Index of content:
Volume 77, Issue 1, January 1985

A simple, complete numerical solution to the problem of diffraction of S H waves by an irregular surface
View Description Hide DescriptionWe present a new method to calculate the diffraction of elasticS Hwaves by irregular surfaces. The technique developed is applicable to boundaries of arbitrary shape and steepness as well as to periodically corrugated surfaces; it is valid at all frequencies. The approach consists of determining the surface forces which cancel the incident stress along the surface. The method relies on the introduction of a periodicity in the surface shape and on a discretization of the boundary at regular spacing. The surface sources which radiate the scatteredwave field are obtained by iteration. Examples of calculations and comparisons with other methods are presented.

Complex eigenfrequencies of rigid and soft spheroids
View Description Hide DescriptionThe complex eigenfrequencies of impenetrable or penetrable target objects form a pattern which is characteristic for a given target, as far as its shape and/or composition is concerned; they manifest themselves as poles (resonances) in the amplitude of waves scattered from the object. We here obtain the eigenfrequency patterns of acoustically rigid and soft spheroids in the complex frequency plane, and study their displacements when the eccentricity of the spheroids is varied. The eigenfrequencies were obtained numerically by subjecting spheroidal wavefunctions to the Neumann or Dirichlet boundary conditions, respectively.

A time‐domain energy theorem for scattering of plane acoustic waves in fluids
View Description Hide DescriptionA time‐domain energy theorem for the scattering of plane acoustic waves in fluids by an obstacle of bounded extent is derived. It is the counterpart in the time domain of the ‘‘optical theorem’’ or the ‘‘extinction cross section theorem’’ in the frequency domain. No assumptions as to the acoustic behavior of the obstacle need to be made; so, the obstacle may be fluid or solid, acoustically nonlinear, and/or time variant (a kind of behavior that is excluded in the frequency‐domain result). As to the wave motion, three different kinds of time behavior are distinguished: (a) transient, (b) periodic, and (c) perpetuating, but with finite mean power flow density. For all three cases the total energy [case (a)] or the time‐averaged power [cases (b) and (c)] that is both absorbed and scattered by the obstacle is related to a certain time interaction integral of the incident plane‐wave and the spherical‐wave amplitude of the scatteredwave in the farfield region, when observed in the direction of propagation of the incident wave.

Sound scattering by a group of oscillatory cylinders
View Description Hide DescriptionThis paper is mainly concerned with an analytical study of multiple scattering of a plane sound wave by a group of circular, rigid cylinders oscillating in an ideal fluid. The objectives of the study are to investigate the phenomenon of multiple scattering due to the presence and the movement of many scatterers in the passage of sound waves and to determine the effects of multiple scattering and scatterers’ oscillations on the associated scattering functions. The fluid medium is assumed inviscid and compressible and the solid cylinders are assumed to move freely under the action of the sound waves. The acoustical radiation field caused by the translatory oscillations of the cylinders was taken into account for the correction to the main scattering caused by the mere presence of the rigid cylinders.

Wavelength‐dependent bulk parameters for coherent sound in correlated distributions of small‐spaced scatterers
View Description Hide DescriptionEarlier results for coherent propagation of sound in correlated random distributions of two‐parameter particles of radius a (with minimum separation b≥2a small compared to wavelength λ=2π/k) are generalized to obtain the refractive and absorptive terms and the corresponding bulk parameters to order (k a)^{2}. The present development includes higher order terms of the earlier multiple scattering by monopoles and dipoles, as well as scattering and multipole‐coupling effects through quadrupole terms. The correlation aspects are determined by the statistical mechanics radial distribution functionf(R) for impenetrable particles of diameter b. The new terms for slab scatterers and spheres involve the integral of f R (first moment), or of R f ln R for cylinders. The new packing factor is evaluated exactly for slabs as a simple algebraic function of the volume fraction w, and it is shown that the bulk index of refraction reduces to that of one particle in the limit w=1. Similar results are obtained for spheres in terms of the Percus–Yevick approximation and the unrealizable limit w=1.

