Index of content:
Volume 62, Issue 1, July 1977

Waves in thin‐walled, nonuniform, perfectly elastic tubes containing incompressible inviscid fluid
View Description Hide DescriptionWave propagation in a semi‐infinite, nonuniform, elastic thin‐walled tube filled with incompressible, inviscid fluid is considered. A one‐dimensional problem, with the tube and fluid initially at rest and a pressure disturbance applied at the end, is solved for different axial variations of the tube properties. Formal asymptotic techniques are applied to the linearized partial differential equation governing the pressure and simple progressing wave and high‐frequency solutions are obtained for Heaviside and oscillatory‐pressure boundary conditions, respectively. These asymptotic series solutions terminate for certain parameter variations to give exact solutions for the pressure. Numerical results are presented and some interesting observations concerning the accuracy of the formal results are made.

Acoustic coupling between two finite‐sized spherical sources
View Description Hide DescriptionThe problem of acoustic radiation from a pair of spherical sources vibrating with time‐harmonic velocity distributions which are constant in strength and axisymmetric about the same axis is considered. In particular, the modification of the radiation load on one source due to the presence of the other is evaluated. Numerical results are presented for the four cases of equisize sources which are either in phase or 180° out of phase from one another and vibrating in either the pulsating (monopole) or oscillating (dipole) modes. For sources which are small relative to the wavelength, the results are essentially as predicted by previous analyses of point sources, with the exception of the in‐phase dipoles where, for small wavelength separations between the sources, the radiation resistance of one dipole is not doubled by the presence of the other. As the wavelength size of a source is increased, the near presence of another source affects the reactive component of the radiation loading more than the resistive component.

Stable arrays of resonant bubbles in a 1‐MHz standing‐wave acoustic field
View Description Hide DescriptionAs observed microscopically, bubbles in a standing‐wave acoustic field move to the pressure nulls and oscillate, in elliptical orbits, about a common axis. The orbits of individual bubbles are equally spaced about 100 μm apart along the axis, forming a linear array. These arrays form in tap water for peak pressure amplitudes of 10–20 bar, but persist at levels as low as 1.5 bar. The 7‐μm diameter of the bubbles is approximately the theoretical size for resonant air bubbles in water driven at the 986 kHz frequency of the field. The radius of the orbits is approximately inversely proportional to the pressure gradient at the pressure null, with proportionality constant 0.25 bar. In a simplified model of the orbit phenomenon the expected proportionality constant is given by (2)^{1/2} p _{ s }, where p _{ s } is the threshold pressure amplitude for rectified diffusion and has the value 0.18 bar. Calculations of p _{ s }, based on current theories for rectified diffusion, are in substantial agreement with the this value. The period of the orbital motion is about 1 msec for an orbit radius B of 35 μm, and increases to about 6.5 msec for B=100 μm. Two adjacent bubbles are synchronized in their orbits approximately 90° out of phase, as required for stability of the arrays under Bjerknes forces.

Measurements of the acoustic radiation pressure on a sphere in a standing wave field
View Description Hide DescriptionThe force on a small sphere due to radiation pressure in a plane wave field was measured and was found to be in excellent quantitative agreement with L. V. King’s predictions [Proc. R. Soc. London Ser. A 147, 212 (1934)]. Reynolds numbers as high as 2500 were used.

Nonlinear mode coupling of elastic waves
View Description Hide DescriptionThe theory of nonlinear elasticity is applied to a study of mode coupling of elastic waves at a particular frequency, called the critical frequency, in a long circular wire. It is assumed that the wire is of homogeneous isotropic elasticmaterial and that the nonlinearity of medium (the effects of higher‐order elasticity) is primary rather than that involved in the Lagrangianstress and straintensors. The latter is suggested from the fact that the third‐order elastic constants are of larger order of magnitude than the Lamé constants. The method of multiple scales is employed to obtain a system of equations which describes the behavior of the amplitudes involved in the mode coupling. The analysis of the equations shows that nonlinear mode coupling can occur at the critical frequency and that, except at this frequency, the wave undergoes only a phase shift. Further, progressive wave solutions show that the two wave amplitudes can be expressed in terms of Jacobian elliptic functions, and energy exchange between two modes takes place. Under special conditions, these periodic solutions degenerate to the solitary or shocklike solutions.

