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Jul 1971

Volume 50, Issue 1B, pp. 157-388

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Acoustic Force on a Liquid Droplet in an Acoustic Stationary Wave

Lawrence A. Crum

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 157-163 (1971); (7 pages) | Cited 15 times

Online Publication Date: 11 Aug 2005

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This paper considers the time‐averaged acoustic force exerted on a spherical liquid droplet in an acoustic stationary wave. Experimental and theoretical values are presented for the minimum acoustic pressure amplitudes required to trap small individual droplets of various liquids near the pressure antinodes of a stationary sound field in a cylinder filled with water. The liquids used were paraldehyde, hexane, benzene, toluene, chlorobenzene, and carbon tetrachloride. Droplet radii ranged from 400 to 800 μ, and acoustic‐pressure amplitudes required to trap the droplets ranged from 1 to 15 bars. Calculated and observed values for the acoustic force are in substantial agreement, provided the compressibility of the liquid droplets is considered.

Ultrasonic Absorption in Naphthalene Single Crystals at Low Temperatures

J. D. Wilson and S. S. Yun

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 164-171 (1971); (8 pages)

Online Publication Date: 11 Aug 2005

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The attenuation of ultrasonic waves was measured in single crystals of naphthalene from 23° to −185°C for frequencies from 15 to 45 MHz. A maximum was observed in the absorption coefficient at low temperatures, and from the frequency dependence of the absorption, the result was examined in terms of relaxation phenomena. The experimental results are compared to the relaxation maximum predicted by the Liebermann theory assuming the temperature‐cubed term of the transition probability to be the dominant temperature dependence. The transition probability is calculated from the experimental data and compared directly to the theoretical values. Also, a transition probability with exponential temperature dependence is shown to agree equally as well with the experimental results.

Field due to a Point Source in an Inhomogeneous Elastic Medium

Hemendra K. Acharya

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 172-175 (1971); (4 pages)

Online Publication Date: 11 Aug 2005

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Wave propagation in an inhomogeneous elastic half‐space is investigated. Integral expressions for vertical and horizontal displacement due to a point source have been obtained in terms of reflection coefficients for a medium in which compressional‐ and shear‐wave velocities increase monotonically with depth. These expressions are further shown to reduce to known expressions in the case of homogeneous solid and stratified liquid.

Surface Wave Dispersion in a Mass‐Loaded Half‐Space

L. E. Alsop, A. S. Goodman, and E. Ash

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 176-180 (1971); (5 pages)

Online Publication Date: 11 Aug 2005

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The effect of a layer on surface wave propagation on a half‐space can be separated into terms arising from elastic and from inertial restraining forces. In a number of situations of practical importance, it turns out that the inertial terms are dominant. The period equations governing the dispersion for this pure mass loading are obtained in suitable form and numerical solutions for Rayleigh waves for both solid and fluid loading are obtained. It is shown that by presenting the results in terms of appropriate variables, extremely simple, approximately linear, dispersion characteristics are found. A single computation suffices for substrate materials having the same Poisson ratio. The validity of this approximation is explored for modified Rayleigh waves for both solid and liquid layers, and for Love waves.

Scattering of Sound by Sound

H. O. Berktay and C. A. Al‐Temimi

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 181-187 (1971); (7 pages)

Online Publication Date: 11 Aug 2005

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The debate about scattering of interaction‐frequency components when two sound waves interact at a non‐zero angle has not been resolved because no positive evidence of such scattering outside the interaction volume has been put forward. In this contribution, an attempt is made to review the situation in view of the available experimental evidence relating to interaction between a plane wave and a “collimated” pump wave.

Potentials for Elastic Displacement in Spherically Symmetric Media

Paul G. Richards

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 188-197 (1971); (10 pages)

Online Publication Date: 11 Aug 2005

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The choice of P and S designations is somewhat arbitrary in heterogeneous elastic media, but becomes precise in the high‐frequency limit of ray theory. This fact is used in a radially heterogeneous isotropic medium to establish three potentials (P,S,T) with the following properties: (1) every displacement solution is represented by some (P,S,T); (2) T(r,t) is decoupled from P and S, is a potential for SH motion, and satisfies second‐order wave equation; and (3) the coupling of P and SV is represented by coupled equations in potentials P and S. At high frequencies these equations decouple (for an important class of sources) into separate second‐order wave equations for P and S. An important role, in this decoupled case, is played by the variable density. Several possibilities suggested by the general P and SV equations are also outlined.

