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Nov 1970

Volume 48, Issue 5B, pp. 1077-1298

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Generation of Fractional Harmonics in a Resonant Ultrasonic Wave System

Laszlo Adler and M. A. Breazeale

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1077-1083 (1970); (7 pages) | Cited 10 times

Online Publication Date: 03 Aug 2005

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The problem of a fluid‐filled cavity caused to resonate by an ultrasonic wave is described as a parametric phenomenon. Variation of the cavity resonance frequency as a result of the periodic change of length produces the condition for parametric resonance. As a result, fractional harmonics of the driver transducer frequency are generated. The wave equation describing the system is transformed into an ordinary differential equation with periodic coefficients. The solution of this differential equation (Mathieu's equation) predicts frequency doublets which have been observed experimentally. A threshold condition of parametric excitation is derived from the region of unstable solutions of Mathieu's equation. This threshold condition relates the amplitude and frequency of the driver transducer to the cavity length and to the absorption per wavelength of the medium. Reasonable agreement between theory and experiment is obtained.

A Graphic Solution for Wave Velocities of Sound in Crystals

W. L. Bond

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1084-1085 (1970); (2 pages)

Online Publication Date: 03 Aug 2005

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A method is presented for solving the cubic equation involved in calculating velocities of sound in any direction in crystals.

Optical Measurements of Ultrasonic Attenuation and Reflection Losses in Fused Silica

Charles Krischer

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1086-1092 (1970); (7 pages) | Cited 4 times

Online Publication Date: 03 Aug 2005

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The ultrasonic attenuation in fused silica was measured by the Bragg diffraction of a 6328‐Å He‐Ne laser beam; two complementary techniques were used to obtain room‐temperature data over the frequency range 200–980 MHz. The frequency dependence of the attenuation is given by f1.97 and f1.98, for longitudinal and transverse waves, respectively. If an exact square‐law dependence is assumed, the material loss at 25.0°C can be characterized by the constants B (longitudinal)  =  (6.1±0.2) × 10−18 dB ⋅ sec, and B (transverse)  =  (5.7±0.2) × 10−18 dB ⋅ sec, where A (dB/μsec)  =  B f2. The acoustic‐wave reflection losses at the free surface and transducer‐bond surface of the sample were evaluated. Although in the former case the loss was negligible, in the latter large reflection losses were observed, in spite of the low conversion efficiency of the transducer. A study of the angular distribution of the acoustic intensity for the generated and reflected beams showed that this loss was mainly dissipative, although a deformation of the plane wavefront was also a contributing factor.

New Ultrasonic Technique for the Determination of the Ratios of Strain‐Optical Constants

Howard E. Pettersen

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1093-1097 (1970); (5 pages)

Online Publication Date: 03 Aug 2005

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A new ultrasonic technique for the determination of the ratios of strain‐optical constants is presented. The new technique makes use of the Raman‐Nath theory for the optical diffraction that is produced by a standing ultrasonic wave. It does not require extrapolation to zero sound intensity, which has been the standard procedure for the past 32 years. The intensity of the light in the zero order of the diffraction pattern is observed for light beams which are polarized parallel and perpendicular, respectively, to the ultrasonic wavefront. These data can then be interpreted in either of two ways to determine the ratios of the strain‐optical constants. The new technique has been used in studies of various optical glasses and of sodium chloride. In all cases, the results have been in agreement with values obtained by other investigations using old techniques. The numerical values obtained for sodium chloride are ∣p12/p11∣  =  1.37, ∣p44/p11∣  =  0.088.

Electrical and Mechanical Loading of a Piezoelectric Surface Supporting Surface Waves

Halvor Skeie

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1098-1109 (1970); (12 pages) | Cited 7 times

Online Publication Date: 03 Aug 2005

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The influence of surface loading on the propagation of surface waves on a piezoelectric substrate is analyzed. Both mechanical and electrical loading are described by means of a simple first‐order perturbation theory. General formulas for the perturbation of the surface‐wave phase velocity caused by deposition of a uniform thin film or by electrical interaction with an adjacent conducting or semiconducting medium are developed. The scattering of surface waves from discrete strips is also analyzed. Results from scattering and wave‐propagation analysis are utilized to describe the interdigital surface‐wave transducer. An equivalent circuit for a basic transducer element is developed, and the total transducer is analyzed by means of transmission‐line theory applied to a network of cascade‐coupled elements. The effect of electrode mass loading is specially treated, and the results are compared with measurements made on a Y‐cut Z‐propagation LiNbO3 crystal.

