Volume 83, Issue 2, February 1988
Index of content:
83(1988); http://dx.doi.org/10.1121/1.396191View Description Hide Description
The objective of this paper is to highlight gaps of information regarding mechanisms of vascular, neurological, and musculo‐skeletal damage caused by vibration. Also addressed is evidence that high noise level may act synergistically to the development of vibration syndrome of the hand and arm. Areas of research currently active in psychophysical and neurophysiological investigations to increase our understanding of tactile and spatial discrimination are discussed. Although the importance of sensory loss or ‘‘fine touch’’ is understood, there is neither a proven objective scientific test with which the syndrome can be diagnosed nor is there a scale of damage assessment. Determining the exact role of the central nervous system in assessing damage from vibration is difficult in view of nonspecific symptoms reported from eastern Europe and from Japan. To complicate matters still further, there is the possibility that repeated, rapid mechanical movements of the hand and arm associated with handling heavy tools produce carpal tunnel syndrome but that the injury is not directly attributed to vibration. Therefore, it follows that there could exist an element of carpal tunnel syndrome in many vibration syndrome cases.
83(1988); http://dx.doi.org/10.1121/1.396543View Description Hide Description
A flexible membrane backed by a rigid cavity is set into an infinite plane baffle. The upper half‐space contains an acoustic fluid, and the cavity which lies in the lower half‐space, contains another acoustic fluid. A time harmonic wave in the upper half‐space is incident on the plane. When the frequency of the incident wave is bounded away from the resonant (natural) frequencies of the membrane, and of the acoustic fluid in the cavity, the reaction of the fluid on the cavity‐backed membrane (CBM) is small. However, near a resonant frequency, the fluid–CBM coupling is significant. The method of matched asymptotic expansions is employed to obtain an asymptotic expansion of the scattered field as ε→0 that is uniformly valid in the frequency of the incident wave. Here, ε≪1 is the ratio of the upper half‐space fluid and membrane densities. Simple and double resonant frequencies are analyzed; but the method is applicable to higher‐order resonant frequencies. The method is applied to the normal incidence of a plane wave on a baffled circular membrane that is backed by a circular cylindrical cavity. It is found that the CBM is a more ‘‘susceptible’’ scatterer than the vacuum‐backed membrane (VBM). In addition, the signature of the CBM differs from the signature of the VBM. For example, the scattered amplitude for the CBM has peaks with bandwidths of O(ε2), in addition to the peaks with bandwidths of O(ε) corresponding to the membrane resonant frequencies. Moreover, the CBM can have resonant ‘‘packets’’ that are of total bandwidth (ε)1/2.
83(1988); http://dx.doi.org/10.1121/1.396192View Description Hide Description
A flexible membrane backed by a rigid cavity is set into an infinite plane baffle. The membrane lies in the plane, and the cavity is in the lower half‐space. The upper half‐space contains a homogeneous acoustic fluid. The cavity is filled with another homogeneous acoustic fluid. A pulse, which satisfies the acoustic waveequation in the upper half‐space, is incident on this baffled membrane. Asymptotic expansions as ε→0 that are uniformly valid in t are obtained for the membrane’s motion and the scattered and cavity acoustic fields. Here, ε≪1 is the ratio of the density of the fluid in the upper half‐space to the membrane’s density. If the bandwidth of the pulse’s spectrum is sufficiently narrow, so that it is free of any of the resonant (natural) frequencies of the membrane or of the cavity, then the pulse is essentially reflected as though the baffled, cavity‐backed membrane is rigid. However, if the pulse’s spectrum is sufficiently broad, so that it contains cavity and membrane resonant frequencies, an additional scattered field is produced by its interaction with the membrane’s motion and the acoustic field inside the cavity. This scattered field insonifies distant observation points after the rigidly reflected pulse arrives. It is a complicated sum of slightly damped and oscillating outgoing spherical waves. The damping occurs on the two time scales εt and ε2 t. Some of these damped spherical waves are perturbations, due to the cavity fluid, of the ‘‘decayed ringing’’ of the vacuum‐backed, baffled membrane. Application is given to the circular membrane that is backed by a cylindrical cavity, of the same radius as the membrane, and insonified by the normally incident, plane, spiked pulse. Graphs of the membranes motion are presented.
83(1988); http://dx.doi.org/10.1121/1.396193View Description Hide Description
The properties of the renormalized speed of sound and of the scattering and transport mean‐free paths in two‐ and three‐dimensional media containing random distributions of identical, finite‐size scattering centers are analyzed. In particular, the connections between the frequency dependence of these parameters and the structure of the exact single‐scatterer cross section are investigated. Since a careful evaluation of the mean‐free paths is necessary for the accurate prediction of localization phenomena, the implications of the results to the localization of acoustic excitations are discussed in detail.