Spectral analysis of echoes for backscattering coefficient measurement
View Description Hide DescriptionThis paper describes spectral analyses of echoesscattered by a random medium and a plane reflector by using mathematical expressions of echoes which have been proposed by us before [M. Ueda and H. Ichikawa, J. Acoust. Soc. Am. 7 0, 1768–1775 (1981): 7 5, 1012 (1984)]. It becomes possible to express the spectrum of echoesscattered by the random medium in terms of a backscattering coefficient of the random medium and a velocity potential of an ultrasonic transducer. The expressions hold for any sound field if a correlation length of the random medium is much smaller than a beamwidth and a radius of the transducer. Then the spectrum of the echoscattered by the plane reflector is expressed in terms of a directivity of the transducer. By using a ratio of the two spectrums an expression which gives the backscattering coefficient of the random medium is formulated. It works in a farfield of a flat circular transducer and at a focal plane of a concave one. It is shown that our formula contains those cases which have been proposed so far as the extreme cases of the conditions. Finally, the backscattering coefficients of sponges are measured with several transducers. The results show that our formula gives the coefficients regardless of the transducer geometry.

Experiments on sound‐absorbing Shaw‐type horns with spatially varying effective density
View Description Hide DescriptionAn experimental investigation of Shaw’s theory of sound propagation in acoustic horns with spatially varying density and elasticity is reported. The density‐variation technique was used to simulate a conical horn in a tube of uniform cross section using perforated sheet metal plates. The performances of the density variation horn and the equivalent conical horn were evaluated by comparison of the acoustic impedance and the acoustic pressure within the horns. It was observed that the density‐variation conical horn had sound‐absorbingproperties as a result of the use of the perforated plates. Due to the absorptionproperties of the density‐variation cone it can be used as a muffler. A muffler was designed and its performance evaluated using both a loudspeaker and an internal combustion engine as sound sources.

Saturation of a nonlinear cylindrical sound wave generated by a sinusoidal source
View Description Hide DescriptionThe propagation of a cylindrical sound wavegenerated by a sinusoidal source is studied in a nonlinear case by means of a generalized Burgers’ equation with two dimensionless parameters. The amplitude of the wave at a large distance from the source, where all higher harmonics are absorbed, is determined in a region for the two parameters where the amplitude is given by a single number not depending on the parameters. The method is to find a series expansion of the solution of the generalized Burgers’ equation. The series converges both far from the source and in the Taylor shock region nearer to the source. Despite the slow convergence of the series in the latter region it is possible to find the desired amplitude by means of an asymptotic expression for the terms in the series and some numerical work.

Nonlinear resonant oscillations in closed tubes—An application of the averaging method
View Description Hide DescriptionThe application of the averaging method to the one‐dimensional inhomogeneous, nonlinear acousticwave equation with dissipative term makes it possible to give asymptotic solutions for any kind of external resonance excitation. It shows that the lowest‐order solution consists of the superposition of two modulated counterpropagating waves, where the amplitude of each is a solution of Burgers equation. The method is extended to the treatment of oscillating boundaries; in that case it also leads to Burgers equations. Explicit stationary solutions are given for the particularly important forms of the external excitation, harmonic distributed forces, and harmonic oscillating boundaries. The application of several other computational methods to this problem leads to the same results.

Propagation of sound above a finite layer of snow
View Description Hide DescriptionMeasurements of the sound field from a point source above a relatively soft surface layer backed by an acoustically hard material are reported. These were made outdoors over layers of snow from 5 to 50 cm thick and to propagation distances of up to 15 m. The conditions of the snow layer varied from newly fallen to aged and windblown snow. Experiments were also conducted indoors at shorter distances above reticulated foam of similar thicknesses. The theory of Pyett [Acustica 3, 375–382 (1953)] for the acoustic impedance of a porous layer is used to extend the solution for reflection of spherical waves from a porous half‐plane to reflection from a porous layer. This simple theory shows good agreement with the indoor measurements at all frequencies. Similarly good agreement between this theory and experiments over snow layers outdoors is obtained above about 200 to 500 Hz depending on the geometrical configuration. However below these frequencies the measurements suggest that the layer of snow behaves as semi‐infinite porous ground.

A Markov process model of ocean sediments
View Description Hide DescriptionMonochromatic plane‐wave illumination of a randomly stratified, laterally homogeneous sediment layer is considered. The deposition process creating the stochastic layering is assumed to be a continuous parameter, finite state Markov chain. A Riccati equation for the plane‐wave reflection coefficient is formulated and first‐order partial differential equations for relevant probability density functions are subsequently obtained. These equations are solved numerically for a two‐material turbidite model similar to the one considered by Gilbert [J. Acoust. Soc. Am. 6 8, 1454–1458 (1980)]. Statistical moments of the reflection coefficient are computed at 25 and 250 Hz as a function of overall sediment thickness. These equations are also used to derive the nonrandom or ‘‘smooth’’ geoacoustic model that is appropriate in the low‐frequency limit.