Harmonic generation of longitudinal elastic waves
View Description Hide DescriptionThe propagation of the fundamental and harmonically generated longitudinal elastic waves is treated by means of an asymptotic iterative procedure directly in the governing nonlinear differential equation. Explicit results are obtained for the steady‐state, spatial growth of the second and third harmonic and the depletion of the input wave. As expected, the analysis indicates that the amplitude of the Nth harmonic depends on all the elastic constants up to order N+1. However, the forms for the amplitudes obtained in the asymptotic solution reveal that, for the known range of ratios of elastic constants of successively increasing order and propagation distances commonly encountered in harmonic generation experiments, only the quadratic nonlinearity, which depends on the second‐ and third‐order elastic constants, is required to accurately account for the experimental results. In addition, the amplitude dependence of the phase velocity of the fundamental longitudinal wave is determined.

Numerical technique for computing the wide‐angle acoustic field in an ocean with range‐dependent velocity profiles
View Description Hide DescriptionA numerical technique for the propagation of sound in the ocean where velocity is a function of both range and depth has been developed. The technique is not restricted to the narrow‐angle (parabolic) approximation and it reduces to an exact solution for a homogeneous media. The given field is transformed into a sum of plane waves via an FFT. This transformed field is propagated without approximation through a homogeneous space represented by an average wave number for that space. Updating the average wave number provides for Snell’s law bending in range. The variations from the average velocity are accounted for by summing deviations from the nominal phase to develop a group of direction‐sensitive phase correction masks. A weighted group of plane waves centered about each direction are inverse transformed for multiplication by the phase mask with the results summed. The choice of overlapping weights in the transformed space provides an approximate continuous phase correction mask for all directions. The functional relationship of range‐step size to frequency, angular spectrum, and velocity profiles are developed. Several results for a 1500‐m channel are shown.

Backscattering spectra of preserved zooplankton
View Description Hide DescriptionMeasuredbackscattering spectra for preserved specimens of three zooplankters (copepod, euphausiid, sergestid shrimp) are compared to fluid sphere scattering models. Quantitative agreement is found at low k a for all species, however the copepod results are increasingly higher than predicted for k a≳1 and the euphausiid and sergestid shirmp are found to be directional scatterers. A fluid prolate spheroid model is proposed fo the latter species.

Combined influence of spatially uniform currents and tidally varying sound speed on acoustic propogation in the deep ocean
View Description Hide DescriptionThe effects of a combination of sound‐speed and current fluctuations on propagation of a cw signal in a deep‐ocean model are analyzed. The mean sound‐speed structure is assumed bilinear, and the channel boundaries are horizontal. The horizontally independent sound speed oscillates with a 12‐h period, while the spatially uniform currents consist of quasisteady and diurnally varying components. The total acoustic field for surface‐reflected–bottom‐reflected rays is investigated for dependence on time, source‐receiver separation, and environmental parameters. Multipath propagation is demonstrated for larger propagation ranges, for which case the number, depths, and occurrence times of amplitude fades are shown to be very sensitive to parameter changes. Where the total field is dominated by one ray, contributions from combined sound‐speed and current fluctuations to phase are investigated. In both cases, phase generally can be influenced by both sound‐speed and current fluctuations, but the former more effectively influence amplitude.

Statistical analysis of ambient noise
View Description Hide DescriptionThis paper presents an approach to the characterization of the low‐frequency ambient‐noise continuum. A tutorial presentation of several statistical tests is given, followed by the application of these tests to the characterization of narrow‐band low‐frequency ambient noise as a function of space, time, and frequency. Measurements of temporal stationarity, spatial homogeneity, and frequency homogeneity are presented.

