Volume 59, Issue 4, April 1976
Index of content:
59(1976); http://dx.doi.org/10.1121/1.380937View Description Hide Description
A recent theoretical formulation by Westervelt and Larson predicts the development of highly directive sound beams in water through the thermalization of modulated laser light. The present paper reports the experimental validation of this theory with measurements carried out in a fresh water lake. Additional theory pertinent to practical implementation is also presented and verified. The experimental apparatus includes an optically pumped laser system operating in the conventional mode at wavelengths in either the red or infrared regions of the optical spectrum. Modulation of the stochastic light burst is provided by a half‐wave Pockels cell. The acoustic measurements began with an existence test which confirmed that an acoustic signal is produced by thermo‐optic demodulation of laser light in the water. The sound pulse was generated in a beam with a width and source level that are in reasonable agreement with theory. Acoustic diffraction effects associated with laser beams of finite size were also examined, as were the nearfield effects of this type of array. The relation of laser technology to further work in the blue–green spectrum is analyzed.
Subject Classification: 20.55; 85.40; 35.65.
59(1976); http://dx.doi.org/10.1121/1.380938View Description Hide Description
A description of the acoustic pressure versus time is obtained for a finite cylindrical source whose initial overpressure is constant and uniform. Small signal analysis is used and the medium is considered dissipationless. The results show a short leading condensation followed immediately by a rarefactive impulse with a long tail which ends in a second rarefactive pulse of smaller amplitude. The analytical results are amenable to numerical methods for obtaining pressure disturbances from cylindrical sources of given lengths and radii.
Subject Classifacation: 20.55, 20.15.
59(1976); http://dx.doi.org/10.1121/1.380939View Description Hide Description
The acoustic nearfield of a circular piston is investigated using the impulse response technique. Although the harmonic field can be expressed as either a convolution integral or Fourier transform, the integrals cannot be simply evaluated. An asymptotic evaluation of the Fourier transform of the spatially dependent impulse response for the circular piston is, however, readily performed. The resulting expressions very simply illustrate the nearfield behavior of the piston. Furthermore, the expressions are shown to be in agreement with the asymptotic properties of known nearfield results and are consistent with the usual farfield expressions.
Subject Classification: 20.55, 20.15.
59(1976); http://dx.doi.org/10.1121/1.380940View Description Hide Description
An approach suggested by Westervelt [3rd Int. Congr. Acoust., Stuttgart, 1959] has previously been used to predict with remarkable accuracy the excess absorption due to nonlinear effects in a plane, traveling sound wave. The same approach is applied here to spherically diverging sound waves. A number of cases of practical importance in underwater acoustics are evaluated and compared with other theoretical results.
Subject Classification: 25.22; 30.75.
59(1976); http://dx.doi.org/10.1121/1.380941View Description Hide Description
Earlier studies [J. Acoust. Soc. Am. 29, 934 (1957)] of the mutual nonlinear interaction of two plane waves of sound with each other exhibited a singularity when the waves became collinear. The singularity is removed in this study, which leads to a method for calculating the pressureabsorption coefficient α of a wave with wave vector k1 resulting from interaction with isotropic acoustic waves having the energy density spectrumu (k). Thus, α= (4ρ0 c 2 0)−1(1+1/2Λ)2π F k 1 0 k u (k) d k+k 1F∞ d 1 2u (k) idk+k 2 1F k 1 1 k −1 u (k) d k], in which ρ0 and c 0 represent the density and velocity of sound of the fluid which is assumed to be dispersionless. The constant 1/2Λ =ρ0 c d0−1(d c/dρ)ρ 0 .
Subject Classification: 25.22, 25.35.
59(1976); http://dx.doi.org/10.1121/1.380942View Description Hide Description
We model mathematically the spectral features of infrasound observed in the ionosphere and believed to be radiated by severe thunderstorms. We explain the dominant 2–5‐min wave period as an effect of atmospheric filtering; shorter periods are excessively attenuated by absorption in transit to the ionosphere, and longer periods are attenuated in portions of the atmosphere where the waves are evanescent because their frequencies are below the acoustic cutoff. An observed spectral ’’fine structure’’ within the 2–5‐min band is explained in terms of resonant interactions between the waves and the atmospheric temperature structure. Accurate quantitative modeling of all these details of the storm‐to‐ionosphere transmission coefficient requires numerical integration of the acoustic‐gravity wave equation, including the effects of ground reflection, absorption, and partial reflections in the atmosphere.
