Volume 56, Issue 6, December 1974

Propagation of radiation from a finite beam or source through an anisotropic random medium
View Description Hide DescriptionIn a previous paper, we solved the problem of propagation of a plane wave in an anisotropic random medium. The characteristic correlation distances in the horizontal propagation direction were assumed to be large compared to the radiation wavelength divided by 2π, (λ̄/2π), while in the vertical direction, these distances were, roughly speaking, assumed to be of the same order or smaller than λ̄/2π. For this medium, we derive here the equation governing the propagation of the coherence function for a finite beam or source of characteristic dimension a. This equation is then averaged over the vertical direction and solved. The solution is given in terms of a definite integral over the horizontal spectrum of the index‐of‐refraction field. The point source solution (a → 0) and the plane‐wave case (a → ∞) are given as special cases. Explicit solutions are given for the propagation of an acoustic field in the ocean under conditions for which the spectrum satisfies a minus two power law.

Coherent analysis of ray propagation with moving source and fixed receiver
View Description Hide DescriptionRay propagation has been analyzed coherently for a moving‐source‐fixed‐receiver system by taking into account source motion from the results of a fixed model in which spreading loss, travel time, boundary losses, and boundary phase shifts are calculated. Specific examples of the amplitude and phase time series are given for a source moving at 5 knots from 500 to 520 km radially from the receiver. These time series are given for sampling intervals of 1 min and in shorter sections for 0.2 sec, indicating the effects on phase of the source motion. The data clearly indicate the effect of multipath and the usefulness of this technique in the study of spatial variations in the medium. It is demonstrated that multipath interference due to source motion in the medium is a major contributor to transmission fluctuations in both phase and amplitude.

Diffraction of waves and stress intensity factors in a cracked layered composite
View Description Hide DescriptionElastodynamic stress intensity factors are computed for diffraction of antiplane shear waves by a crack in a layered composite. The crack is normal to and bisected by the midplane of the layer. Both cases of a partially broken layer and a completely broken layer are studied. Integral transform techniques are used to formulate the problem as a singular integral equation. The propagation of symmetric modes (Love waves) is studied numerically, and stress intensity factors are obtained for several values of frequency, geometrical parameters, and material constants. The amplitude ratios of the incident waves to incident plus scattered waves at a large distance from the crack are also calculated.

Scattering of sound from time‐varying irregular free surfaces
View Description Hide DescriptionThe problem of sound scattering from a time‐varying irregular free surface is treated anew. The wave equation with its complicated surface boundary condition is transformed to another partial differential equation with a simple, perfectly reflecting, boundary condition. An integral equation for the Green's functionG′ of this latter equation is found which admits a Neumann series solution. The Green's functionG for the original wave equation is determined from G′ via a simple transformation. The Green's functionG is explicitly calculated to second order in the surface wave height. A plane‐wave scattering formalism is developed in which scattered‐wave amplitudes are expressed in terms of G′. The differential cross section for surface scattering is expressed in terms of the scattered‐wave amplitudes and is explicitly calculated to second order in the wave height and expressed in terms of the space‐time covariance of the irregular surface. With suitable additional approximations, the autocovariance and power spectrum are computed to second order for an acoustic signal generated from a fixed sinusoidal source. The results are expressed in terms of previously derived plane‐wave quantities, the differential cross section, and forwardscattering amplitude. The perturbation calculations are valid provided the rms wave height is small compared to the principal wavelength of sound used.

Multiple scattering of waves by a uniform random distribution of discrete isotropic scatterers
View Description Hide DescriptionIntegral equations describing the multiple‐scattering effects of waves propagating in a discrete random medium are solved using Fourier transform techniques. The average intensity in the medium for a given sourceradiation is expressed in terms of a Green's function which consists of residue contribution at a pole representing diffusion and a branch cut integration pertaining to nearfield. It is shown that for a plane wave, multiple scattering becomes significant when the particles are mostly scattering (albedo, b > 0.5) for all distances greater than a fraction of an optical depthZ. When the particles are mostly absorbing, multiple scattering will not take effect until at least Z > 2. For a spherical wave, the multiple‐scattering influence does not become significant until several optical depths, except when the scatterers are extremely low loss (b → 1).

Three‐dimensional acoustic streaming near a stagnation point
View Description Hide DescriptionThe general three‐dimensional high‐frequency oscillatory flow near a stagnation point is investigated through the method of matched asymptotic expansions. The nonlinear Reynolds's stresses create a steady streaming motion in the fluid. It is found that this streaming is minimized when the surface near the stagnation point is axisymmetric and is maximized when the surface is a saddle.

Low‐frequency acoustic scattering from a trailing vortex
View Description Hide DescriptionThe cross section for the scattering of low‐frequency (∼ 100 Hz) sound by an aircraft trailing vortex is computed using the Born approximation. The predicted cross section is large enough to permit size and strength measurements. Although precise location of a vortex is better done with high‐frequency refraction, a monitoring system based on low‐frequency acoustic radar is possible, and a system combining the best features of each is also feasible.

