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Journal of the Acoustical Society of America

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May 1978

Volume 63, Issue 5, pp. 1265-1646

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The contribution of ultrasonic measurements to the study of liquid crystals. I. Nematics

G. G. Natale

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1265-1278 (1978); (14 pages) | Cited 1 time

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The investigation of ultrasonic propagation properties in liquid crystals in recent years has provided a considerable contribution to the study of these systems. In this paper most ultrasonic measurements performed to date on nematic liquid crystals are examined and presented in a systematic way, in order to provide a compact and coherent view of the current experimental situation in this field. The review of the available experimental data and their comparison with the predictions of various theories point out areas which necessitate further investigation by ultrasonic experiments.
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43.10.Ln Surveys and tutorial papers relating to acoustics research; tutorial papers on applied acoustics
43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions
61.30.-v Liquid crystals

Test of the Born and Rytov approximations using the Epstein problem

W. James Hadden, Jr. and David Mintzer

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1279-1286 (1978); (8 pages) | Cited 3 times

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The Born and Rytov approximations for solutions of the Helmholtz equation are compared with the exact solutions of three one‐dimensional problems which involve continuously varying indices of refraction (based on Epstein’s model). Limiting values of the spatial parameters which characterize the index of refraction functions are used as the bases for detailed comparisons of expressions for the complex wave field and for its amplitude and phase. The results of these comparisons reaffirm earlier findings that the two approximation methods are equivalent vis‐a‐vis the perturbation strength parameter of the index of refraction functions. It is shown that in one extreme of the spatial parameter in one of the problems, there is an advantageous range‐dependence in the Rytov method. The conceptual extension of the results of this comparison to three‐dimensional problems is discussed.
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43.20.Bi Mathematical theory of wave propagation
43.30.Bp Normal mode propagation of sound in water

Reflection of acoustic waves at the interface of two highly stressed elastic half‐spaces

J. L. Nowinski

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1287-1291 (1978); (5 pages)

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Using the method of incremental deformations formulated by Biot [Mechanics of Incremental Deformation (Wiley, New York, l965)], the amount of prestressing in a half‐space of an incompressible material is determined by analyzing the value of the reflection coefficient of the acoustic equivoluminal waves impinging upon the deformed boundary of the half‐space. An illustrative example, solved in detail, shows that the results may serve as a basis for a nondestrictive evaluation of the level of prestressing.
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43.20.Fn Scattering of acoustic waves
43.20.Bi Mathematical theory of wave propagation

Reflection of Rayleigh waves by strips, grooves, and periodic arrays of strips or grooves

Donald A. Simons

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1292-1301 (1978); (10 pages) | Cited 10 times

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The plane‐strain version of the title problem is solved by a perturbation scheme. The fields are represented as convolutions of Green’s functions with unknown surface‐traction distributions. Integral equations governing these tractions are obtained by applying boundary conditions which represent the effect of the surface layers. The equations are solved by singular perturbation techniques, asymptotically as the ratio of layer thickness to incident wavelength or strip width tends to zero. The cases of a fixed number of strips and a number of strips which become infinite in the asymptotic limit, are treated separately. Closed‐form expressions for the reflection coefficient are obtained.
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43.20.Fn Scattering of acoustic waves
43.35.Pt Surface waves in solids and liquids
43.20.Bi Mathematical theory of wave propagation

Time‐harmonic solution of the elastic head wave problem incorporating the influence of Rayleigh poles

Leung Tsang

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1302-1309 (1978); (8 pages) | Cited 4 times

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The classical Lamb problem of a time‐harmonic line load applied to the surface of an elastic solid is considered in this paper. In the past, ordinary asymptotic methods have been applied to the branch‐cut evaluation of the time‐harmonic compressional and shear head waves. It is shown here that the application of these methods generally leads to erroneous results. The problem of the shear branch cut is associated with the Rayleigh pole, and the problem of the compressional branch cut is associated with the other two roots of the Rayleigh equation, which lie in the neighborhood of the compressional branch point. These two roots affect the compressional branch‐cut integration and can contribute a residue to the total solution. To evaluate the time‐harmonic fields, we utilize the following methods of integration—the modified saddle‐point method, the method of numerical integration along the branch cut, and the method of numerical integration along the Sommerfeld contour. With the inclusion of the effects of all three roots of the Rayleigh equation, the results from the three methods are in excellent agreement.
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43.20.Fn Scattering of acoustic waves

Multiple scattering of elastic waves by cylinders of arbitrary cross section. I. SH waves

Vijay K. Varadan, Vasundara V. Varadan, and Yih‐Hsing Pao

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1310-1319 (1978); (10 pages) | Cited 15 times