Subject Classification: 28.30.
59(1976); http://dx.doi.org/10.1121/1.380943View Description Hide Description
The problem of finding a solution of the scalar wavefield produced by a point source in the presence of an infinite ’’impedance’’ boundary is treated. The analysis is made with a method used by Ingard, which has been corrected. It is shown that it is possible to rewrite the exact solution in terms of a single integral along a steepest‐descent contour and a Hankel function. Asymptotical expansions of the solution is in consistency with expansions by Wenzel, who found that in a special case expansions of his and Ingard’s solution differ by a ’’surface wave’’ term. The asymptotical expansions are given as examples. The main result, the single integral and the Hankel function, could easily be integrated numerically.
Subject Classification: 28.40; 20.15, 20.30, 20.55.
59(1976); http://dx.doi.org/10.1121/1.380944View Description Hide Description
The specific dependence of the properties of a cw Dopplerultrasonicscattered signal, and of its autocorrelation and spectral density functions, on various scatterer flow parameters and diagnostic signal beam parameters is shown. These factors include the scatterer average velocity profile and the extent of any turbulence together with the signal beam angle and beam width.
Subject Classification: 30.40; 35.65; 20.15, 20.30.
59(1976); http://dx.doi.org/10.1121/1.380930View Description Hide Description
Underwater ambient noise spectra are described for data recorded during late spring conditions under the ice sheet in McMurdo Sound. The ambient noise was at all times marked by intense biological activity, but a diurnal component became apparent during a three‐day recording period. This noise was found to be similar to that described in Arctic work and undoubtedly arose as the result of surface cracking under the influence of thermal stressing. The characteristics of this noise component, however, were found to differ in certain respects from those reported from comparable Arctic measurements.
Subject Classification: 30.20, 30.70; 28.65.
59(1976); http://dx.doi.org/10.1121/1.380931View Description Hide Description
A general asymptotic theory of scattering by a moving rough surface is presented. The theory is valid for a slowly varying refractive index, and for ocean‐surface wave heights that are small compared with the acoustic wavelength and the ocean‐surface correlation length. In contrast with the Kirchhoff or physical optics approximation, this theory is valid when the acoustic wavelength and ocean‐surface correlation length are of the same order. The oceansurface is described as a sum of gravity waves of varying frequency progressing in different directions. It is demonstrated that, to a given order of approximation in the asymptotic theory, the average energy associated with signal sideband rays is precisely accounted for by a reduction of intensity of the reflected carrier. Wave number diagrams are introduced which are extremely useful for depicting the directions of the incident and scatteres rays at the surface, demonstrating the effect of varying surface‐wave and acoustic frequency, and demonstrating the frequency cutoff of the sideband power spectrum. The phenomenon of Bragg resonance at glancing incidence of the carrier is also easily depicted. The theory can accomodate the effects of ray focusing, both in the carrier and sidebands, through the use of uniformly valid asymptotic expansions which account for the presence of caustics.
Subject Classification: 30.40, 30.20, 30.25, 30.30.
59(1976); http://dx.doi.org/10.1121/1.380932View Description Hide Description
Experimental measurements are presented for the target strength and directivity patterns of the reflections from stainless steel spherical shells filled with a mixture of carbon tetrachloride and freon (F113) in the frequency range 30–130 kHz. Five spheres were tested having nominal outside diameters of 6, 7, 10, 12, and 18 in. with varying wall thicknesses. Target strength measurements were made separately on echo components arising from reflections from the front and rear surfaces of the sphere; the focused rear‐surface reflections showed target strengths up to 21 dB higher than those corresponding to the front surface, controlled by the sphere wall material and thickness, and by the index of refraction of the fluid.
Subject Classification: 30.30.