Acoustic radiation from point excited rib‐reinforced plate
View Description Hide DescriptionAn analytic solution for the acoustic radiation from a rib‐reinforced infinite elastic plate which is excited by a point force located on the rib was obtained. The solution exhibits a new coincidence angle, where the radiated pressure peaks, which depends on the relative stiffness and mass of the attached beam. An expression for the radiated power was also obtained which shows the general reduction of radiated power explicitly as a function of the mass and stiffness of the attached beam. Approximate formulas for the complex interaction between the beam and the plate were developed for frequencies above and below the coincidence frequency. Approximate expressions for the radiated power were obtained from simplified physical models.

Estimation of background ambient noise levels from the spectral analysis of time series with application to cw propagation‐loss measurements
View Description Hide DescriptionAn application of percentile measurements is presented as a method for estimating background ambient noise levels from spectral density functions. The advantage of a percentile method over an average method is that it allows an accurate measure of background noise containing a sine wave, that is essentially independent of the sine‐wave amplitude. This feature makes the percentile method very useful in the measurement of cw propagation loss, where it is frequently necessary to subtract an estimate of the background noise from a signal‐plus‐noise measurement, including the case when the noise contains sine waves close in frequency to the cw signal. A percentile‐level estimate may be easily used to calculate an average level estimate for chi‐square data and it is found that a percentile estimator is just as accurate and essentially just as stable as an average estimator. Theory based on chi‐square statistics and experimental data from the ambient sound field in the deep ocean are shown to be in good agreement.

Low‐frequency technique for the underwater calibration of individual elements of a line hydrophone array
View Description Hide DescriptionA calibrator for use with long line hydrophones (seismic streamers) has been designed, constructed, and tested. Comparison calibrations may be obtained for individual elements or small groups of interconnected elements of a line hydrophone array in the frequency range of 20 to 3000 Hz. Absolute calibrations may be obtained in the frequency range of 20 to 100 Hz. The calibrator may be operated in either of two configurations. The first configuration has the calibrator submerged in a water trough. In the second configuration the calibrator, with the hydrophone inserted, forms a closed chamber through which water is continuously circulated during operation. A comparison between results obtained by using the calibrator, and independent measurements is presented. The theory of operation of the device, and of the sonic resistors used to reduce standing waves within the calibrator, is presented in the appendixes.

New ultrasonic imaging system using a moving random phase mask and a stationary‐point receiver
View Description Hide DescriptionA new ultrasonic imaging system and apparatus are proposed which use a moving random phase mask placed just behind a coherently illuminated object, and a stationary‐point receiver located in the farfield. The power spectrum of the received signal represents the shadow of an object on the receiver plane and hence gives the image of the object under suitable conditions. The second‐order correlation function of the received signal gives the exact image of the object provided a reference‐point source is located nearby. The system constructed includes a minicomputer for signal processing and real‐time imaging. Experimental results for one‐dimensional objects are presented. It is also demonstrated experimentally that the system has advantages over conventional coherent ultrasonic imaging systems when propagating through a turbulent medium.

Ultrasonic spectrum analysis for nondestructive testing of layered composite materials
View Description Hide DescriptionIn this paper, a simple model is presented which predicts the ultrasonic frequency spectra for a broad class of layered composite materials having a finite number of laminas. This model predicts spectra for arrays of glass plates in water and these spectra are experimentally verified. Precisely regular spectra are predicted for single plates, while irregular spectra are predicted for all of the arrays studied. Results relating to nondestructive testing which have emerged from this investigation include methods for predicting spectra for layered composite materials and techniques for mapping small changes in the modulus and thickness of composite materials. Also discussed is the existence of forbidden frequency bands for which ultrasound transmission is strongly attenuated in thick layered composites.

Shallow surface‐wave simulator for the study of jet‐noise sources
View Description Hide DescriptionA shallow liquid surface‐wave analogy to turbulence‐induced sound was utilized to investigate the mechanisms of noise generation and propagation in jets.Theoreticalanalysis was used to determine the wave‐power dependence on Mach number and to derive the relationship between wave and turbulence spectra. The experimental investigation utilized a 24 ft^{2}mercury ripple tank. The waves were produced by the turbulence in a mercury jet exhausting into the tank. The results substantiate the validity of the surface‐wave analogy as a jet‐noise simulator. Measurement of mean and turbulent velocity profiles proved that the jet development was similar to the theoretical plane‐free jet. Farfield measurements of wave power, directivity, and spectra compared favorably with the acoustic case. However, the wave spectra showed little of the higher‐frequency content found with the turbulence spectra. This difference was attributed to the vertical spatial integration of the turbulence‐source terms, which is not found in jet noise.