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A scattering matrix approach, that involves only the transition matrix of a single obstacle, is proposed for studying the multiple scattering of elastic waves in a medium (matrix) containing identical, long, parallel, randomly distributed cylinders of arbitrary cross section. The elastic properties of the cylinders are assumed to be different from those of the matrix. A statistical approach in conjunction with Lax’s ’’quasicrystalline’’ approximation is employed to obtain equations for the average amplitudes of the scattered and exciting fields which may then be solved to yield the dispersion relations of the composite medium. Dynamic elastic properties of the composite medium containing circular and elliptical cylinders are found in the Rayleigh or low‐frequency limit. Numerical results displaying phase velocity and damping effect of the composite medium are presented for a wide range of frequencies.
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43.20.Fn Scattering of acoustic waves
43.60.Cg Statistical properties of signals and noise

Matrix theory of elastic wave scattering. II. A new conservation law

P. C. Waterman

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1320-1325 (1978); (6 pages) | Cited 3 times

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Upon resolving the surface traction into spatial derivatives and surface derivatives of the displacement, a new conserved elastodynamic field quantity is found, having dimensions of energy density. For periodic time dependence, the flux associated with this new quantity differs from the true energy‐flux vector by only a solenoidal term, and is far simpler to compute. The conservation requirement is shown to be the basis of one form of Huygens’ principle, and in addition leads directly to the T‐matrix equations without the necessity of introducing the Green’s dyadic.
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43.20.Fn Scattering of acoustic waves
43.20.Bi Mathematical theory of wave propagation

Parametric acoustic sources of rectangular aperture

Mark B. Moffett, Robert H. Mellen, and William L. Konrad

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1326-1331 (1978); (6 pages) | Cited 2 times

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A model is presented for predicting source levels and beam patterns generated by parametric acoustic sources of rectangular aperture. This model is a generalization of a previous model for square and circular apertures [J. Acoust. Soc. Am. 61, 325–337 (1977)]. Because the nonlinear absorption of the primary beams is less for a rectangular projector than for a square projector of equal area and primary source level, it is possible to obtain larger difference‐frequency source levels from rectangular projectors than from their square (or circular) couterparts. The conditions required for such enhanced source levels are discussed, and the results of an experimental test of the model are presented.
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43.25.Lj Parametric arrays, interaction of sound with sound, virtual sources

Fourth‐order acoustic torque in intense sound fields

T. G. Wang, H. Kanber, and E. E. Olli

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1332-1334 (1978); (3 pages)

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We report the first observation of a fourth‐order acoustic torque in intense sound fields. The torque was determined by measuring the acoustically induced angular deflection of a polished cylinder suspended by a torsion fiber. This torque was measured in a sound field of amplitude greater than that in which first‐order acoustic torque has been observed.
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43.25.Gf Standing waves; resonance
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
43.75.Pq Reed woodwind instruments

A comparison of Doppler sodar antenna configurations used for horizontal wind measurement

Robert F. Davey

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1335-1341 (1978); (7 pages)

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The performance of two antenna configurations is evaluated using a parametric optimization technique that predicts the relative accuracy of horizontal wind measurement. Consideration is given to the effect of atmospheric attenuation and the relation between the thermal‐ and velocity‐structure parameters as well as to the geometric effects. Using a baseline case with a maximum measuring altitude of 500 m, optimum antenna orientations are determined for the familiar axisymmetric three‐transmitter configuration and for a two‐transmitter system using a tilted receiver antenna. The sensitivity of each system to small changes in the geometry and to modifications in the assumed attenuation and structure parameter ratio is examined. The two‐transmitter system is found to generate velocity measurements with accuracy comparable to the three‐transmitter geometry at the design point. However, the effect of the preferred orientation at lower heights results in poorer comparative performance.
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43.28.Tc Sound-in-air measurements, methods and instrumentation for location, navigation, altimetry, and sound ranging
43.28.Bj Mechanisms affecting sound propagation in air, sound speed in the air

Bottom reverberation‐derived scattering strengths in shallow water off the Argentinian coast

S. Blanc, J. C. Novarini, and A. L. Núñez

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1342-1346 (1978); (5 pages) | Cited 2 times

