Index of content:
Volume 71, Issue 2, February 1982

A method for analyzing wave propagation in random media
View Description Hide DescriptionA method for analyzing wave propagation in random media is proposed. The method, which is referred to as the quasi‐Rytov method, is similar to the Rytov method, but is shown to be more convenient for the calculation of statistics of the wave field. The main advantages of the quasi‐Rytov method, as compared to the ordinary Rytov method, are that it involves no heuristic assumptions and that it generally leads to simpler analytical expressions for field statistics.

Asymptotic analysis of the modes of wave propagation in a piezoelectric solid cylinder
View Description Hide DescriptionAn asymptotic method due to ’’Achenbach’’ is used to analyze the longitudinal and circumferential modes of wave propagation in a piezoelectricsolid circular cylinder of crystal class (6 mm) or ceramics (∞m). Information obtained in this method is useful for the frequency spectrum at long wavelengths. In this method the displacement components, electric potential, and the frequency are expressed as power series of the dimensionless wavenumber, ε = 2π× radius/wavelength. Substituting these expansions in the field equations and the boundary conditions, a system of coupled second‐order inhomogeneous ordinary differential equations with radial coordinate as the independent variable is obtained by collecting the terms of same order ε^{ m }. Integration of such systems of differential equations yields the various terms in the series expansions for the above modes and for the whole range of frequencies, when the real valued dimensionless wavenumber is less than unity (0<ε<1). To test the correctness of the present scheme, the roots of the exact frequency equation are computed and the results thus obtained are compared with the results obtained in the present analysis.

Scattering of transient elastic waves by an inhomogeneous obstacle: Contrast in volume density of mass
View Description Hide DescriptionA method is described to compute the scattering of transient elastic waves by arbitrarily shaped, three‐dimensional, inhomogeneous, penetrable objects of bounded extent that only differ from their surroundings in their volume density of mass. The problem is formulated in terms of a volume‐integral equation over the interior of the scatterer. This integral equation is solved numerically by the marching‐on‐in‐time method. Also, another numerical method to solve the integral equation by iteration is discussed. Comparison is made with analytical results for a spherical, homogeneous scatterer, while some numerical results for scatterers of different shapes are presented.

Elastic wave scattering from elliptical shells
View Description Hide DescriptionThe extended boundary condition approach to elastic wave scattering is reformulated for inclusions obeying thin shell theory. Results are presented for the scattering of plane p and s v waves from infinite cylinders of elliptical cross section for ratios of minor to major axis varying from 0.5 to 1.0 (circular). Calculations were made for cylinders of plastic and steel and for elastomers having three different shear moduli.

Resonance theory of the effective properties of perforated solids
View Description Hide DescriptionWe develop an analytic, unified, and systematic methodology based on scattering theory, for determining the dynamic (frequency‐dependent) effective properties of micro‐inhomogeneous (visco) elastic media, such as effective elastic moduli,wave speeds, and wave attenuations. The small inhomogeneities are modeled deterministically as fluid‐filled spherical cavities, and the Ament–Toksöz method for obtaining static effective properties is extended to the dynamic (resonant) case by retaining those higher‐order terms in a long wavelength expansion which give rise to the ultrasonic resonances of the microinhomogeneities. Rescattering from the inhomogeneities has been neglected, thus restricting the applicability of our results to the case of moderate inhomogeneity concentrations. The results of the present analysis are affected by the presence of shear waves in the solid matrix, and they contain all the findings of our previous dynamic resonance theory of gas bubbles in liquids, as well as nearly all the static results available in the earlier literature which do not take rescattering effects into account, as particular cases. We graphically display many numerical results for fluid‐filled cavities in rubber matrices.

Acoustic propagation in finite length elastic cylinders. Part I: Axisymmetric excitation
View Description Hide DescriptionThe acoustic propagation in a perfect finite length thin elastic cylinder is studied from an exact solution to the coupled elasto‐acoustic equations of motion. Eigenfunction expansions are obtained for Koiter’s consistent shell equations and the Helmholtz equation governing the acoustic field. The acoustic pressure is expressed as the sum of modal acoustic pressures each factored by a normalized influence coefficient related to the corresponding generalized coordinate in the elastic cylinder eigenfunction. A set of nonlinear homogeneous algebraic equations in the generalized coordinates are obtained when satisfying the coupled equations and the compatibility condition at the fluid–cylinder interface. The method when applied to a clamped cylinder filled with water and excited by a plane wave demonstrates the existence of narrow nonresonant peaks in maximum cylinder displacement and a frequency range where the average response rises considerably.