83(1988); http://dx.doi.org/10.1121/1.396138View Description Hide Description
The measurement of attenuation is performed by directly determining the attenuation operator (or the impulse response of the medium) in the time domain. In this way, it is possible to separate the attenuation operator from other nonattenuation effects, e.g., reflections. The Wiener filtering technique, or the damped least squares, is used to calculate the attenuation operator. For the damped least squares, we have corrected for the effect due to the addition of the damping constant using a perturbation method. Numerical tests are carried out to illustrate the technique. The geometric beam spreading of ultrasonic waves generated by a source of finite size can strongly affect the result of attenuationmeasurements. Corrections are made by equating the received signal to the average pressure over the receiver surface. The technique is used to measureultrasonic attenuation in water, glycerol, and mud. The measurement in water offers a test of the corrections made for the geometric beam spreading. The measurement in glycerol and mud shows that, in the frequency range of 0.2–1.5 MHz, the attenuation of glycerol increases rapidly with frequency, whereas the attenuation of mud is proportional to frequency, exhibiting a constant Q behavior. The measurements show that the technique used here is an effective approach to the measurement of attenuation.
83(1988); http://dx.doi.org/10.1121/1.396139View Description Hide Description
In order to investigate the effect of borehole fluid viscosity on the attenuation and dispersion of the guided waves present in full waveform acoustic logs, the problem of wave propagation in a borehole containing a viscoelastic fluid surrounded by an infinite elastic formation is solved using boundary layer theory. The results indicate that the losses due to viscous drag along the borehole wall are a small component of the overall guided waveattenuation for the frequencies of interest in full waveform acoustic logging (2–15 kHz) and for reasonable viscosity values (1–1000 cP). These losses, however, can be significant at low frequencies. In addition, the variations in viscosity have a negligible effect on the guided wave dispersion for this range of frequency and viscosity. These findings indicate that friction between grains in fluid suspension may be the dominant attenuation mechanism in the drilling fluids present in boreholes.
Transient and harmonic fluid loading on vibrating plates in a uniform flow field via a wave‐vector/time domain method83(1988); http://dx.doi.org/10.1121/1.396141View Description Hide Description
A new approach is presented to evaluate the fluid loading on vibrating elastic vibrators with specified time‐dependent velocities in uniform flows. An i n v a c u o eigenfunction expansion with time‐dependent coefficients is used to describe the specified normal velocity of the plate. Acoustic fluid loading on the plate is expressed as an eigenfunction expansion in which each modal coefficient is expressed as a summation of convolution integrals involving fluid/modal impulse responses and the modal velocity coefficients. Wave‐vector/time domain methods are used to develop expressions for the fluid modal impulse responses. Numerical results are presented to illustrate the characteristics of the fluid/modal impulse responses and fluid loading for various modes of simply supported plates and Mach numbers.
83(1988); http://dx.doi.org/10.1121/1.396142View Description Hide Description
It is shown that the generalized Hooke’s law—the constitutive relation for all solid materials that behave mechanically in a linear fashion—defines the topology of equivalent networks analogous to such solids insofar as mechanical behavior is concerned. Two equivalent networks are reported, one representing each of the two forms in which Hooke’s law is usually expressed. Each analog is a six‐port network that can be decomposed into a pair of independent three‐port networks. One three‐port network in each pair reflects the extensional behavior of a material and one its distortional behavior. Elastic moduli and compliances appear as immittances in the networks. Since network topology is determined only by the analytic form of Hooke’s law and by the symmetry intrinsic in the material considered, such immittances can be mathematical entities more general than complex quantities. Some results from linear elasticity theory are interpreted using the analog networks, and their application in describing the viscoelastic behavior of materials is considered briefly. The analysis pertains principally to homogeneous isotropic materials.
83(1988); http://dx.doi.org/10.1121/1.396143View Description Hide Description
This article is a theoretical study of the nonlinear interaction between two sound beams in a lossless fluid, intersecting each other at arbitrary angles. The governing equation for the sum and difference frequency components is solved in the quasilinear approximation for prescribed conditions on the sources of the two beams. A solution that is uniformly valid in space is obtained in the form of a Fourier integral. Asymptotic evaluations at large distance from the sources lead to simple formulas that relate the amplitude and phase of the generated sound to the on‐source conditions. Diffraction effects are fully accounted for, and shown to be important even at large distances. Relevance to earlier literature on the scattering of sound by sound is discussed.
83(1988); http://dx.doi.org/10.1121/1.396144View Description Hide Description
Levitation of large dense samples (e.g., 1‐cm diameter steel balls) has been performed in a 1‐g environment. A siren was used to study the effects of reflector geometry and variable‐frequency operation in order to attain stable acoustic positioning. The harmonic content and spatial distribution of the acoustic field have been investigated. The best stability was obtained with an open reflector system, using a flat lower reflector and a slightly concave upper reflector while operating at a frequency slightly below resonance.