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Measurements were carried out in shallow water 23 m deep off the Argentinian coast in quasi‐isovelocity conditions. The data were analyzed for grazing angles in the interval 1°50′–8°. A method to make an indirect determination of bottom‐scattering strengths in shallow water has been worked out. It consists of separating the surface, volume, and bottom contributions according to their time decays in recordings of signals from distant explosions. For this purpose, a simplified model based on the equivalence of both bistatic and monostatic experimental geometries was used. The results show a slight increase in bottom‐scattering strength with grazing angle and with frequency according to the 1.0 power 3 dB/octave). An attempt to correlate scattering strength with type and roughness of the sea bed was also carried out. The coincidence between our results and direct measurements made under similar conditions by others suggests the validity of the present method.
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43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries

Spectral structure of an ultrasound wave scattered by a random surface: Application to the scattering of sound from the sea surface

C. Gazanhes, J. Leandre, and J. P. Lefebvre

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1347-1352 (1978); (6 pages)

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The scattering of a sound wave by the sea surface is accompanied by random fluctuations of amplitude and phase which depend on the surface conditions. A theoretical model based on Helmholtz’s theorem is proposed, which leads to a simple expression for the power spectral density of a scattered signal. This expression permits a computer simulation of the phenomena to be made that may be verified experimentally by means of spectral analysis. The technique employed leads to a resolution of 0.25 Hz. The experiments were conducted on a reduced model in an acoustic tank. Measurements were made using a monochromatic signal of 150 kHz for specular reflection and for three different surface conditions. The results of the numerical simulation are in good agreement with experiment.
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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
43.20.Bi Mathematical theory of wave propagation

Deep‐water acoustical analysis of stationary and moving broadband sound sources

G. M. Jacyna and M. J. Jacobson

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1353-1364 (1978); (12 pages)

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Deep‐water sound transmission from a moving source to a fixed receiver is studied, where the source emits a random broadband signal whose expected distribution is normal. A bilinear sound‐speed profile is employed, the source is located above the SOFAR axis, and the receiver below. Long ranges are assumed, so that only SOFAR rays need be considered. Basic propagation equations are given, and travel time and spreading loss expressions are approximated in stability regions within which all four SOFAR rays exist for each number of SOFAR‐axis crossings. General equations are derived for the received average power spectrum and power in terms of the spectrum at the source. Then, the broadband signal is taken to be bandlimited white noise. The received spectrum is simplified and examined for nonmultipath, multipath, and Doppler contributions. The influences of range, source speed, frequency, and observation time are considered. Average power at the receiver is studied similarly. Received spectra for a stationary source are investigated, and exhibit greater variations than those arising from a moving source. However, received average power for stationary and moving broadband sources are about equal. Average received power from cw and broadband sources, both moving and stationary, are compared. Power variations in the cw case are found to be much larger than in the broadband case.
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43.30.Bp Normal mode propagation of sound in water
43.30.Cq Ray propagation of sound in water

Penetration into a sand sediment of difference‐frequency sound generated by a parametric array

J. Jarzynski and L. Flax

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1365-1371 (1978); (7 pages)

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A theoretical investigation is made of the sound field in a sand sediment due to a parametric array located in the overlying water. The following approximations are used. First, the array is represented by a line distribution of end‐fired virtual sources. Secondly, the ray method is used to calculate the sound field in the sand from each source. Attenuation in the sand is treated as a perturbation. That is, the ray paths are found for an equivalent lossless medium, while the fields along these paths are obtained using the measured attenuation coefficient of the sand. The sound field of the array is then calculated by summing the contributions from the line distribution of virtual sources extending from the projector to the sand surface. Numerical results are obtained for array grazing angles in the range 10°–40° and for difference frequencies of 5, 10, and 20 kHz. The results are compared with experimental data.
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43.30.Qd Global scale acoustics; ocean basin thermometry, transbasin acoustics
43.25.Ba Parameters of nonlinearity of the medium
91.50.Jc Marine sediments, turbidity currents—processes and transport

Calculation of mode conversion rates

Suzanne T. McDaniel

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1372-1374 (1978); (3 pages)

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The rate at which energy is exchanged between acoustic normal modes due to scattering from ocean bottom roughness is calculated using measured correlation functions of ocean bottom slopes. Estimates of the resulting attenuation of the coherent component of the first normal mode are obtained and are compared to scattering losses predicted using the Kirchhoff approximation.
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43.30.Bp Normal mode propagation of sound in water

Range dependence of underwater echoes from randomly rough surfaces

E. Eugene Mikeska and Chester M. McKinney

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1375-1380 (1978); (6 pages) | Cited 1 time