Wave Propagation in a Fluid‐Filled Tube

S. I. Rubinow and Joseph B. Keller

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 198-223 (1971); (26 pages) | Cited 4 times

Online Publication Date: 11 Aug 2005

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A circular cylindrical viscoelastic solid tube filled with a compressible viscous fluid is considered. The outer surface of the tube is assumed to be constrained so that it cannot move freely. Axially symmetric wave solutions are obtained for the linearized equations governing the motion of the fluid and the solid. The solutions lead to a complicated transcendental dispersion equation relating the wave frequency and the propagation constant. This equation is simplified by taking the fluid to be inviscid and the tube to be thin. Then it is studied by both analytical and numerical means. Formulas and graphs are given for the propagation constant, the phase velocity, the group velocity, etc., as functions of the frequency for various sets of parameter values. There are infinitely many modes of propagation, two of which are “tube modes” and the rest of which are acoustic modes. The case of a viscous fluid and a tube of any thickness are to be treated in a subsequent paper.

Thermoelastic Damping of Stress Waves Induced by Volumetric Energy Deposition

D. C. Stickler and R. E. Nickell

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 224-229 (1971); (6 pages)

Online Publication Date: 11 Aug 2005

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The effects of high‐intensity electromagnetic energy deposition in solids can be catastrophic. Among the mechanisms which could be considered as thermal shock wave mitigators is the dissipative mechanism of thermoelastic damping. In order to assess this concept, a coupled linear one‐dimensional thermoelastic problem with a volumetric heat input is solved by an approximate technique. The problem corresponds to the impulsive heating of a partially transparent (to radiative flux) medium. The approximate solution has the correct behavior for small and large times, satisfies the boundary conditions, and duplicates the behavior of the discontinuities in the field variables (in particular, the stress field). For parameters in the range of physical interest, the solution obtained here differs little from the uncoupled solution, with one exception. In this case, the effect of thermoelastic coupling is essentially to remove the discontinuities from the fields so that changes in the neighborhood of the wavefront are rapid but continuous. Failure criteria are essentially unaffected, since the peak tensile stress is very nearly the same for coupled and uncoupled solutions.

Waves in a Thin‐Walled Tube due to Sudden Release of a Radial Ring Pressure

Jamie C. Hsu and R. J. Clifton

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 230-240 (1971); (11 pages)

Online Publication Date: 11 Aug 2005

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The approximate thin‐shell theory of Herrmann and Mirsky is used to study stress wave propagation in a thin‐walled cylindrical tube due to sudden release of a concentrated ring pressure. The tube is assumed to be of infinite length, so that the problem is a pure initial‐value problem for which the solution can be represented as a superposition of harmonic plane waves. Numerical results are plotted for profiles of strains, stress resultants, and displacements versus distance along the tube axis at several times after the load is released.

Response of a Thin‐Walled Cylindrical Duct to Internal Airflow

H. Khosrovani, R. Cohen, and R. C. Chanaud

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 241-247 (1971); (7 pages)

Online Publication Date: 11 Aug 2005

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The vibration of a thin cylindrical duct, due to an internal random pressure field caused by airflow, was studied both experimentally and theoretically. The Reynolds number for the experiments was near 105 and the Mach number was less than 0.1, typical of large air handling applications. Although a muffler was used to simulate acoustically a much longer duct, the acoustic pressure was found to be a significant cause of duct vibration. A simple model (white noise) of the pressure field was convolved with the dynamic Green's function of the duct to compute numerically the radial displacement cross covariances. In spite of this simplification, the measured displacement covariances were in good agreement with those calculated. The displacement spectral density was predicted to vary as ω−3 with white‐noise excitation. The observed dependence was ω−4.8 and was accounted for by the fact that the forcing function was not white noise, but had a frequency dependence near ω−2.