Ocean acoustic tomography: Travel time biases
View Description Hide DescriptionThe travel times of acoustic rays traced through a climatological sound‐speed profile are compared with travel times computed through the same profile containing an eddy field. The exact travel time difference is compared with its constituent terms, one of which is linearly related to the deviation of the sound speed (referenced to the climatological profile) and the others which are nonlinearly related to the deviation. At ranges that are much greater than the eddy scale and for eddy fields whose range‐averaged temperature anomaly is small, the numerical results are: (1) the values of the nonlinear terms are insensitive to changes in the positions of the eddies and (2) the nonlinear terms are approximately proportional to the range between the source and receiver and to the square of the eddy anomaly. At a 1084‐km range in the east Atlantic at 24 °N (36 °N) the nonlinear terms can account for 17% (90%) of the exact travel time change where the temperature anomalies associated with the eddies are typically ±0.5 °C (±1 °C). Linearized inversions (based on the linear estimator of the travel time difference) which use the e x a c t travel time differences for data should yield biased results since the average values of the nonlinear terms are not zero. If an a p r i o r i knowledge of the eddy spectrum is known, the nonlinear terms could be computed for each ray and subtracted from the exact travel time change. It may then be beneficial to use the corrected set of travel time differences in a linear inversion which would require no iteration.

The range dependence of normal incidence acoustic backscatter from a rough surface
View Description Hide DescriptionA theoretical expression for the normal incidence, high‐frequency, backscattering coefficient as a function of range from an isotropic rough surface which has both a Gaussian height distribution and a Gaussian autocorrelation function is presented and its correctness substantiated with a series of experimental measurements. Ideally the backscattering coefficient of a rough surface should be dependent only on properties of the surface. For the usual definition of backscattering coefficient this is shown to be true in the farfield of the surface scattering patch. In the nearfield of the surface, the backscattering coefficient is shown to be independent of all statistical properties of the surface and dependent only on its reflection coefficient. In a range interval between the nearfield and farfield, the backscattering coefficient is shown to depend on both the surface statistics and the measurement geometry.

The use of self‐resonating cavitating water jets for underwater sound generation
View Description Hide DescriptionA self‐excited cavitating jet assembly is examined for possible use as an underwater noisegenerator. The principles of the system are based on matching the natural frequency of a submerged jet with that of a resonant chamber through a feedback mechanism. The case of an organ piperesonant feed tube is thoroughly investigated. In this case, feedback is obtained by shaping the nozzle in order to optimize its interaction with instabilities in the shear layer of the jet. The performance of the noisegenerator is evaluated and its characteristics analyzed, including the influence of the pressure drop across the nozzle, the cavitation number, and the organ pipe length. It is observed that the efficiency of STRATOJETs (self‐resonating cavitating jets) is more than two orders of magnitude higher than that of a conventional cavitating jet. The knowledge developed in this study allows for selection of the amplitude and frequency of the emitted noise by proper dimensioning of the assembly and correct choice of the functioning conditions.

Propagation of noise above ground having an impedance discontinuity
View Description Hide DescriptionControlled measurements above ground with an impedance discontinuity are described. The measurements were made outdoors with a source above asphalt and a receiver above grass, and indoors above surfaces of known impedance in the absence of atmospheric turbulence. The results were obtained for several sources and receiver heights and for various percentages of hard–soft ground to propagation distances of 2.4 m indoors and 10 m outdoors. The measurements are also extended to include the case of a source above ground of finite impedance but which is still harder than the ground on the receiver side. The measurements are compared with recent theory which includes semiempiricalsolutions and solutions obtained numerically from Green’s theorem. Good agreement between the measured results and all the theories is obtained in most cases. However, in more extreme situations, including the ‘‘soft–softer’’ ground case, the semiempiricalsolutions are in difficulty. Earlier work [Nicolas e t a l., J. Acoust. Soc. Am. 7 3, 44–54 (1983)] is also extended by calculating the insertion loss of a barrier on ground with an impedance discontinuity. The previously measured insertion loss is recompared with the predicted insertion loss and good agreement is now obtained.

On the resolution of planar ultrasonic tomography
View Description Hide DescriptionA theoretical study of depth and lateral resolution of image reconstruction in planar ultrasonic tomography is presented. An ambiguity function of this system is derived based on the back‐and‐forth propagation with plane‐wave insonification. We show that both the depth and lateral resolution are dependent on the wavelength of the insonification and the range of values of the incident angles employed. The analysis yields a theoretical resolution limit for this type of planar ultrasonic tomography. We conclude that the depth resolution in particular can be significantly improved by increasing the extent of the angular view.