Experimental Investigation of the Resolution Capability of Microwave Ultrasonic‐Beam Visualization Techniques Using Bragg Diffraction of a Laser Beam

C. S. Tsai and H. V. Hance

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1110-1118 (1970); (9 pages)

Online Publication Date: 03 Aug 2005

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The theoretical resolution capability of Bragg‐imaging technique for two‐dimensional problems has been verified using ultrasonic waves in solids at frequencies in the vhf and L‐band range. The resolution was investigated as a function of ultrasonic wavelength and laser‐beam convergence angle. With an optical arrangement which utilizes a combination of a diffraction‐limited spherical lens and low‐grade cylindrical lenses, resolution nearly equal to the theoretical value was obtained. For this investigation it was necessary to devise techniques for generating multiple ultrasonic beams in one‐ and two‐dimensional array configurations with well‐defined beam dimensions and separations. It is found that the most reliable method of fabricating such configurations is to deposit a gold‐film back electrode with an identical array pattern on a uniform CdS film transducer. The application of Bragg‐imaging technique for visualizing the activity pattern of a CdS thin‐film transducer is also illustrated.

Ultrasonic Absorption in H2S

T. G. Winter and H. E. Bass

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1119-1122 (1970); (4 pages) | Cited 4 times

Online Publication Date: 03 Aug 2005

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Ultrasonic absorption has been measured in H2S in the temperature range 300°–683°K. These data were analyzed to obtain vibrational and rotational relaxation times. The vibrational collision numbers seem to increase with temperature from 300° to 473°K and then decrease with temperature. This behavior can be explained by the v‐r theory of Shields and Burks. The rotational collision numbers compare favorably with thermal transpiration measurements.

Propagation of Sound in a Turbulent Atmosphere

S. F. Clifford and E. H. Brown

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1123-1127 (1970); (5 pages) | Cited 1 time

Online Publication Date: 03 Aug 2005

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Applying a perturbation technique to the correct form of the equation for the acoustic pressure field in a viscous turbulent atmosphere yields the power spectra for the amplitude and phase fluctuations of a propagating plane wave. The development includes the effects of absorption and removes the restrictions on wavenumber that previously prevented solution of the problem for other than ultrasonic frequencies. For a wide range of propagation parameters, the amplitude and phase spectra found by Tatarski for optical propagation are shown to be good approximations for acoustic waves. Complete expressions, without limitation on the assumed refractive‐index spectra, determine the range of validity of this result and also provide an exact first‐order solution.

Radiation by Finite Circular Pistons Imbedded in a Rigid Circular Baffle. I. Eigenfunction Solution

R. V. DeVore, D. B. Hodge, and R. G. Kouyoumjian

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1128-1134 (1970); (7 pages)

Online Publication Date: 03 Aug 2005

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Spheroidal wavefunctions have been used to calculate the patterns and radiation impedances of several piston configurations mounted in a rigid circular baffle. The results are of some practical interest, and they also may be used to check approximate solutions. For one of the configurations there is no diffraction at the edge of the baffle; in this instance, the radiation characteristics are identical with those of the infinite baffle case.

Observation of Waves Radiated from Circular Cylinders Caused by an Incident Pulse

Werner G. Neubauer and Louis R. Dragonette

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1135-1149 (1970); (15 pages) | Cited 7 times

Online Publication Date: 03 Aug 2005

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Schlieren visualization and hydrophone measurements are used to observe the radiated wavefronts which result when an acoustic pulse is incident on a metal cylinder in water. The range of size parameter ka from 138 to 1419 is considered. The wavefront positions are traced by the refraction, internal reflection, and radiation of shear and compressional waves. In the case of solid cylinders, many wavefronts display an apparent circumferential property derived from the incidence of energy from the normal to the appropriate critical angle. Identification of one of these wavefronts as resulting from previously identified “Rayleigh‐type” wave propagation and a single incident angle is denied, although the circumferential property is verified. A previously identified faster circumferential wave is attributed to a composite wavefront resulting from direct compressional transmission and an increasing number of its internal reflections. Other wavefronts depending on mode conversions are also identified. A mechanism is presented to account for the apparent dispersion indicated by an increasing circumferential wave speed determined from previous hydrophone measurements below ka = 200. Simultaneous schlieren and hydrophone receptions that show the wavefront incident on a hydrophone as well as the resultant hydrophone output at ka values of 355 and 138 are presented. For shells, a prominent wave is seen to exist, in the same position, for both air‐ and water‐filled cases. The wave is shown to be a characteristic of thin shells, originating from the transmitted compressional wave and subsequent mode conversion to a shear wave. The radiated wavefronts disclose a circumferential property for the waves that cause them. One such wavefront, believed to be the same described elsewhere as an antisymmetric Lamb wave, is proven in our case to be caused by direct transmission through the interior of a water‐filled shell. The wave previously attributed to a Rayleigh‐type circumferential propagation is shown to exist in aluminum shells as thin as those with a 0.9 ratio of inner to outer radius.