Axially Symmetric Waves in Transversely Isotropic Rods

Y. Mengi and H. D. McNiven

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 248-257 (1971); (10 pages)

Online Publication Date: 11 Aug 2005

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In this study, a three‐mode approximate theory governing axisymmetric motions in transversely isotropic rods is developed. The development of this approximate theory follows closely the method adopted by Mindlin and McNiven when they developed a three‐mode theory for isotropic rods. There is, however, one significant departure. After the generalized displacements and generalized strains are defined, the equilibrium and constitutive equations and the kinematic relations are derived using a variational theorem due to Hu and Washizu. The approximate theory is analyzed numerically for two transversely isotropic materials, and spectral lines derived from the theory are compared with those from the exact three‐dimensional theory.

Analysis of the Transient Excitation of a Transversely Isotropic Rod

Y. Mengi and H. D. McNiven

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 258-265 (1971); (8 pages)

Online Publication Date: 11 Aug 2005

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The response of a semiinfinite transversely isotropic rod to a time‐dependent input on the end of the rod is found using the method of characteristics. The rod is of circular section and the material of the rod is arranged so that the axes of isotropy are parallel to the axis of the rod. To reduce the problem to one where motions depend on only one space variable and time, use is made of an approximate theory developed by the authors in a previous study. Numerical results are found for an input which has a step distribution in time and for two different materials, magnesium and a fiber‐reinforced material. For each material the response is found in terms of four quantities: radial strain, axial strain both on the lateral surface and along the axis of the rod, and the generalized axial stress.

Free Vibrations of Generally Orthotropic Plates

D. Mohan and H. B. Kingsbury

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 266-269 (1971); (4 pages) | Cited 1 time

Online Publication Date: 11 Aug 2005

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An analytical study of the natural frequencies and mode shapes of anisotropic thin plates is presented. The plates are considered to be constructed from an orthotropic material such that the principal elastic axes of the materials are not parallel to the plate edges. By use of Galerkin's method, the change in natural frequencies and mode shapes are investigated as the material elastic axes are rotated with respect to the natural geometric coordinates. Three sets of edge conditions are considered: (1) all edges simply supported; (2) one pair of opposite edges fixed with the other pair free; and (3) one edge fixed with remaining edges free. The results of this investigation show that the plate mode shapes are strongly affected by the orientation of the elastic axes and that they cannot be predicted on the basis of conventional isotropic‐ or orthotropic‐plate analysis.

Dynamic Coupling of Elastic and Fluid Modes in an Infinite Elastic Plate in Contact with an Inviscid Liquid Layer

W. W. Walter and G. L. Anderson

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 270-276 (1971); (7 pages)

Online Publication Date: 11 Aug 2005

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The first five branches of the dispersion curves for straight‐crested waves propagating in an infinite isotropic elastic plate, in a state of plane strain, that is covered by a layer of an incompressible inviscid liquid are determined numerically from the exact dispersion relation. Using the classical theory of flexure, the Mindlin theory of flexure, and the Kane‐Mindlin theory of extensional motion in elastic plates, approximate dispersion relations are derived, and the effect of coupling between the flexural, extensional, and fluid modes is studied. Upon comparison of the exact and approximate results, it is found that the coupling of flexural and extensional motions arising through the velocity continuity condition at the liquid‐plate interface is rather weak, so that good approximations to the fluid, flexural, and thickness‐shear branches of the dispersion curves can be obtained by neglecting the coupling with the extensional and thickness‐stretch branches. Furthermore, the extensional branch is not appreciably influenced by the coupling condition, and the thickness‐stretch approximation is a good one in the low‐frequency range only if the mass density of the plate is much greater than that of the liquid.

Cavitation Erosion of Aluminum at Elevated Pressure

F. A. Angona

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 277-285 (1971); (9 pages)

Online Publication Date: 11 Aug 2005

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An experimental investigation of the effect of hydrostatic pressure on cavitation erosion is described. A focusing acoustic system enclosed in a pressure chamber permitted the sound pressure and the hydrostatic pressure to be varied independently over the range of 1–20 atm. The intensity of cavitation, as measured by the erosion rate of aluminum, was found to grow at an increasing rate with hydrostatic pressure. Experimental results obtained in this pressure range correlate with published Russian data taken at pressures up to 75 atm. A correspondence between cavitation erosion and electromagnetic radiation is postulated. The agreement between experimental results and those predicted by this correspondence is quite good.