59(1976); http://dx.doi.org/10.1121/1.380933View Description Hide Description
We have derived expressions for the mean‐square phase and intensity fluctuations and their spectra for cw sound propagating through a channeled fluctuating ocean. The ’’supereikonal’’ approximation reduces to the geometric optics (eikonal) limit for short acoustic wavelengths: λ≪2πL 2 H /R and λ≪L 2 V /(R tan2ϑ), where L H and L V are horizontal and vertical correlation lengths of the fluctuations, R is range, and tanϑ is the ray slope, replacing the traditional (and much more severe) Fresnel condition λ≪2πL 2/R for a homogeneous isotropic ocean. The results can be expressed in closed form for an exponentially stratified oceanmodel and associated ’’canonical sound channel,’’ with superimposed fluctuations from an internal wavemodel spectrum based on oceanographic observations. The parameters are the stratification scale B, the inertial and buoyancy frequencies ωin and n (z), the scale j * of internal wave mode numbers, and the internal wave energy per unit area. The results are in reasonable agreement with numerical experiments based on the parabolic wave equation. For the ’’singlepath’’ 4‐kHz transmission over Cobb Seamount the observed and computed rms fluctuations in phase are 1.6 and 2.5 cycles, respectively; in intensity these are 5.5 and 2.2 dB, respectively, with anomalous intensities measured at high frequencies (’’sporadic’’ multipathing?). For the multipath 406‐Hz MIMI transmission, we obtain 4×10−3 and 5×10−3 sec−1, respectively, for the experimentally determined and the computed rms phase rates.
Subject Classification: 30.20, 30.40; 20.15.
59(1976); http://dx.doi.org/10.1121/1.380934View Description Hide Description
The influence of the sea bottom on shallow‐water sound propagation can be especially pronounced for the sound field near the boundaries. Comparison of the near‐surface sound field with the mid‐depth field, for example, can serve as a useful diagnostic tool for understanding the frequency‐dependent influence of the sea bottom on sound propagation in shallow water. Broad‐band shallow‐water sound‐propagation data analyzed in one‐third octave bands are compared for a very shallow receiver (2 m) and a mid‐depth receiver (50 m). The data are also compared with results from modal calculations. The interplay between the behavior of the modal depth functions and modal attenuations, as frequency is varied, provides a convenient model for interpreting the results.
Subject Classification: 30.20, 30.30.
59(1976); http://dx.doi.org/10.1121/1.380935View Description Hide Description
Classical wave theoretical treatments can be used to predict the general characteristics of the acoustic field scattered from a roughened time‐varying sea surface. Various approximations can then be invoked to handle the so‐called slightly rough and very rough surface cases. In this paper an expression for the spectrum of the scattered sound is derived for the very rough case in terms of specific surface‐wave parameters. This expression is then evaluated for several surface spectra, including the fully aroused Neuman–Pierson and Pierson–Moskowitz surface wave spectra. Finally, these results for special cases of the Neuman–Pierson spectra are compared with those obtained by numerically integrating the general form for the same spectra, a technique that does not involve the very rough case approximation.
Subject Classification: 30.40; 20.15.
59(1976); http://dx.doi.org/10.1121/1.380936View Description Hide Description
Results of a previous hydrodynamical study of a uniform, deep‐ocean flow are used to develop simple approximations to the sound‐speed and current distributions in the flow. The behavior of sound speed with depth, surface current, and source and receiver locations is examined. The effects of the flow on ray geometry, travel time, and spreading loss are investigated for a surfaced cw sound source and bottomed receiver. Total‐field amplitude and phase are determined and are found to be highly sensitive to surface‐current variations and to source and receiver locations. A simple method is presented for accurately estimating amplitude and phase. Then, an approximate phase formula is developed that is proportional to surface current, linear in source location, and sinusoidal in the orientation angle of the source–receiver range.
Subject Classification: 30.20; 28.60.
59(1976); http://dx.doi.org/10.1121/1.380945View Description Hide Description
A solution is given for the problem of the forced longitudinal vibration of an elastic circular rod, one end of which is attached to the surface of an elastic half‐space and to another end of which a periodic disturbing force is applied. Resonance curves for the motions of rods are derived using specific boundary conditions. Attention is directed to the effective damping of the motion of the rod due to dissipation of waves to infinity.
Subject Classification: 40.20; 20.22.