Visualization of Plane‐Strain Vibration Modes of a Long Cylinder Capable of Producing Sound Radiation

E. K. Sittig and G. A. Coquin

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1150-1159 (1970); (10 pages) | Cited 3 times

Online Publication Date: 03 Aug 2005

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This paper points out that a class of plane‐strain vibration modes in an isotropic solid cylinder has properties suitable for interaction with a sound field in a fluid medium surrounding the cylinder. A resonance‐type theory of such modes is presented. Experimental verification of this theory is obtained by observing stress birefringence patterns of resonating glass cylinders. The circumferential waves arising from these modes are likely to play a part in the scattering phenomena occurring in the medium surrounding the cylinder.

Harmonic Nonaxisymmetric Waves with Short Wavelengths Propagating in Composite Rods

Anthony E. Armenàkas and Henry E. Keck

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1160-1169 (1970); (10 pages)

Online Publication Date: 03 Aug 2005

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The asymptotic phase velocities, at very large wavenumbers, of nonaxisymmetric waves traveling in composite rods are established analytically. Frequency spectra and mode shapes of composite rods are presented and compared with those of simple (made of one material) rods.

Response of a Covering Plate to Noise in a Viscoelastic Half‐Space

Paul J. Remington and Stephen H. Crandall

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1170-1178 (1970); (9 pages)

Online Publication Date: 03 Aug 2005

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The steady‐state response of an infinite Bernoulli‐Euler plate placed on the surface of a vibrating viscoelastic half‐space is studied both theoretically and experimentally. The surface displacements of the half‐space before the plate is added are assumed to be stationary homogeneous random functions of position and time. Given the wavenumber‐frequency spectra of these displacements, the frequency spectra of the displacements of the plate‐half‐space interface are calculated, assuming that there is no shear stress between the plate and the half‐space. A test of the theory was performed in which several Plexiglas plates of varying thickness were placed on the vibrating surface of an “experimental half‐space,” a tub filled with Plasticine (a modeling clay). Wavenumber spectra transformed from correlation measurements, made on the surface of the clay, were used in the theory to obtain response predictions that agreed to within 3 dB of measured response levels.

The Role of Impurities in Cavitation‐Threshold Determination

Robert E. Apfel

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1179-1186 (1970); (8 pages) | Cited 14 times

Online Publication Date: 03 Aug 2005

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We have extended the theoretical work of Harvey et al. [J. Cellular Comp. Physiol. 24, 1–22 (1944)] and Strasberg [J. Acoust. Soc. Amer. 31, 163–176 (1959)] in order to consider the conditions that must exist in a liquid for a vapor cavity to be nucleated from an imperfectly wetted solid impurity (mote) in the liquid. It is found that, for sufficiently small and readily wetted motes, the tensile stress required for nucleation increases with increasing surface tension and decreasing mote size but is almost independent of the gas content and history of the liquid. On the other hand, for sufficiently large and imperfectly wetted motes, the gas content of the liquid and its history are crucial, whereas the mote size and the liquid‐vapor surface tension play no role in determining the conditions for nucleation. The qualitative predictions of this theory of moted‐induced nucleation bring some semblance of order to a wide variety of observations of statically induced cavitation and low‐frequency acoustic cavitation reported in the literature.

Sound Propagation in a Channel with Lossy Boundaries

Homer P. Bucker

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1187-1194 (1970); (8 pages) | Cited 4 times

Online Publication Date: 03 Aug 2005

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The sound field of a CW point source in a duct with lossy boundaries is written as a normal‐mode sum. It is assumed that the boundaries are parallel and that the sound velocity varies only with depth in the duct. As an illustrative example, calculations are made for a shallow water duct and compared to field data.

Measurement of the Effect of Air Bubbles on the Speed of Sound in Water

Frederick W. Gibson

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1195-1197 (1970); (3 pages) | Cited 2 times

Online Publication Date: 03 Aug 2005

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A simple technique for measuring the effect of air bubbles on the speed of sound in water, and hence on the attenuation of pressure pulses in water, has been developed. The good agreement of the experimental data with computed values indicates the adequacy of the experimental method.