83(1988); http://dx.doi.org/10.1121/1.396145View Description Hide Description
The standard approach to the analysis of the pulsations of a driven gas bubble is to assume that the pressure within the bubble follows a polytropic relation of the form p=p 0(R 0/R)3κ, where p is the pressure within the bubble, R is the radius, κ is the polytropic exponent, and the subscript zero indicates equilibrium values. For nonlinear oscillations of the gas bubble, however, this approximation has several limitations and needs to be reconsidered. A new formulation of the dynamics of bubble oscillations is presented in which the internal pressure is obtained numerically and the polytropic approximation is no longer required. Several comparisons are given of the two formulations, which describe in some detail the limitations of the polytropic approximation.
83(1988); http://dx.doi.org/10.1121/1.396146View Description Hide Description
The results of acoustical and optical experiments in which ‘‘moderately’’ underexpanded sonic round jets impinge on flat plates normal to the jet axis are presented and analyzed. Periodic unstable oscillations of the jet flow, with the resultant radiation of sound of discrete frequencies, occur over a wide variation of control parameters, namely, pressure ratio, plate size, and spacing of the plate from the jet nozzle. For ‘‘small’’ plates, the principal oscillations with λ/D about 4 (λ=acoustic wavelength, D=nozzle diameter) occur when the standoff shock wave lies in a pressure recovery region of the periodic cellular structure of the choked jet and is, therefore, highly unstable; then the oscillations have key characteristics in common with the high‐harmonic excitation of Hartmann’s acoustic air‐jet generator. An analogous feedback mechanism in the standoff zone is suggested in which pressurewaves reflected from the plate trigger the motion of the unstable shock wave. For ‘‘large’’ plates, acoustic feedback to the nozzle occurs, and the principal tones have λ/D about 2 with frequencies nearly independent of pressure ratio (velocity) and plate size. They exhibit the sawtooth characteristic familiar in similar situations (edge tone, hole tone, and for subsonic jets interacting with flat plates), there being at least seven stages, frequently with frequency jumps between them.
A feedback mechanism is suggested, and a formula for the frequency of oscillation is derived, the form of which is consistent with experimental data. Secondary tones also occur, at least some of those of higher frequency (λ/D≊1) appearing to be extensions of the large‐plate principal tones, but those of lower frequency, while of the precisely same character, presumably are from a differing instability mode. The characteristics of these principal and secondary tones provide the means of analysis of the limited existing pertinent literature. Several sets of data can be classified into the small‐ and large‐plate classes for ‘‘moderate’’ and ‘‘high’’ degrees of underexpansion. For ‘‘very highly’’ underexpanded jets, the mechanism for small and large plates appears to merge, and, correspondingly, there is no longer the distinction between the phenomena for small and large plates as pertains at lower pressure ratios.
83(1988); http://dx.doi.org/10.1121/1.396147View Description Hide Description
Projectiles containing axisymmetric ring cavities constitute aeroacoustic sources. These produce high‐intensity tones that are used for coding in the simulation of area weapons effects (SAWE) system. Experimental data obtained in a free‐jet facility are presented describing the effects of yaw, spin, and geometric projectile parameters on sound pressure and drag. In general, the sound pressure decreases with increasing yaw angle whereas the drag increases. Spin tends to increase sound‐pressure levels because of a reduction in asymmetry of flow. Drag increases at zero yaw approximately as the 2.5 power of sound wavelength. Drag increase appears to be due to energy loss by sound radiation at low wavelengths and due to wake modification at large wavelengths.
83(1988); http://dx.doi.org/10.1121/1.396148View Description Hide Description
It is shown that data on wind noise in spherical and cylindrical windscreens may be represented by a single universal curve if the data are plotted in nondimensional form. Appropriate dimensionless variables are a dimensionless frequency ( f D/V) plotted against a sound pressure coefficient (p̃1 / 3/ρV 2) or a dimensionless spectral density f S/ρ2 V 4), where f is frequency, D is screen diameter, V is wind speed, p̃1 / 3 is sound pressure of the wind noise in a 1/3‐octave band, ρ is fluid density, and S is spectral density of the wind noise at frequency f. Data obtained from various disparate sources form a single curve with surprisingly small scatter for values of dimensionless frequency ( f D/V) up to 5.
83(1988); http://dx.doi.org/10.1121/1.396149View Description Hide Description
Various modes of sea ice motion in the Beaufort Sea are correlated with under‐ice noise at 10, 32, and 1000 Hz. Seasonal variations are considered, and a parameterization of ice microfracturing caused by sensible heat flux is included in the correlations. During the summer, the correlations indicate that all frequencies are primarily a response to the ice rushing through the water. During the fall, 10‐ and 32‐Hz noise correlate best with a linear combination of the speed of the ice parcel plus the total rate of change in the shape of the ice parcel. This latter factor indicates noise generation due to the individual ice floes moving past one another as they rearrange into new shapes. The correlations indicate differential motions of other forms (primarily iceconvergence) become important in generating lower frequency noise only during winter. As for 1000 Hz during fall and winter, the correlations are low and the results are ambiguous. Several factors are discussed that emphasize our lack of knowledge about higher frequency arctic ambient noise.
