hydrophone placed in front of an elastic plate backed by a compliant baffle layer. The baffle layer is the compliant tube array modeled by Junger [J. Acoust. Soc. Am. 78, 1010 (1985)] to represent a homogeneous, dispersive fluid layer. Noise reduction baffles such as compliant tubes are acoustically soft and thus tend to degrade the signal received. This paper describes the development of a theoretical model for evaluating the signal reception, and a comparison of theoretical results with experimental data is presented.
Show PACS
43.20.Tb Interaction of vibrating structures with surrounding medium
43.20.Ye Measurement methods and instrumentation
43.30.Jx Radiation from objects vibrating under water, acoustic and mechanical impedance
43.30.Wi Passive sonar systems and algorithms, matched field processing in underwater acoustics

An eigenvector method to determine the transient response of cylindrical shells in a fluid with uniform axial flow

Peter R. Stepanishen and D. D. Ebenezer

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 565-573 (1991); (9 pages) | Cited 1 time

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A general time domain approach is presented to evaluate the vibratory response of cylindrical shells in time‐invariant axial flows to broadband time‐dependent excitations. The approach is based on the use of an in vacuo eigenvector expansion with time‐dependent coefficients for the velocity field of the shell. A set of convolution integral equations are developed for the eigenvelocities that are coupled due to the fluid loading. These equations are similiar to those developed for planar vibrators and are readily solved by marching forward in time. The known terms in the equations are the ρc fluid‐loaded admittances of each eigenvector and the radition impulse responses. Since these are easily obtained, a large number of eigenvectors can be included in the analysis. Numerical results illustrating the responses of a simply supported cylindrical shell to an impulsive ring excitation are presented.
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43.20.Tb Interaction of vibrating structures with surrounding medium
43.20.Dk Ray acoustics
43.20.Rz Steady-state radiation from sources, impedance, radiation patterns, boundary element methods
43.28.Py Interaction of fluid motion and sound, Doppler effect, and sound in flow ducts

Ray tracing for reconstructive tomography in the presence of object discontinuity boundaries: A comparative analysis of recursive schemes

Anders H. Andersen

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 574-582 (1991); (9 pages)

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A comparative analysis of recursive ray tracing strategies for tomographic reconstruction from projections with diffracting sources is presented. One algorithm employs ray tracing in reprojection toward a correction of the true projection values for subsequent straight‐ray reconstruction. The other algorithm performs curved‐ray reconstruction along the retraced rays by algebraic methods for each recursive step. The performance for reconstruction of objects exhibiting discontinuity boundaries is studied. Within the geometrical optics approximation, the forward process is also shown to lead to multiple linking refracted rays. In an object of low velocity, there may be ranges of receive positions over which no linking refracted rays exist. Geometrically diffracted rays are introduced to describe the signal actually received over the ‘‘forbidden’’ range.
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43.20.Dk Ray acoustics
43.20.Fn Scattering of acoustic waves
43.30.Cq Ray propagation of sound in water

Noncollinear interaction of a tone with noise

Stephen J. Lind and Mark F. Hamilton

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 583-591 (1991); (9 pages)

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An experiment was performed to investigate the noncollinear interaction of a high‐frequency tone with low‐frequency noise. The nonlinear interaction took place in an air‐filled rectangular duct. A low‐frequency band of noise was transmitted in the (0,0) mode together with a high‐frequency tone in the (1,0) mode. The angle between the two interacting waves was 55°. Measurements of the frequency spectra were made at locations that were well within the shock formation distance of either primary wave. The spectral shapes of the sum and difference frequency sidebands of noise are scalloped in appearance, and the number of nulls in each sideband increases with range from the source. Theoretical predictions for the nonlinearly generated sidebands are in good overall agreement with experiment. The predictions are based on a quasilinear analysis developed previously to describe the noncollinear interaction of two tones in a rectangular duct [M. F. Hamilton and J. A. TenCate, J. Acoust. Soc. Am. 81, 1703–1712 (1987)]. Comparisons are made with the corresponding case of collinear interaction, in which both primary waves propagate in the (0,0) mode.
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43.25.Hg Interaction of intense sound waves with noise
43.25.Lj Parametric arrays, interaction of sound with sound, virtual sources

Finite‐element solution of the inverse problem in bubble swarm acoustics

Kerry W. Commander and Robert J. McDonald

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 592-597 (1991); (6 pages) | Cited 7 times