Investigation of the aerodynamic noise generating region of a jet engine by means of the simple source fluid dilatation model
View Description Hide DescriptionAn experiment was conducted on a full‐scale jet engine to investigate the aerodynamic noise generating regions in the free jet. Cross‐correlation measurements were made between the static pressure fluctuations and the farfield radiated sound. These measurements were made for two different static pressure probe positions and a large number of farfield positions (at various angles). In addition, each test geometry was run for four different jet exit velocities. The measured, normalized cross‐correlation functions varied between 0.004 and 0.155. A new Q‐function, based on the above normalized cross correlation is defined and plotted. This function represents the source strength per unit volume within the jet region. This Q‐function shows dependence on the probe position, the angular position of the farfield microphone, and the jet exit Mach number. Third‐octave analyses of both the probe signal and the farfield radiated sound were made. The results show that cross‐correlation techniques are a valuable tool in the investigation of the aerodynamic noise generating regions of an actual jet engine.

Deep scattering layer spectra in the Atlantic and Pacific Oceans and adjacent seas
View Description Hide DescriptionThe acoustic properties of deep scattering layers were examined using explosive sources at a few hundred sites in the main basins of the North and South Atlantic and the North and South Pacific, in the Labrador, Norwegian, Mediterranean, and Caribbean Seas, and in Baffin Bay. Representative day and night spectra of column strength are presented for these areas in the frequency band 0.8–25.6 kHz along with estimates of the effective radii of the swimbladders of the dominant scatterers. The spectra tend to fall into homogeneous groups, with the most pronounced changes in type taking place near known faunal boundaries. In mid‐ocean, in the North and South Atlantic and the South Pacific, scattering is high near the equator and at mid‐latitudes, with considerably lower values in between. Very low scattering strengths are also found in the cold waters at high latitudes in both hemispheres. In a number of cold water areas in the northern hemisphere there is a pronounced peak in sound scattering at low frequencies, caused by scatterers with effective radii of swimbladders of 1 cm or greater. As some of these relatively large scatterers are probably commercial fish, it appears that a measurement technique similar to that used in this investigation would be a useful tool in resource management of commercial fisheries.

Application of the USRD type E8 transducer as an acoustic parametric source
View Description Hide DescriptionThe USRD type E8 transducer was operated as an acoustic parametric source, and its performance as such was measured in two separate laboratory experiments and at sea. The parametric source was driven by a primary signal that consisted either of two high‐frequency components or of an amplitude‐modulated high‐frequency carrier. The primary signal was centered at the transducerresonance frequency near 1.4 MHz, and the observed difference frequencies ranged from 20 to 200 kHz. During typical operation the primary electrical signal had a total power of approximately 6 W, and a difference‐frequency signal at 50 kHz had a source level of about 154 dB re 1 μPa m. This paper describes the design and performance of the parametric source. It also presents a sequence of radiation patterns and values of beamwidth that illustrate difference‐frequency beam formation in the nearfield of the parametric source.

Rectified diffusion in the presence of, and absence of, acoustic streaming
View Description Hide DescriptionIndividual air bubbles held in the central interior of a water‐filled chamber by a 20‐kHz pressure‐gradient force, were observed dissolving in undersaturated water and growing by rectified diffusion in saturated water. When bubbles grew or dissolved in the absence of nearby acoustic streaming, present theories for normal diffusion and for rectified diffusion in the absence of streaming gave reasonable agreement with experiment. When crispations appeared on a bubble, acoustic streaming accompanied the surface activity and the rate of dissolution or growth of the bubble was intensified up to twentyfold. Measurements of threshold sonic pressures for onset of crispation revealed that, in general, the larger the bubble the lower the pressure required. Present theories for diffusion in the presence of acoustic streaming imply, in contrast to experiment, that streaming should inhibit rectified diffusion in saturated and undersaturated liquids. For gas bubbles dissolving in undersaturated liquids, the effects of sound on mass transfer can be made negligible, and experimental measurements of the diffusion coefficient of the gas in the liquid can be obtained.

Modified ray theory for bounded media
View Description Hide DescriptionIn earlier investigations, “modified ray theory” has been developed using a generalized version of the WKB or geometrical‐optics approximation based on Weber functions for solutions of the scalar wave equation for the “two‐turning‐point” unbounded sound‐propagation problem. This wavelength‐dependent theory provides a ray representation in reflection and transmission regions for some of the diffraction phenomena that arise in a stratified medium. In the present paper, both Airy and Weber functions are used as a basis for the generalized WKB procedure to carry out analysis for various classes of sound‐speed profiles, and the development of modified ray theory is extended to include the effect of boundaries of a type pertinent for underwater sound propagation.