Acoustic propagation in finite length elastic cylinders. Part II: Asymmetric excitation
View Description Hide DescriptionThe propagation of acoustic waves in a perfect finite length elastic cylinder due to an asymmetric excitation is studied. The frequency response of the coupled system involves sharp resonant peaks lagging the rounded peaks at the empty cylinder resonances and nonresonant maxima often caused by modulated coincidence. The maximum acoustic pressure drops off as an empty cylinder resonance is crossed, then recovers gradually with decaying fluctuations as the frequency nears a higher empty cylinder resonance. Although a definite cutoff frequency exists when the boundaries are rigid, the effect is diffused due to the elasticity of the cylinder wall. Nonresonant peaks become more frequent for modes with a circumferential wavenumber that corresponds to the minimum resonance in the empty cylinder spectrum.

Field patterns of pulsed, focused, ultrasonic radiators in attenuating and nonattenuating media
View Description Hide DescriptionA theoretical method which can be used to calculate the pressure field patterns of pulsed, focused, ultrasonic radiators in attenuating and nonattenuating media is discussed in this paper. The underlying principle involved is the superposition of continuous wave beams to form pressure pulses. The method is adapted to the circumstances associated with using a hydrophone to measure field patterns. Experimentally obtained hydrophone signals are then compared to theoretical predictions. The field patterns of four transducer‐pulser combinations are investigated. A medium with tissue‐mimicking acoustical properties is used to attenuate the ultrasonic beam in these studies. The theory compares favorably with experiment whether an attenuating medium is present or not. However, the theory fails at positions very close to the transducer face (∠1 cm) and when significant nonlinear effects occur during the transmission of the pulse through the medium. This work may have significant applications in research devoted to designing ultrasonic transducers for particular studies, determining dose profiles of medical ultrasonic machines, and analyzing the ultrasonic signals backscattered from within patients.

Determination of the nonlinearity parameters for liquids using thermodynamic constants
View Description Hide DescriptionOn the basis of thermodynamic relations, the expression for the nonlinearity parameter B/A is obtained in the form of a polynomial in terms of the ratio of specific heats. The values of B/A for liquids are calculated by using the available thermodynamic data. In the case of 35%_{ o }seawater, comparison between our approach and the conventional one using the T and P coefficients of sound velocity is within 1.5%.

Anomalous infrasound generated by the Alaskan earthquake of 28 March 1964
View Description Hide DescriptionIn this paper we present and analyze data recorded at three microphone arrays (Boulder, Colorado; Boston, Massachusetts; and Washington, DC) associated with the Alaskan earthquake of 03 h 36 min 13 s UT, 28 March 1964 (61.05N, 147.50W). We show that the recordings from all three stations contain not only the epicentral and locally generated air waves reported by other authors, but also contain evidence of atmospheric radiation apparently generated from seismic surface waves along the Rocky Mountains. The latter became decoupled from the surface wave and traveled at about 314 m/s through the air to the arrays.

Ducted propagation of Concorde‐generated shock waves
View Description Hide DescriptionMeasurements with an array of low‐frequency microphones are compared to ray calculations, describing the long range propagation of acoustic energy from the shock cone of the Concorde SST. This energy is ducted between the surface and the strong soundvelocity gradient of the upper stratosphere. The measured pressure signatures are composed of one to five distinct wave groups arriving over a period of minutes; the number and sequence of arrivals is different for the Dulles‐bound and JFK‐bound airplanes. With respect to arrival time and azimuth of phase propagation, we find close correspondence between the highest amplitude wave groups and the refracted arrival predicted by ray calculations. Subsidiary wave groups apparently result from the diffracted ’’ground’’ wave and from volume scattering of acoustic energy into shadow zones.