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The bubble population near the ocean surface is of considerable interest. This population affects surface scattering strength, propagation near the surface, and the exchange of gases between the atmosphere and the sea. Both optical and acoustical means have been used to measure the bubble population with varying degrees of success. The acoustic method requires measurements at multiple frequencies and their subsequent conversion to bubble densities through either the resonance theory approximation or numerical solution of the resulting integral equation. In this paper, a numerical solution to the integral equation is obtained using the method of weighted residuals with linear B splines as basis functions. A regularization technique is employed to stabilize the solution. A number of plausible bubble distribution functions are generated along with their acoustic properties to test the robustness of the technique. This approach is shown to yield very accurate bubble distributions from high‐quality attenuation data.
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43.25.Yw Nonlinear acoustics of bubbly liquids

Continuous wave phase detection for probing nonlinear elastic wave interactions in rocks

Paul A. Johnson, Albert Migliori, and Thomas J. Shankland

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 598-603 (1991); (6 pages)

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A new method that uses nonlinear elastic wave generation to produce a continuous wave (cw) phase measurement from which dimensions or velocities of a body can be obtained is described. Like the technique of standing wave resonance for obtaining sound velocities, this method takes advantage of the high accuracy characteristic of frequency measurements. In the experiment, two intersecting, high‐frequency primary signals f1 and f2 are mixed inside a sample, creating a directional beam at the difference frequency Δf=f1−f2. An externally generated, low‐pass‐filtered Δf signal is electronically mixed with the signal obtained from the sample. As either primary frequency is swept, the dc component from the mixer varies between relative maximum and minimum values at characteristic frequency intervals depending on the phase differences. The resulting interference signal can be used to calculate the distance from the mixing volume in the sample to the detector and to the two primary signal transmitters, providing that a single characteristic distance and wave velocities are known. The reverse experiment is determining velocities from known dimensions.
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43.25.Zx Measurement methods and instrumentation for nonlinear acoustics

Coherent propagation of sound in correlated distributions of resonant spherical scatterers

N. E. Berger and V. Twersky

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 604-616 (1991); (13 pages)

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Expressions for underwater propagation in bubble regions based on the index of refraction (η) in uncorrelated random distributions of monopole resonators are restricted to sparse bubble packing (very small volume fraction w). As w increases, correlations arise, and coupling with higher‐order multipoles is not necessarily negligible. To provide prototypes for data inversion, integral equations are analyzed for η in correlated distributions of spheres (including up to quadrupole coefficients) in terms of shell and moment expansions of the Percus–Yevick correlation function. Graphical results for w up to 20% indicate the decrease in magnitudes at resonance, the increase in resonance frequency, and the broadening of the resonance region relative to the uncorrelated case. A simple explicit three‐moment approximation is derived for distributions of monopoles plus dipoles that provides good accord with machine computations (based on ten‐moment or on eight‐shell expansions) to about w=7.5%, and also holds at least qualitatively for larger w. The explicit form may also be used with the first three moments of other correlation functions.
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43.30.Bp Normal mode propagation of sound in water
43.30.Ft Volume scattering

Echoes from vertically striated subresonant bubble clouds: A model for ocean surface reverberation

B. Edward McDonald

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 617-622 (1991); (6 pages) | Cited 2 times

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A surface reverberation model for acoustic frequencies below several kHz is proposed based on weak scatter from inhomogeneities whose geometry is descriptive of recent ocean observation [e.g., Farmer and Vagle, J. Acoust. Soc. Am. 86, 1897 (1989)]. Scatterers in this model are vertical cylinders of elliptical cross section representing either filamentary‐ or sheetlike subresonant microbubble clouds whose population decreases exponentially with depth. This geometry approximates intermediate‐aged fossils of breaking waves and/or convective processes. Born approximation (weak scatter) results from this model show substantial agreement with observed surface backscatter cross sections as a function of wind speed, grazing angle, and acoustic frequency in the range 0.2–20 kHz. It is demonstrated that almost all the high‐frequency weak backscatter in the model is specular reflection from surfaces of volume scatterers. Some preliminary speculations involving Langmuir circulation are offered for the application of this model to surface reverberation at frequencies below a few hundred Hz, where data are scarce.
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43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries
43.30.Zk Experimental modeling

Simulations of rough interface scattering

David H. Berman

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 623-636 (1991); (14 pages) | Cited 7 times

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This paper describes numerical simulations of rough interface scattering. Both Dirichlet and fluid–solid boundary conditions are treated. The Rayleigh–Fourier method is used to compute exact plane‐wave scattering amplitudes and results are compared to various approximations. The small‐slope approximation of Voronovich performs remarkably well, while the tangent‐plane approximation is shown to miss some essential physics of scattering. It is observed that at the Rayleigh angle there is a peak in the backscattering amplitude, even for plane‐wave incidence. It is argued that the statistics of plane‐wave scattering amplitudes are Gaussian.
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43.30.Hw Rough interface scattering
43.20.Fn Scattering of acoustic waves