Bottom‐Reflection‐Loss Model with a Velocity Gradient

Halcyon E. Morris

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1198-1202 (1970); (5 pages) | Cited 1 time

Online Publication Date: 03 Aug 2005

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Theoretical bottom‐reflection losses are computed using a multilayered model of the ocean bottom in which the layers are considered to be absorbing liquid sediments with velocity gradients. The sound velocity of each sediment layer is assumed to be a nearly linear function of depth z. In this case, the acoustic field in the sediment layers can be represented as a linear combination of Airy functions. Comparisons of theoretical and measured bottom‐reflection losses are made for three areas at frequencies from 0.1 to 1.6 kHz.

Asymptotic Solution of the Stochastic Helmholtz Equation for Turbulent Water

Jerome A. Neubert

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1203-1211 (1970); (9 pages) | Cited 4 times

Online Publication Date: 03 Aug 2005

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It is concluded that a two‐variable expansion is sufficient for representing sound propagation through a continuous weakly inhomogeneous medium and that the Debye approximation is a proper two‐variable expansion. Its application to the stochastic Helmholtz equation yields, to order ασκ(Rt)½/λg2k02, the eikonal equation and the transport equation; α is the rms refractive index variation, σκ is the Prandtl number, Rt is the turbulent Reynolds number, λg is the Taylor microscale, and k0 is the wavenumber. The resultant acoustic frequency limitations for the Stone and Mintzer experiment and for the turbulent upper ocean are developed and compared. The solution of the eikonal and transport equations in a continuous fluid renders a Lagrangian pressure relation. Finally, the Debye and Born approximations are compared for one‐dimensional sound propagation.

Derivation of the Stochastic Helmholtz Equation for Sound Propagation in a Turbulent Fluid

Jerome A. Neubert and John L. Lumley

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1212-1218 (1970); (7 pages) | Cited 3 times

Online Publication Date: 03 Aug 2005

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The basic stochastic wave equation for sound propagation through a turbulent field is derived from first principles as represented by the continuity equation, the Navier‐Stokes equations, and an appropriate equation of state. It is shown that, for very low turbulent Mach numbers and monochromatic transmissions sound propagation in a turbulent field can be adequately represented by the stochastic Helmholtz equation, ∇2p+k02μ2p  =  0, if the acoustic wavelength does not exceed the Taylor microscale λg divided by [(σκ)½(u/c)]½, where σκ is the Prandtl number and u/c is the turbulent Mach number. In addition, the comparison of similar turbulent flows in air and in water, with respect to estimating their acoustic frequency limitations, is illustrated by contrasting: (1) the Baerg and Schwartz experiments with the Stone and Mintzer experiments, and (2) the turbulent lower atmosphere with the turbulent upper ocean.

Ray Theory for Sources and Receivers on an Axis of Minimum Velocity

Melvin A. Pedersen and DeWayne White

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1219-1248 (1970); (30 pages) | Cited 1 time

Online Publication Date: 03 Aug 2005

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This article presents a detailed analysis and numerical investigation of the ray theory of four simple velocity profiles in common use as models of the deep sound channel in underwater acoustics. Comparison with ray‐theory results for range and group velocity, obtained after fitting a 19‐parameter curve to a realistic ocean profile, indicates that these simple profiles are inadequate. Numerical examples exhibit more completely the significant effect of discontinuities in the second‐ and third‐profile derivatives evaluated at the axis. Some general theoretical results are developed and illustrated by examples. These results include: (1) scaling laws interrelating ray theory results for different sets of profile parameters, (2) the development of range and group velocity in series expansions of the phase velocity, (3) group velocity inequalities, and (4) the role of points of inflection in producing multiple caustics. A method is presented which determines and demonstrates the near‐axial ray‐theory properties of a velocity profile by comparison with a cosh profile.

A New Approach to the Determination of Acquiring Rays in Singly and Doubly Layered Oceans

David T. Raphael

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1249-1256 (1970); (8 pages)

Online Publication Date: 03 Aug 2005

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For singly or doubly layered oceans, it is possible to determine by means of an exact closed‐form solution those rays having initial angles at the source depth which lead to acquisition of the point target. For the specific problems considered, the stationary target coordinates relative to the source plus the oceanic sound‐velocity profile composed of either one or two linear‐gradient layers are assumed to be known. An algebraic as well as an alternative geometric derivation of the closed solution for the initial target‐acquiring ray angle at the source depth is first presented. The resultant solution is then used to solve the following two problems: (1) a ray having undergone n reflections from a horizontal surface, with source located at the surface depth and (2) a ray having undergone n interface crossings, with source located at the interface. Four cases need to be treated in order to solve this two‐layer problem completely. For problems 1 and 2, existence conditions are developed which must be satisfied before the closed‐form solution can be used. The acquiring‐ray initial angles then obtained are related to the corresponding intensity equations developed in a previous article by P. Uginčius [J. Acoust. Soc. Amer. 45, 198–200 (1969)]. As a consequence of the aforementioned existence conditions, it is possible to determine the equations of the caustic curves which form the envelopes of the solution sets.