59(1976); http://dx.doi.org/10.1121/1.380946View Description Hide Description
Electroelastic equations containing terms up to cubic in the small mechanical displacement field, but no higher than linear in the electric variables, are applied in the analysis of nonlinear resonance in rotated Y‐cut quartz oscillators. Both pure thickness‐shear vibrators and essentially thickness‐shear trapped‐energy resonators are treated. This is a natural continuation of earlier work on intermodulation in the same resonators. Since in each equation each nonlinear term is negligible compared to an associated linear term, the solutions are obtained by employing an asymptotic iterative procedure and expanding in the eigensolutions of the associated linear problem and, in the vicinity of a resonance, retaining only that nonlinear term correcting the dominant eigensolution. Lumped parameter representations of the solutions, which are valid in the vicinity of a resonance and relate the amplitude of the dominant mode nonlinearly to the voltage across the crystal, are presented for both the pure thickness‐shear and trapped energy thickness‐shear problems. In each instance the expression for the current through the crystal is determined, the influence of the external circuitry is included in the analysis and, ultimately, an expression cubic in the mode amplitude and linear in the driving voltage is obtained. The analyses hold for the fundamental and odd overtone thickness‐shear modes. Nonlinear resonance curves are presented for AT‐cut quartz using the nonlinear coefficient γ determined in earlier work on intermodulation.
Subject Classification: 40.24, 40.30; 85.52.
Analysis of trapped‐energy resonators operating in overtones of coupled thickness‐shear and thickness‐twist59(1976); http://dx.doi.org/10.1121/1.380947View Description Hide Description
The equations of three‐dimensional linear piezoelectricity are applied in the analysis of trapped‐energy resonators with rectangular electrodes vibrating in coupled thickness shear and thickness twist in the vicinity of the fundmantal and odd overtone thickness‐shear frequencies. Closed form asymptotic expressions for the frequency wave‐number dispersion relations for the fundamental and odd overtone coupled thickness‐shear and thickness‐twist waves near cutoff are obtained for both the electroded and unelectroded regions of the trapped‐energy resonator. The influence of piezoelectric stiffening, electrode mass loading, and electrical shorting is included in the analysis. Simple approximate boundary conditions at a junction between an electroded and unelectroded region of the plate are obtained in a manner exhibiting the natural limitations inherent in the approximation. In order that these boundary conditions can be satisfied at each such junction, in the adjacent regions the wave numbers in the direction of the junction line are assumed to be the same. The boundary conditions to be satisfied at the junctions between the unelectroded corner region and the unelectroded regions adjacent to the electroded region are obtained from an extended version of the variational principle of linear piezoelectricity. These latter conditions result in the form of the solution in the corner region. One result of the foregoing analysis is the determination of a two‐dimensional condition which is a generalization of Bechmann’s number in one dimension. The above‐mentioned dispersion relations and edge conditions are applied in the analysis of the steady‐state vibrations of a trapped‐energy resonator and a lumped parameter representation of the admittance, which is valid in the vicinity of a resonance, is obtained.
Subject Classification: 40.24; 85.52, 85.32.
59(1976); http://dx.doi.org/10.1121/1.380948View Description Hide Description
The perceived pitch mixture of two tones of a dichotically presented chord was studied as a function of the difference between the intensities of the right and left ear tones (ΔI). Previous experiments have shown that, within a wide range of ΔI, the pitch mixture is independent of ΔI. This intensity independence of the pitch mixture of dichotic chords is not seen with monaural chords. Within the range of ΔI over which intensity independence is seen, the pitch mixture of the dichotic chord is determined by another property of the central pitch processor—the ear dominance function. In previous experiments the intensity independent function could only be detected in those subjects with a weak ear dominance function. In the present experiments subjects adjusted the relative intensities of the two tones of a binaural chord to match the pitch mixture of a dichotic chord. Using this method, the intensity independent function was measured directly in all subjects. In addition, the present method provides a direct measure of the magnitude of the suject’s ear dominance function and clarifies the relationship between the effects of the two functions.
Subject Classification: 65.75, 65.54, 65.62.
Mechanical impedance of human headbones (forehead and mastoid portion of the temporal bone) measured under ISO/IEC conditions59(1976); http://dx.doi.org/10.1121/1.380949View Description Hide Description
Mechanical impedances of the mastoid portion of the temporal bone and of the forehead are presented for 60 human subjects of both sexes and of ages between 9 and 71 years. Measurements were carried out using a plane circular surface of 1.75 cm2 and a static force of 5.4 N (ISO/IEC conditions). Impedance is found to vary with age and to a lesser extent with sex. Results are consistent with earlier measurements carried out under somewhat different conditions, but deviate rather substantially at most frequencies from the recommended ISO/IEC mechanical impedance for an artificial headbone. A study of the influence of variations in the mechanical headbone impedance upon bone vibrator performance by means of an analogous electrical network is reported.
Subject Classification: 65.64; 85.20.