Acoustic propagation through baffles with rectangular compliant tubes

J. A. Moore

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 637-647 (1991); (11 pages)

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Compliant tube baffles have been designed as effective barriers for acoustic propagation underwater over wide bands of frequencies. Acoustic energy reflection occurs due to compliant cross‐sectional resonances in the tubes that exhibit significant volume deformation. Additional bandwidth is achieved with multiple layers of compliant tubes tuned to different frequencies. The design challenge is to provide sufficient baffle insertion loss levels and bandwidth while limiting adverse transmission peaks associated with interactions between noncompliant tube resonances and, tube and fluid layer system resonances. This paper discusses the acoustic performance of baffles with compliant tubes of rectangular cross section as opposed to the conventional designs with elliptical cross section. The tubes consist of flat face plates held apart along their edges by spacers. The knifelike edge support constitutes a simple support boundary condition for bending deformation of the face plate. This compliant tube configuration allows added design flexibility and degrees of freedom in minimizing the adverse effects of transmission peaks in a baffle’s insertion loss. Unequal face plate thicknesses and varied mass of the edge spacer have been effectively utilized in this regard.
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43.30.Ky Structures and materials for absorbing sound in water; propagation in fluid-filled permeable material

A comparison of broadband and narrow‐band modal inversions for bottom geoacoustic properties at a site near Corpus Christi, Texas

James F. Lynch, Subramaniam D. Rajan, and George V. Frisk

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 648-665 (1991); (18 pages) | Cited 13 times

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Abstract Unavailable
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43.30.Ma Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics

Modeling the acoustic scattering by under‐ice‐ridge keels

David Rubenstein and Robert Greene

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 666-672 (1991); (7 pages)

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In this paper, the exact solution of scattering off a flat surface with a single semielliptical cylindrical boss of infinite extent is developed. The cylindrical boss approximates the geometric shape of an ice‐ridge keel. A far‐field approximation and the results to a grid of randomly distributed scatterers are applied. First, the case where the simulated keels have a single, constant depth is examined. In the frequency range below 200 Hz, energy is scattered mostly into steep angles, where it is eventually lost to bottom absorption. Above 200 Hz, a significant fraction of the scattered energy is directed into shallow angles, where it becomes a propagating incoherent component. Statistics are developed that describe a Rayleigh distribution of keel depths. A formula is developed that relates the standard deviation of surface roughness to mean keel depth and mean ice‐ridge spacing. Then the model is applied to find that for a given ice roughness, a Rayleigh distribution yields less coherent reflection loss, and slightly less scattering loss, than a field of constant keel depths.

Modeling high‐frequency vertical directional spectra

Robert M. Kennedy and Thomas K. Szlyk

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 673-681 (1991); (9 pages) | Cited 4 times

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A measurement of the acoustic ambient arriving from a horizontal direction along with total sound‐pressure‐level spectrum allows one to infer directional spectra and some physical characteristics of sea surface‐generated sound. A 1‐year measurement of these two quantities was made at high frequency, i.e., 8–32 kHz, in The Tongue of the Ocean, The Bahamas. The horizontally directed ambient was measured using vertically oriented line arrays (broadside beam only available) and was observed at wind speeds ranging from 1–30 kn. The resulting database was used to estimate the statistics of anisotropic “noise gain.” The measured statistics showed two distinct cases: whitecaps present and not present. The relationship of these results to the total vertical directional spectrum is investigated by comparisons with a model that includes spatially diffuse near‐surface sources, media scattering, and thermal noise. A comparison of the model and experiment results quantified an “effective” thickness of an acoustically active sublayer of monopole sources and a frequency‐dependent media smearing of the source‐to‐receiver ray paths.

Stabilized high‐resolution beamforming with horizontal arrays: Two experimental trials in shallow water

Robert F. Gragg and Bruce H. Pasewark

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 682-690 (1991); (9 pages) | Cited 1 time

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High‐resolution algorithms are potentially able to outperform conventional linear methods at the task of beamforming, i.e., spatial‐spectrum estimation, and in controlled experiments or simple computer simulations they often do prove superior. In marine environments, however, high‐resolution techniques frequently fall short of these expectations. Their outputs can take on an unstable appearance characterized by fading of the true target peak and by the occurrence of multiple false targets. In recent years a class of stabilization techniques has evolved to moderate these effects by suppressing contributions from the smaller eigenvalues of the cross‐spectral density matrix. While such techniques generally produce good results in simulations with the maximum likelihood estimator and even with the more sensitive maximum entropy estimator, they have seen little use on sea data. Here, results are presented of two sea trials of a simple eigenvalue stabilization procedure in a relatively demanding class of environments—shallow water. The technique provided what is considered to be marginal stabilization for the maximum likelihood estimator and none at all for maximum entropy.