Studies in reverberation. I. Scattering of sound by a plane vortex sheet
View Description Hide DescriptionA plane wave is incident obliquely at a boundary between two liquid half spaces, of which the lower one moves with velocityU parallel to the interface relative to the upper one. It is found that the reflection coefficient depends only on the component of U parallel to the direction of the incident wave. Total reflection occurs when the wave has a component of propagation in the direction of U, but not in the reverse case. It is shown that in the case when U is any function of depth z below the interface, the reflection coefficient vanishes for normal incidence. For U of the order of c/1000, the reflection coefficient is appreciable only near grazing incidence.

Low‐frequency power radiation from a flat plate into an acoustic fluid
View Description Hide DescriptionThe power transmitted into an acoustic fluid by a periodically supported flat plate vibrating with low frequency is investigated. Utilizing a direct analysis of the field equations, closed‐form expressions for radiated power and oscillation amplitude are obtained. It is shown that several null power frequencies can exist which are distinct from the null midspan amplitudes of oscillation of the plate. These null power frequencies are strictly a low‐frequency effect, while the null midspan amplitude frequencies will occur over the entire frequency spectrum. Numerical results for a steel plate clamped at its periodic supports and in contact with water are obtained and presented graphically.

Absorption of sound waves by chemical equilibria occurring in solution
View Description Hide DescriptionExpressions previously developed by Tabuchi for the velocity and absorption of sound waves in a liquid in which a reversible chemical reaction is occurring are corrected, taking into account the effect of pressure on the chemical equilibrium.

Ultrasonic bounded beam reflection effects at a liquid‐anisotropic‐solid interface
View Description Hide DescriptionSchlieren techniques are used to show that a bounded ultrasonic beam impinging on a liquid‐single‐crystal‐copper interface, and generating generalized surface and pseudo surface waves, can produce reradiation fields which result in changes in the reflected beam similar to effects observed at liquid‐isotropic‐solid interfaces when Rayleigh waves are generated. The existence of these reflected beam effects at water‐single‐crystal‐copper interfaces is attributed to the component of the particle displacement ellipse of the generated surface wave which is perpendicular to the crystal surface. A parameter β, characteristic of this perpendicular particle motion, is introduced and its value calculated from existing surface‐wave particle‐motion data. Observed reflected beam effects are described in terms of the parameter β.

Time‐frequency‐domain formulation of ultrasonic frequency analysis
View Description Hide DescriptionThe ultrasonic frequency spectrum is interpreted by Fourier analysis techniques. This approach leads to the same conclusions concerning flaw characterization as previous interference models; in addition, a number of other spectral characteristics are easily explained. Finally, the present treatment indicates that frequency analysis may be applicable to many additional problems, viz., timing measurements of any type (e.g., thickness or velocity measurements), wide‐band attenuation measurements, and phase‐shift measurements (e.g., determination of relative acoustic impedance).

Vibrational response of sonar transducers using piezoelectric finite elements
View Description Hide DescriptionThe finite element method is applied to the vibrational analysis of electromechanical sonartransducers of arbitrary geometry. Three‐dimensional hexahedral finite elements which include the effects of piezoelectric coupling are formulated, and the solution of the resulting coupled electroelasticequations of motion is presented. The vibrational response of a particular transducer element is computed, and comparisons with experimental mesurements are made. The calculated deformations of the transducer are presented in the form of computer generated displays. A data reduction scheme is also utilized to clarify the physical meaning of the transducer response.

Free and forced vibrations of rods according to Bishop's theory
View Description Hide DescriptionThe equations of motion of longitudinal vibrations of rods according to the theory of Bishop are rederived using Hamilton's principle, in the process of which the associated boundary conditions are also obtained. The frequency equations and mode shapes for ten different combinations of boundary conditions are given. The influence of the secondary effects an the fundamental frequency of rods is illustrated and it is shown that the effect of lateral inertia is almost three times as important as the effect of shear stiffness. Studies of free and forced vibrations of rods by the eigenfunction expansion process show that the higher‐order theory predicts a maximum response which is less than the one predicted by the elementary theory of rods. Comparison with the available experimental data show that the Bishop theory represents a better model for predicting the response of a free‐free rod subjected to a suddenly applied force.

Estimation of error in motor‐vehicle noise‐level measurements
View Description Hide DescriptionIn several SAE standards for the measurement of noise levels of motor vehicles, the allowance for measurement error is given as 2 dBA. A number of investigators, however, found the variations of certain influencing factors to be larger than 2 dBA. These investigators then use these results to suggest that the overall measurement would exhibit errors of the same magnitude as the variation in the influencing factors. However, as this note shows, the measurement of sound‐pressure levels according to the SAE procedure has a lower variance than that of the distribution of instantaneous sound‐pressure levels.