The Characteristics of the Acoustical Pulses Emitted by Boiling Bubbles in Water

R. F. Saxe and R. K. Cothren

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1257-1265 (1970); (9 pages) | Cited 1 time

Online Publication Date: 03 Aug 2005

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An investigation of the acoustic emissions from boiling bubbles in water has been made using two methods—frequency analysis and pulse‐height analysis. Pulse‐height analysis, using coincidence techniques, shows that the pulse‐height spectrum of boiling bubbles in water has a distribution which is independent of the amount of boiling, indicating that the distribution is governed by liquid, vapor, and possible wire‐surface characteristics. The addition of wetting agent to the water has an appreciable effect on the pulse‐height distribution. Frequency analysis is shown to produce no information about pulse characteristics.

Volume‐Scattering‐Strength Dependence on Depth and Frequency in the Pacific Ocean off San Francisco

J. A. Scrimger and R. G. Turner

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1266-1274 (1970); (9 pages)

Online Publication Date: 03 Aug 2005

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A time series of measurements of volume scattering was made in the N.E. Pacific Ocean at a site approximately 55 miles west of Pt. Reyes (near San Francisco). The technique involved the firing of small explosive charges close to a receiving hydrophone and monitoring the broad‐band scattered returns originating nearby (approximately 100‐ft radius). Lowering the hydrophone‐charge combination to various depths enabled the scattering characteristics in the top 2100 ft of the ocean to be examined. The data are presented as spectra of scattering strength versus frequency at 10 evenly spaced depths between 200 and 2000 ft and also as a set of eight profiles of scattering strength versus depth in each of four octave frequency bands between 0.625 and 10 kHz. These profiles are obtained in the course of a 30‐min lowering of the equipment—eight of which were carried out between 0600 PST (about 1½ h before dawn) and 2000 PST (about 2 h after sunset). Scattering‐strength profiles were integrated against depth to give column scattering strength values which are displayed as a function of time. In addition, a comparison was made between integrated scattering strength versus depth profiles obtained both from a scattering strength versus depth profile and from a surface‐fired charge.

Analysis of the Frequency Response of Simple Geometric Targets

D. J. Shirley and K. J. Diercks

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1275-1282 (1970); (8 pages) | Cited 3 times

Online Publication Date: 03 Aug 2005

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Measurements of pulse‐echo forms and steady‐state frequency response of air‐ and water‐filled aluminum spheres and cylinders in water are presented. These compare favorably with theoretical results. The nondimensional frequency (ka) range is 24≦ka≦60. Scattering paths defined by the cross‐sectional geometry of the targets are identified, and it is shown that it is constructive and destructive interference between the energy returned along the different scattering paths that generates the frequency response of the target as frequency is changed. Similarities in the backscattered echoes from spheres and cylinders at normal incidence due to similarities in the scattering geometry are described. Measurements of circumferential waves in spherical shells, believed to be the first reported for this target form, are presented.

Depth Dependence of Bubble Pulse Periods of Point and End‐Fired Line Charges

R. A. Wentzell, R. H. Adlington, and J. C. Moldon

J. Acoust. Soc. Am. Volume 48, Issue 5B, pp. 1283-1286 (1970); (4 pages) | Cited 1 time

Online Publication Date: 03 Aug 2005

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A theory of the depth dependence of the first bubble pulse period of an infinitely long cylindrical charge is developed. The charge is represented by a cylinder of adiabatic gas and the time equation for expansion from its initial radius to equilibrium is derived as a function of the weight of explosive per unit length and the hydrostatic head. Theoretical results are compared with measured bubble pulse periods of end‐fired line charges detonated at depths between 90 and 10 600 ft. The length‐to‐diameter ratio of the charges varied from 45 to 320 and the weight of explosive per unit length varied from 0.11 to 0.43 lb/ft. There is substantial agreement between theory and experiment, the agreement improving as the length‐to‐diameter ratio of the charge increases.
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