An Investigation of a Double Family of Normal Modes in an Isovelocity Underwater Acoustic Surface Duct

Whitlow W. L. Au

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 286-299 (1971); (14 pages)

Online Publication Date: 11 Aug 2005

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This article treats an underwater isovelocity surface duct overlying a negative velocity gradient layer that requires two distinct families of normal modes to represent the acoustic field in the image‐interference region. Each family contains an infinite number of modes. The significance of the two families of modes at short ranges is demonstrated by comparing numerical results obtained from ray theory with results from normal‐mode theory. The contribution to the total normal‐mode solution by the second family of modes is a complicated function of the gradient below the surface channel, the range, and the receiver depth. Within the image‐interference region, the second family of modes becomes increasingly important as the range and gradient decrease and the receiver depth increases. However, beyond the image‐interference region, the second family of modes may be neglected without appreciable error. The properties of the various modal elements are investigated and some generalizations concerning the second family are derived.

Finite‐ and Small‐Amplitude Underwater Gas Bubble Oscillations Compared

David Epstein

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 300-305 (1971); (6 pages)

Online Publication Date: 11 Aug 2005

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Underwater gas bubble expansion as a function of the ambient‐pressure to bubble‐pressure ratio p′, in the interval 0⩽p′⩽1, is investigated. At the endpoints, a simple analytic solution to the nonlinear equations of motion in closed form may be found; but, for intermediate values of p′, an approximation is required. In the noncompressive case, representations suitable for large bubble radii, near p′=0, and small‐amplitude motion, near p′=1, are derived. A result of this analysis is that the Willis bubble pulse formula, correct in the limit p′ → 0, in agreement with experiment, appears to be valid over much of the interval, but it starts to break down as p′ → 1. The power law governing finite‐ and small‐amplitude periods is different; the actual period has no simple power law dependence, but may be deduced for all p′ by fitting a curve to the asymptotically correct values at p′=0 and p′=1, respectively. Owing to radiation and other loss mechanisms, bubble starting out as finite‐amplitude pulsation, with a cusplike shape at the minimum, is gradually transformed into a small‐amplitude damped sine wave; concurrently T1 → T̄. (Analysis in this paper refers to case γ  =  math.)

Acoustic Attenuation in Composite Materials

R. W. Higgs and L. J. Eriksson

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 306-309 (1971); (4 pages)

Online Publication Date: 11 Aug 2005

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An experimental study of sound attenuation in lead‐wool‐polyurethane composites and nickel‐Cerrobend composites was conducted for different compositions, frequencies, and pressures. At specific compositions, the attenuation reached a maximum considerably higher than the attenuation of the components. The maximum attenuation occurred where the compressional modulus is changing most rapidly with composition; at this composition, the attenuation is most unstable with pressure.

A Method of Selecting Element Positions in a Hydrophone Array to Reduce Minor Lobes

Paul M. Kendig

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 310-313 (1971); (4 pages)

Online Publication Date: 11 Aug 2005

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It is shown that, if the sensitivities and resonant frequencies of elements in a hydrophone array can be accurately determined before they are placed in an array, it is possible to select their positions in the array so as to reduce minor lobes significantly. An expression for the sensitivity of an individual element that depends on easily and accurately measured quantities has been derived. The variation in phase depends primarily on the resonant frequencies of the elements, if element positions can be held to sufficiently close tolerances. Comparisons of calculated results are made with experimental measurements and with computed results of random placement of the transducer elements.

A Digital System for Volume Reverberation Studies

J. C. Nickles and R. K. Johnson

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 314-320 (1971); (7 pages)

Online Publication Date: 11 Aug 2005

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An experimental apparatus has been developed as part of a continuing program of deep‐sea acoustic‐scattering research. It consists of a computer‐based shipboard console and a cable‐suspended package which contains the acoustic sources and receivers. The computer provides for preprocessing, recording, and display of the data, and for control of the experimental sequence. The sensor package operates at depths to 1600 m, acquiring scattering data for eight frequencies from 4 to 25 kHz.