Active incoherent ultrasonic imaging through an inhomogeneous layer
View Description Hide DescriptionIn this paper, a method of active incoherent ultrasonic imaging which has been proposed in previous work [Sato e t a l., A c o u s t i c a l I m a g i n g (Plenum, New York, 1982), Vol. 11, pp. 289–308; Yokota and Sato, A c o u s t i c a l I m a g i n g (Plenum, New York, 1983), Vol. 12, pp. 621–634] is extended to the case where an inhomogeneous layer exists between the objects and aperture. Data acquisition is carried out by repeating transmission of burst ultrasonic waves from each transducer on the aperture and reception of the reflected waves on the same aperture. The compensation for the effect of the inhomogeneous layer is then carried out by using the space invariant property of the spatial frequency components of the object. The coherence function of the revised wave field is derived from these data, and the image is reconstructed by means of the nonlinear 2‐D power spectral estimation. An algorithm of image reconstruction which includes cases where the inhomogeneous layer is located some distance from the aperture is demonstrated by several computer simulations and experiments.

Morphometric analysis of hair cells in the chinchilla cochlea
View Description Hide DescriptionTen chinchilla cochleas which ranged in length from 16.00 to 19.71 mm were used for this study. The cross‐sectional area and perimeter of the inner and outer hair cells and their nuclei were determined at two locations per cochlear turn and at the junction between each of the turns (11 locations from apex to base). Some interanimal variation in hair cell dimensions was noted. However, none of these size variations could be attributed to any known differences among the animals. It was concluded that the data reported here represent the natural variation in hair cell size in chinchillas. The data establish a baseline to which the dimensions of cells from abnormal cochleas can be compared, regardless of the length of the cochlea or the base‐to‐apex location of the cells.

Frequency characteristics of the middle ear
View Description Hide DescriptionFor 68 temporal bones, frequency curves for the round window volume displacement have been measured for a constant sound pressure at the eardrum. Phase curves were measured for 33 of the specimens. The level averaged amplitude curve is approximately flat below 1 kHz, where the round window volume displacement per unit sound pressure at the eardrum is 6.8×10^{−} ^{5} mm^{3}/Pa, and falls off by about 15 dB/oct at higher frequencies. For the 20 ears having the largest sound transmission magnitude at low frequencies, the corresponding amplitude curve is displaced about 5 dB towards higher levels. The phase of the round window volume displacement lags the eardrum sound pressure phase. In average for 33 temporal bones, the phase lag increases from zero at the lowest frequencies to π near 2 kHz and to about 1.5 π at 10 kHz.

Influence of direct current on dc receptor potentials from cochlear inner hair cells in the guinea pig
View Description Hide DescriptionInner hair cellresponses to sound were monitored while direct current was applied across the membranous labyrinth in the first turn of the guinea pig cochlea. The current injection electrodes were positioned in the scala vestibuli and on the round window membrane. Positive and negative current (<100 μA) caused changes in the sound‐evoked dc receptor potentials which were dependent on the sound frequency and intensity. The frequencies most affected by this extracellular current were those comprising the ‘‘tip’’ portion of the inner hair cell frequency tuning characteristic (FTC). The influence of current increased with increasing frequency. Positive current increased the amount of dc receptor potential for the affected frequencies while negative current decreased the potential. Current‐induced changes (on a percentage basis) were greater for low intensity sounds and the negative current direction. These frequency specific changes are evidenced as a loss in sensitivity for the tip area of the FTC and a downward shift of the inner hair cellcharacteristic frequency. Larger current levels (>160 μA) cause more complex changes including unrecoverable loss of cell performance. In separate experiments positive and negative currents (<1.1 μA) were injected into the inner hair cell from the recording electrode during simultaneous measurement of the sound‐evoked dc receptor potential. This condition caused a shift in IHC sensitivity that was independent of sound frequency and intensity. Positive current decreased the sensitivity of the level of the cell while negative current increased the responses. The effect of current level on sound‐evoked dc receptor potential was nonlinear, as comparatively greater increases in cell response were observed for negative than decreases for positive current. The intracellular current injection results are accounted for by the mechano‐resistive model of hair cell transduction, where nonlinear responses with current level may reflect outward rectification. Response changes induced by extracellular current are evidence of currenteffects on both inner and outer hair cells. The frequency and intensity dependences are hypothesized to represent voltage mediated control of inner hair cell response by the outer hair cells.