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Experimental underwater measurements of the echo reflected or backscattered from randomly rough model pressure relief surfaces in a laboratory tank are presented as a function of range and relative roughness. Measurements of peak echo pressure amplitude were made at a frequency of 100 kHz at normal incidence; Rayleigh parameters of the surfaces were 0, 1.95, 3.90, and 7.82. The results illustrate the transition from mirror image reflection from a plane surface to spherically spreading backscattering from a surface having irregularities larger than the wavelength, with intermediate range dependence for surfaces having moderate relative roughness.
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43.30.Dr Hybrid and asymptotic propagation theories, related experiments
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries

Sound propagation through an East Australian Current eddy

Paul A. Nysen, Paul Scully‐Power, and David G. Browning

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1381-1388 (1978); (8 pages)

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Sound transmission through an East Australian Current summer eddy was measured for the frequencies 25 Hz–2 kHz. Such eddies are typified by a central subsurface warm core which caused an elongation of the convergence zone range by 8 km. This isothermal and isohaline core results in the eddy having a double‐duct structure: a shallow surface duct and a deeper, thicker, and much lower sound‐speed eddy duct. This eddy duct behaved as a classical leaky acoustic waveguide with an optimum transmission frequency of 100 Hz. Strong acoustic coupling was observed from the surface duct to the eddy duct. This coupling was independent of range but dependent on frequency, being weakest around 300 Hz. At lower frequencies, coupling progressively increased due to diffraction, and at higher frequencies it also increased due to scattering. The overall effect, however, of both coupling and leakage was that the highest levels of coupled energy received within the eddy duct were at 100 Hz.
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43.30.Bp Normal mode propagation of sound in water
43.30.Cq Ray propagation of sound in water
43.30.Ft Volume scattering
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries

Three‐level coincidence‐correlator detectors

Jung Gil Shin and Saleem A. Kassam

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1389-1395 (1978); (7 pages)

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Nonparametric three‐level coincidence‐correlator (CC) detectors are considered for the detection of random signals in noise in two‐input systems. Based on the maximum‐efficacy criterion the structure of the optimum detector is obtained, together with the corresponding efficacy. The results allow the evaluation of practical detection schemes in this class of detectors, in terms of their performance relative to the constrained optimum and to the unconstrained optimum three‐level CC detector. Some specific three‐level CC detectors which are simple extensions of the polarity coincidence correlator are examined and a numerical comparison is made for Gaussian noise.
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43.30.Vh Active sonar systems
43.60.Cg Statistical properties of signals and noise

Piezoelectric polymer flexural disk hydrophone

T. D. Sullivan and J. M. Powers

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1396-1401 (1978); (6 pages) | Cited 5 times

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Piezoelectric polyvinylidene fluoride (PVF2) film has been successfully used as the transduction material in the construction of a practical hydrophone, thus demonstrating the feasibility of using this material in underwater acoustics. The PVF2 film is mounted on a flexing circular plate (disk) for strength under hydrostatic pressure; strains developed on the disk surface by incident acoustic pressure are exploited to excite the PVF2. An analytic expression has been developed to find the free‐field voltage sensitivity of the hydrophone when the disk boundary is simply supported, and the sensitivity of a carefully constructed prototype was measured for experimental verification. Additional hydrophones were constructed to produce better sensitivity and were tested under a wider range of temperatures and pressures. Hydrophones constructed to withstand pressures up to 4 MPa typically exhibited sensitivities of −200 dB//1 V/μPa and were neutrally buoyant in water.
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43.30.Yj Transducers and transducer arrays for underwater sound; transducer calibration
43.38.Fx Piezoelectric and ferroelectric transducers
43.38.Ar Transducing principles, materials, and structures: general

Free oscillations of submerged spherical shells

Y. K. Lou and T. C. Su

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1402-1408 (1978); (7 pages) | Cited 3 times

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Free vibrations of a spherical shell submerged in a fluid medium are investigated. It is found that no undamped natural frequency of the submerged shell can exist even if the surrounding fluid is assumed inviscid. In this case the damping is solely due to the compressibility of the fluid. However, for the intermediate modes, the damping components of the complex frequencies are extremely small; thus, an almost steady‐state, undamped free oscillation is possible for these modes and a pronounced resonance may be observed for the forced vibrations. When the shell is submerged in an ideal fluid, it is shown that there exist two real natural frequencies for each mode. These frequencies are lower than the corresponding in vacuo natural frequencies. The effect of fluid viscosity on the complex natural frequencies has also been examined. It is found that for small viscosities, the viscosity has essentially no effect on the real component of the natural frequencies.
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43.40.Ey Vibrations of shells
43.20.Tb Interaction of vibrating structures with surrounding medium

Analysis of the vibratory excitation of gear systems: Basic theory

William D. Mark

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1409-1430 (1978); (22 pages) | Cited 6 times