Acoustic source‐level measurements for a variety of merchant ships

Paul Scrimger and Richard M. Heitmeyer

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 691-699 (1991); (9 pages) | Cited 6 times

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This report presents a set of 50 source spectra obtained from merchant ships of opportunity near Genova, Italy. The source spectra were calculated from radiated‐noise spectra measured on a towed array together with a transmission‐loss spectrum computed from a parabolic equation model. The aggregate source spectra are characterized in terms of a mean source spectrum and three source‐level histograms computed for different frequency bands. It is shown that the mean spectrum is comparable in level and shape to a spectrum computed from a well‐known empirical model and that the source‐level histograms are approximately Gaussian with standard deviations of 5, 5.5, and 6.8 dB, respectively. Finally, a sub‐sample of 36 spectra is drawn from the aggregate and separated into three identifiable ship classes, namely, passenger/ferries, cargo ships, and tankers. It is seen that the source spectra for the three different ship classes have comparable means and standard deviations. From this result it is conjectured that both the mean spectrum and the source‐level histograms are not sensitive to ship class and can therefore be taken as representative of shipping in other regions with different ship class percentages.

An investigation of the collective oscillations of a bubble cloud

S. W. Yoon, L. A. Crum, A. Prosperetti, and N. Q. Lu

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 700-706 (1991); (7 pages) | Cited 11 times

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It is well known that ocean ambient noise levels in the frequency range from a few hundred hertz to several tens of kilohertz are well correlated with wind speed. A physical mechanism that could account for some of this sound generation is the production of bubble clouds by breaking waves. A simple laboratory study of the sound generated by a column of bubbles is reported here. From measurements of the various characteristics of this column, good evidence is obtained that the bubbles within the column are vibrating in a collective mode of oscillation. Based upon an assumption of collective oscillations, analytical calculations of the predicted frequency of vibration of this column as well as the dependence of this frequency on such parameters as bubble population and column geometry agree closely with the measured values. These results give evidence that the bubble plumes generated by breaking waves can be a strong source of relatively low frequency (< 1 kHz) ambient noise.

Nonlinear effects in the dynamics of clouds of bubbles

Sanjay Kumar and Christopher E. Brennen

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 707-714 (1991); (8 pages) | Cited 4 times

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See Also: Erratum

Show Abstract
This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh‐Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.

Underwater sound generation by rainfall

Frédéric Laville, Grayson D. Abbott, and Matthew J. Miller

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 715-721 (1991); (7 pages) | Cited 2 times

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This paper presents experimental findings on the mechanism of underwater sound generation by rainfall. Although using underwater sound to measure the rate of rainfall is a promising technique, conflicting models have been proposed for the spectral contributions of the two rainfall sound sources (raindrop impacts on the water surface and air bubble resonances) and correlating rainfall rate to spectral level has proven difficult. In order to resolve these problems, high‐speed data acquisition and processing of underwater sounds recorded in a lake under real rain and artificial raindrop conditions were used. The two rainfall sound sources have been identified in the time domain and their respective contributions to the long‐term spectrum have been determined: Bubble resonances were found responsible for the spectral peak around 13–15 kHz and raindrop impacts were found responsible for a broadband spectrum with a negative slope. The poor correlation reported in literature between the rainfall rate and the level at 13–15 kHz is now explained by the sensitivity of bubble generation to raindrop distribution and surface conditions. The better correlation obtained outside this frequency range is explained by the systematic occurrence of raindrop impacts.

Directionality of ice cracking events

Pierre Zakarauskas and Jon M. Thorleifson

J. Acoust. Soc. Am. Volume 89, Issue 2, pp. 722-734 (1991); (13 pages) | Cited 1 time

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This paper presents the measured vertical directivity of ice cracking events extracted from a 341 s sample of ambient noise recorded under the polar ice pack. The sample was taken with a vertical linear array of four hydrophones suspended over the Arctic continental shelf in 500 m of water. The hydrophone spacing was 100 m. The samples from each hydrophone were bandpass filtered between 40 and 1250 Hz, and searched for corresponding peaks in the acoustic pressure. The acoustic events are believed to be due predominantly to thermal ice cracking. The angular distribution of the 765 arrivals detected has its maximum at 15 deg below the horizontal, with most of the arrivals occurring between 0 and 25 deg below the horizontal. An explanation for this observation is given in terms of a simple ray‐based model of the propagation of ice cracking noise. The asymmetry in the angular distribution is shown to be due mostly to the source directivity favoring bottom reflected and refracted rays arriving at negative angles. A dipole source directivity is shown to produce the best fit to the data.
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