Vertical Cross Correlation of Noise from a Horizontal Surface

Charles R. Rein

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 321-325 (1971); (5 pages)

Online Publication Date: 11 Aug 2005

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A theoretical study of the cross correlation of noise from a horizontal surface is presented. Only spatial separations in the vertical direction are considered. The ratio of the depths of the receivers is a parameter considered in the analysis so that the results might apply near the surface of the deep ocean, in the regions of shallow water where there is no bottom reflection, or where the receivers are not sensitive to signals from below. In previous work only receiver depth ratios close to unity were considered, so the results applied only to special cases such as surface‐noise cross correlation in very deep water. The results indicate that the cross‐correlation function depends very strongly on spatial separation of the receivers but very weakly on the ratio of the depths of the receivers. It is suggested, therefore, that the literature which applies to vertical correlation of surface noise in deep water can also be applied when the receivers are close to the surface.

Monostatic and Bistatic Backscattering Measurements from the Deep Ocean Bottom

P. B. Schmidt

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 326-331 (1971); (6 pages) | Cited 1 time

Online Publication Date: 11 Aug 2005

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Monostatic and bistatic backscattering from the ocean bottom was measured at frequencies from 0.5 to 6.3 kHz at four stations in the North Atlantic and North Pacific Oceans. The data can be approximately described by Lambert's law of diffuse reflection at grazing angles below 50°. The average of the scattering constants 10 logμ measured for all frequencies is −29 dB.

The Averaged Impulse Response of a Shallow‐Water Channel

P. W. Smith, Jr.

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 332-336 (1971); (5 pages) | Cited 5 times

Online Publication Date: 11 Aug 2005

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The averaged impulse response for sound transmission in a shallow‐water channel is estimated by a theory based on ray acoustics with lossy specular reflection from the boundaries. Averaging is introduced primarily by strict averaging in depth of the square of the received pressure. Rays need be traced over but a single cycle of their paths. The impulse response contains useful and readily accessible information about environmental loss parameters. The rate of decay of the reverberant tail, which is characteristic of channels with only moderate variations in sound speed, appears to be a particularly valuable measure. Theoretical and experimental data are compared.

The Noise of Melting Icebergs

R. J. Urick

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 337-341 (1971); (5 pages)

Online Publication Date: 11 Aug 2005

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Icebergs seem to have escaped serious attention as sources of underwater sound. The noise of icebergs has been measured by means of sonobuoys dropped by an aircraft at distances between 200 and 10 000 yd. Two isolated icebergs 130 to 150 ft high were measured at a location northeast of Newfoundland. Noise apparently originated by the bergs was found to have a spectrum flat to about 10 kHz, the limit of measurement, with spectrum levels of −37 and −42 dB re 1 dyn/cm2 at 200 yd from the two bergs. Ice sizzle is readily observed with a cube of cloudy ice and a hydrophone in a container of water. It is surmised that this noise is caused by the explosion of tiny air bubbles entrapped in the ice under pressure and released as melting occurs. Alternatively, at deep depths, the process may be one of implosion of the cavities by inrushing water. The level of the noise of icebergs doubtless depends on many factors, such as size, depth, air content, and rate of melting in the surrounding water.

Invariance of Geometric Spreading Loss with Changes in Ray Parametrization

J. T. Warfield and M. J. Jacobson

J. Acoust. Soc. Am. Volume 50, Issue 1B, pp. 342-347 (1971); (6 pages)

Online Publication Date: 11 Aug 2005

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In the ray theory of acoustics, there has been some confusion regarding the variables to be held constant in the evaluation of partial derivatives of the ray position vector in the calculation of geometric spreading loss. It is shown that the general formula for spreading loss remains unchanged when the parameter along a ray is changed from travel time to a new parameter, provided any variable that occurs in the expression for the position vector is regarded as a function of the new parameter and the initial ray angles.
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