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Formulation of the equations of motion of a generic gear system in the frequency domain is shown to require the Fourier‐series coefficients of the components of vibration excitation; these components are the static transmission errors of the individual pairs of meshing gears in the system. A general expression for the static transmission error is derived and decomposed into components attributable to elastic tooth deformations and to deviations of tooth faces from perfect involute surfaces with uniform lead and spacing. The component due to tooth‐face deviations is further decomposed into appropriately defined mean and random components. The harmonic components of the static transmission error that occur at integral multiples of the tooth‐meshing frequency are shown to be caused by tooth deformations and mean deviations of the tooth faces from perfect involute surfaces. Harmonic components that occur at the remaining multiples of gear‐rotation frequencies are shown to be caused by the random components of the tooth‐face deviations. Expressions for the Fourier‐series coefficients of all components of the static transmission error are derived in terms of two‐dimensional Fourier transforms of local tooth‐pair stiffnesses and stiffness‐weighted weighted deviations of tooth faces from perfect involute surfaces. Results are valid for arbitrary, specified tooth‐face contact regions and include spur gears as the special case of helical gears with zero helix angle.
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43.40.At Experimental and theoretical studies of vibrating systems

Statistics of amplitude and spectrum of blasts propagated in the atmosphere

P. D. Schomer, R. J. Goff, and L. M. Little

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1431-1443 (1978); (13 pages) | Cited 6 times

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This paper describes the measurement and analysis of over 11 000 blast recordings. These data are used to develop a statistical base for blast propagation and to establish one‐third octave spectra for these blasts. These results can then be used to predict community blast noise levels. The blasts are divided into rather broad amplitude groupings and it is shown that received blast spectra are dependent only on grouping and not on absolute peak amplitude or distance (2–15 miles). One interesting result is that early in the morning and at far distances (normally over 5 miles) amplitudes are greatest upwind.
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43.50.Vt Topographical and meteorological factors in noise propagation
43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
43.28.Mw Shock and blast waves, sonic boom

Comparison of reverberation measurements using Schroeder’s impulse method and decay‐curve averaging method

W. T. Chu

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1444-1450 (1978); (7 pages) | Cited 8 times

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Utilizing a digital acquisition system and minicomputer, two promising techniques for accurate determination of reverberation times have been studied in detail from the viewpoint of standard reverberation room tests. The first is Schroeder’s ’’integrated impulse method,’’ and special attention was given to the question of repeatability and the influence of signal‐to‐noise ratio on the successful application of the method. The second technique involves taking an ensemble average of a large number of logarithmic decay curves. It was found that, even for nonuniform decays, the average decay curves obtained by the second method compared well with those determined by the Integrated Impulse Method.
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43.55.Mc Room acoustics measuring instruments, computer measurement of room properties
43.55.Br Room acoustics: theory and experiment; reverberation, normal modes, diffusion, transient and steady-state response

Beamforming a towed line array of unknown shape

Homer P. Bucker

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1451-1454 (1978); (4 pages) | Cited 1 time

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Beamforming a curved towed array of known shape is easily done by matching the received signals to the calculated signals for an incident plane wave. If the array shape is unknown, the beam pattern can be calculated for the array moving along an assumed space–time curve. The sharpness of the beam pattern is defined as the sum of the squares of the beam outputs in different look directions. Next the space–time curve is changed by an iteration procedure until the sharpness is maximum. Sample calculations for simulated and actual data show that this method generates an improved beam pattern and, in the simulated data case, a good estimate of the true array space–time curve.
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43.60.Gk Space-time signal processing, other than matched field processing
43.30.Vh Active sonar systems

Measurement of acoustic reflection from an obstruction in a pipe with flow

J. P. Johnston and W. E. Schmidt

J. Acoust. Soc. Am. Volume 63, Issue 5, pp. 1455-1460 (1978); (6 pages) | Cited 1 time

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An alternative to the impedance tube method is proposed for measurement of acoustic reflection coefficients. The new method has the advantage that it may be used to measure the reflection and transmission coefficients for plane sound waves incident on an obstruction (orifice, nozzle, valve, elbow, etc.) in a long, straight, hard‐walled duct in the presence of flow through the duct. It employs the time‐delayed cross correlation between an acoustic signal source and the output signals from microphones located ahead of, and behind, the obstruction. The method is demonstrated for several situations, including the case of flow through square‐edged orifices where Mach number in the jet downstream of one orifice was as high as 0.73.
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43.60.Cg Statistical properties of signals and noise
43.20.Fn Scattering of acoustic waves
43.20.Mv Waveguides, wave propagation in tubes and ducts
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