83(1988); http://dx.doi.org/10.1121/1.396150View Description Hide Description
The problem of determining the spherically symmetrical field generated by an acoustic point source at the center of a fluid sphere that itself is immersed in a second fluid medium is discussed. A method of solving for the field in the internal and external fluid regions is introduced, based on finite Hankel transforms. These transforms and their inverses are constructed in such a way that the boundary conditions (continuity of pressure and normal component of particle velocity) at the spherical interface are satisfied. In particular, the inverse transforms are integrals; that is, there is a continuum of radial wavenumbers. This contrasts with the more usual formalism, involving a Fourier–Bessel series taken over a discrete distribution of radial wavenumbers. The latter type of inversion formula is suitable only for problems involving relatively simple boundary conditions (e.g., Dirichlet or Neumann). Using the new technique, an exact analytical solution is given for the acoustic field in both the sphere and the surrounding fluid.
Matched field processing: Source localization in correlated noise as an optimum parameter estimation problem83(1988); http://dx.doi.org/10.1121/1.396151View Description Hide Description
Matched field processing is a parameter estimation technique for localizing the range, depth, and bearing of a point source from the signal field propagating in an acoustic waveguide. The signal is observed at an array in the presence of additive, spatially correlated noise that also propagates in the same ocean environment as the signal. In a weak signal‐to‐noise situation this parameter estimation requires the maximum exploitation of the physics of both the signal and noise structure which then must be coupled to optimum methods for the signal processing. We study the physics of this processing by modeling the ocean environment as a waveguide that is horizontally stratified with an arbitrary sound‐speed profile in the vertical. Thus, the wave equation describes the underlying structure of the signal and noise, and the signal processing via the generation of the replica fields. Two methods of array processing are examined: (i) the linear cross correlator (Bartlett) and (ii) the maximum likelihood method (MLM) for the parameter estimation procedure. The optimum potential resolution is evaluated using a generalized Cramer–Rao bound. The two processing methods and the lower bound demonstrate that the ability to reject ambiguities is determined not only by the signal‐to‐noise r a t i o but also by the relative spatial s t r u c t u r e s of the signal and noise. Simulations of both the array processing methods and the bounds for shallow water and Arctic environments using full wave modeling of the signal and noise fields illustrate the coupling of the ocean environment to the localization performance.
83(1988); http://dx.doi.org/10.1121/1.396152View Description Hide Description
Downslope sound propagation data collected off the west coast of Vancouver Island, British Columbia for a shallow source and a deep receiver are examined. The approach used in our analysis was, first, to identify ray paths from the source to the receiver and then to model the variation in measured pressure amplitude with range. The bottom interacting rays, bottom penetrating rays, and channel rays with bottom interaction were identified by the travel time differences between different bottom‐bounce paths. Travel times were computed by ray tracing with an algorithm in which the time step along the ray is the independent parameter. Different propagation paths could be identified in different bathymetric regions viz., continental shelf,continental slope, and deep ocean. A ridge at a range of 79 km shadowed some of the propagating rays; ray tracing from the apex of the ridge was used to calculate travel time curves for some of the diffracted arrivals; however, these diffracted arrivals were difficult to identify in the data. Data collected in the range of 1–52 km were modeled by computing synthetic sonograms using a reflectivity technique modified to remove phase from the vertical wavefunctions. These synthetics were used to constrain the velocity, velocity gradient, sediment thickness, and the absorption coefficient in the upper part of the sediment.
83(1988); http://dx.doi.org/10.1121/1.396153View Description Hide Description
The available data for scattered acoustic intensity and attenuation in dilute aqueous suspensions of sand are compared with theory. In theoretical calculations, the scatterer is assumed to be spherical and elastic, or rigid and movable, or rigid and immovable. The rigid movable model provides the best fit to the data. The failure of the elastic model in comparison to the rigid sphere models indicates that resonance excitation does not occur in natural sand grains, probably because of irregularities in shape. The fact that better agreement with experiment is obtained with the rigid movable model than with the rigid immovable model indicates that the inertia of the particles is important. Additional approximate expressions for the form factor and attenuation coefficient have been constructed based on a modified form of the so‐called high‐pass model introduced by Johnson [J. Acoust. Soc. Am. 6 1, 275–277 (1977)]. The modified high‐pass model provides a fit to the data that is as good as, or better than, the rigid movable case.