Caustic corrections using coherence theory
View Description Hide DescriptionIn the vicinity of a caustic the intensity is very different from that calculated on the basis of geometrical acoustics. Using the basic formulation of coherence theory we show here how the correct intensity may be obtained when the source has a finite (i.e., nonzero) size. We use a two‐scale expansion to include the correction term to the geometric acoustic calculation (here already modified to include the effect of a finite source). It is shown that in the limit of a point source the results are the same as those previously obtained. Finally a numerical example is presented.

Analytical model of the truck tire vibration sound mechanism
View Description Hide DescriptionA theoretical model is developed to describe the sound radiation by the surface vibration of in‐service truck tires. The tire is modeled as an infinitely long incomplete circular cylindrical shell. The effects of inflation pressure and structural damping are included. The normal displacement, velocity, and acceleration resulting from a fluctuating load are determined using Flügge’s thin shell theory. Through numerical integration of the surface acoustic intensity, the radiated sound power is calculated as a function of damping, inflation pressure, and bending stiffness. Results indicate that the forced acoustic response is insensitive to small changes in the material loss factor and the bending stiffness. The inflation‐induced membrane stresses determine the acoustic response character to a large extent and total neglect of the bending stiffness does not seriously affect the calculated sound power. The basic sound radiation mechanism is shown to be the damped progressive wave field on the structure in the vicinity of the applied force. The results indicate that the potential sound reduction might best be approached through study of the tire loading and vibration response mechanisms.

Drive point impedance of an infinite orthotropic plate under tension
View Description Hide DescriptionIn this paper an expression is derived for the drive point impedance of an infinite plate under tension. It is shown that at high frequencies the bending behavior is dominant, and at low frequencies the membrane behavior is dominant. In general an orthotropic plate under tension behaves like a resistance and stiffness combined in parallel.

Longitudinal study of hearing in children II: Cross‐sectional studies of noise exposure as measured by dosimetry
View Description Hide DescriptionGeneral Radio and Metrosonics brand portable noise dosimeters were used to record daily average 24‐h log equivalent sound levels [L _{eq(24)}] in 127 children and youths aged 7.0 to 20.0 years (?±S.D. = 14.2±3.5 years). These children were a subset of those participating in a long‐term serial study of hearing in children at the Fels Research Institute. Seventy‐five children had multiple 24‐h recordings; 234 measurements were made in all. The mean L _{eq(24)} was substantial, between 76.7 and 83.8 dB and several children had levels dangerously high, above 90 dB. There were no significant age trends or racial differences for L _{eq(24)} and no significant differences in L _{eq(24)} occurred between tests recorded during the school year (September–May) and those recorded during the summer (June–August). There were, however, small, but significant sex differences; boys had a mean L _{eq(24)} about 2 dB higher than girls. Hearing threshold levels were positively correlated with L _{eq(24)} in girls, but a similar trend was not present in boys. The mean L _{eq(24)} (±1 S.D.) for data collected with Metrosonics dosimeters was 76.7±5.7 dB (n = 58) and 83.8±5.1 (n = 109) for data collected with the General Radio dosimeters. These significantly different means may be explained by the properties of the two dosimeter types arising from differences in the design philosophy of the instruments. These design differences result in systematic measurement errors in the two dosimeter types; the GR dosimeters systematically overestimate actual noise in certain situations while Metrosonics dosimeters underestimate it in different situations. While there are differences between the instruments as to how noise is measured, the data from either instrument provide a reasonable estimate of noise exposure in children, data that are not otherwise available. Furthermore, they provide strong evidence that the noise exposure in children is substantial.