Maximum‐likelihood estimation of source parameters from time‐sampled outputs of a linear array
View Description Hide DescriptionThis paper considers the joint estimation of the bearing and strength parameters of a noise source, by a uniformly spaced array of sensors in the presence of self‐noise, assumed to be independent between any pair of sensors. Contrary to the analogue systems of processing (i.e., correlation and beamforming), the present scheme, which is based on the maximum‐likelihood (ML) principle, operates on a set of time samples representing the bandlimited output of the array’s elements. The system, as a result, does not require the assumption of long observation time normally used in other schemes and is easily implemented on a digital computer. The resulting ML estimator is not in theory a sufficient one. Nevertheless, when the estimator’s variance is compared with the Cramer–Rao lower bound, the estimator virtually attains its asymptotic sufficiency as the number of array elements exceeds a ’’threshold’’ which is a decreasing function of the signal‐to‐noise ratio (SNR) and the length of the observation time. Except when the SNR is very poor and the observation time is quite short, the ’’threshold’’ is found to be surprisingly small. It is also demonstrated, at least when the error in the bearing estimate is small, that the ML estimator is unbiased.

Frequency selectivity of single auditory‐nerve fibers in response to broadband noise stimuli
View Description Hide DescriptionThe tuning of single auditory nerve fibers in the rat in response to broadband noise was studied in a large sound intensity range. Pseudorandom noise was used as stimuli and the cross spectrum between a period histogram of the noise and a period of the noise was used as an approximation of the transfer function from sound to the modulation of the neural discharge rate. In units with a CF higher than 1000 Hz, the width of the cross spectra (at 10‐dB points) invariably increased as the stimulus intensity increased and the center frequency decreased. The few units studied with CF below 1000 Hz seemed to undergo somewhat less of a change in width. The cross correlograms of all fibers with a characteristic frequency (CF) below 5 kHz showed a damped oscillation the duration of which decreased as stimulus intensity was increased. The similarity between the nonlinearity shown here and that shown in measurements of basilar membrane motion using the Mössbauer effect is discussed.

Postnatal development in the acoustic system of the house mouse in the light of developing masked thresholds
View Description Hide DescriptionPostnatal development of masked auditory thresholds in the house mouse M u s m u s c u l u s were behaviorally measured from the 10th to the 24th day. An unconditioned stop reflex and an unconditioned pinna reflex to tones were used for threshold determinations. Masked threshold levels first decrease from day 10 to day 12, then increase or remain constant until day 14, and finally decrease until day 16–18, where the adult levels are reached. The results are in agreement with anatomical and electrophysiological data in the literature. It was concluded that in the developing acoustical system of the mouse two effects superimpose: peripheral completion and central maturation. The data can be interpreted such that the peripheral development which lasts until day 14 dominates between the 12th and 14th postnatal day, whereas development in the central nervous system influences thresholds between day 10 and day 16–18. The widths of critical masking bands are assumed to be constant during development and determined by peripheral mechanisms.

Psychophysical structure of eight complex underwater sounds
View Description Hide DescriptionThe potential usefulness of multidimensional scaling techniques in the perceptual analysis of ’’real world’’ underwater sounds was demonstrated. Nineteen observers (nine with musical training, ten without) used a five‐point scale to judge the similarity of all possible pairs of eight passive sonar recordings. The eight s signals were selected to represent a range of common natural and man‐made underwater sounds. These data were analyzed using the INDSCAL multidimensonal scaling model, revealing an interpretable two‐dimensional psychological space. One of the psychological dimensions was interpreted as reflecting the overall shape of the 1/3‐octave spectra of the eight signals, while the second was seen to reflect the prominence of a low‐frequency periodicity present in some signals. Individual observer analysis revealed substantial differences between the musically trained and musically inexperienced observers in the relative importance or salience of the two dimensions. The relation of these findings to earlier work was discussed.