Sampling rate reduction in multichannel processing of bandpass signals
View Description Hide DescriptionThe uniform sampling rate required to reconstruct a deterministic bandpass signal x(t) having spectrum confined to I _{1}∪I _{2}, where I _{1} = [−ω_{0}−σ/2, −ω_{0}+σ/2), I _{2} = [ω_{0}−σ/2, ω_{0}+σ/2) with ω_{0}?σ/2≳0 depends critically on the positioning of the band and varies from σ/π to 2σ/π samples per second, the minimum rate of σ/π being attained if and only if ω_{0}+σ/2 is an integer multiple of σ. If the bandpass signal x is now used as a common input to an e v e n number m of linear time‐invariant filters to produce m outputs z _{1}(t),...,z _{ m }(t), then it is proved that, under a certain ’’independence’’ requirement on the filters (a matrix function condition), the input x may be reconstructed from samples of the outputs {z _{ k }(t)}, each output being sampled at the uniform rate of σ/mπ samples/second, or (1/m)th the m i n i m u m sampling rate associated with the input. The dependence on band position is removed by a partitioning of the set I _{1}∪I _{2} into m disjoint subsets J _{1},...,J _{ m } of equal length and a subsequent mapping procedure which allows J _{1} to be mapped (discontinuously) in a one‐to‐one manner onto J _{ k } for 1?k?m. As an example, it is shown that samples of the bandpass signal x and its first derivative x′, taken at the common rate of σ/2π samples per second (m = 2), suffice to determine x completely, a generalization of an early theorem due to Fogel [IRE Trans. Inf. Theory, IT‐1, 47–48 (1955)].

Robust adaptive array antennas
View Description Hide DescriptionIn this paper we present a new type of adaptive array antenna. The array optimizes well‐known cost functionals such as mean‐square error or output power, subject to strict inequality constraints on any part; or all the antenna pattern shape, e.g., controlling side‐lobe levels, null placement, directional control, etc. Moreover, the adaptive algorithm determines array gains which are ’’robust’’ in the sense that the antenna pattern will satisfy the pattern shape constraints even if the array weights are implemented with error, as might occur with digitally controlled weights, for example. The antenna pattern also exhibits a robustness property against wavefront distortion, mutual coupling uncertainties, and array geometry errors. Finally, by appropriate choice of constraints the array can have a broadband capability.

Quadrature receivers connected in parallel to improve detection performance in a multipath environment
View Description Hide DescriptionIn active sonar applications, a quadrature receiver is a conventional processor used to detect sinusoidal signals reflected from an underwater object. In an adverse underwater environment, the incoherent combination of multipath returns reduces the coherence of the received signal when the transmit pulse is a cw pulse with a time duration long enough to produce overlapping returns (i.e., nonresolvable multipath). This causes a degradation in the receiver’s performance. For this analysis, the received signal model is assumed to be piecewise constant with Rayleigh amplitude fluctuations and uniform phase fluctuations. The background noise is white Gaussian with zero mean. In this paper, the probability of detection formulas along with the corresponding receiver operating characteristic curves are derived for a parallel quadrature receiver structure where the integration times of the component receivers correspond to successive coherence intervals within the signal duration. For tractability, the signal duration is divided into two equal time intervals with signal correlation characteristics between intervals specified by the correlation coefficient, ρ. The results are compared with a single quadrature receiver structure where the integration is performed once over the signal duration. The performance curves of the two receivers are compared for ρ = 0 and ρ = 1. The results demonstrate that when the two signal parts are not correlated (ρ = 0), the parallel quadrature receiver structure provides a substantial improvement in detection performance; however, when the two signal parts are completely correlated (i.e., coherent signal), this receiver suffers only a slight loss in performance compared with the conventional quadrature receiver.

Side‐lobe behavior of conformal arrays
View Description Hide DescriptionThe side‐lobe pattern of an array that is generated by projecting the elements of a conformal array onto a plane is shown to be generally lower in level than the expected value of the side‐lobe pattern of the original conformal array. It is shown that the discrepancy between the two patterns increases with the angle from the main response axis for all side lobes of the planar array that are lower than a particular value. This is taken as a demonstration that, in this sense, the side‐lobe behavior of conformal arrays is expected to be inferior to that of planar arrays.

Detection threshold microstructure and its effect on temporal integration data
View Description Hide DescriptionAuditory detection thresholds were measured at several preselected frequencies using an adaptive 2IFC procedure. Results confirm the existence of shifts in detection threshold ranging from 2 to 14 dB with quite small changes in signal frequency. There does not appear to be a uniform pattern associated with the microstructure of the detection threshold curve. An additional experiment was performed to determine the effect of signal duration on detection threshold microstructure. Results indicate that the temporal integration function is considerably steeper for more sensitive frequencies (3.7 dB/doubling of duration), than for less sensitive frequencies (1.7 dB/doubling). This probably is not due to differences in processing as much as it is to the effect of the energy spread associated with decreasing signal duration.