Index of content:
Volume 67, Issue 3, March 1980

Rigorous asymptotic theory of evanescent waves for guided propagation
View Description Hide DescriptionChoudhary and Felsen proposed a high‐frequency asymptotic theory of ducted propagation based on the tracking of local evanescent plane waves. In their construction of the asymptotic expansions for the modal fields and eigenvalues they observed that the true modal fields must be analytic on the waveguide axis, and they imposed that condition on the modal amplitude coefficients, although the axis is not included in the domain of uniformity of the asymptotic expansion. Yet, the procedure yielded asymptotic solutions that agree completely with rigorously derived results for special refractive index profiles. The problem is examined here within the framework of the theory of the ordinary differential equation that describes the modal field. It is shown that the asymptotic modal expansion coefficients must be single valued within a strip of the complex coordinate plane, and that this condition yields the same results as the procedure of Choudhary and Felsen. These authors also sought to remedy the nonuniformity of the expansion near the axis by extracting the known exact modal solution for a parabolic refractive index. By constructing a uniform asymptotic representation, this local parabolic approximation is shown here to be valid near the axis, but its domain does not extend far enough to permit overlap with the above‐noted asymptotic expansion away from the axis.

Surface wave interpretation of the eigenfrequencies of a finite‐length fluid cylinder
View Description Hide DescriptionThe eigenfrequencies of a finite‐length fluid cylinder may be interpreted as the resonances caused by the phase‐matching of circumferential waves that circumnavigate the cylinder along certain helical paths, and that get reflected back and forth from its top and bottom flat surfaces. In this paper we obtain the dispersion curves of these circumferential waves that correspond to a series of well‐defined pitch angles of their helix for different values of the cylinder’s length‐to‐radius ratio.

Acoustic radiation pressure on a rigid sphere in a spherical wave field
View Description Hide DescriptionAn analysis has been made of the acoustic radiation pressure acting on a rigid sphere in a spherical sound field for the purpose of completing the work of Embleton [J. Acoust. Soc. Am. 26, 40–45 (1954)] from the angle of practical application. His presentation has been simplified mathematically and improved into a more general form. Numerical calculations have been made with particular emphasis on the difference from the results for incident plane progressive waves as a function of the density of the sphere, the size parameter, and the distance of the sphere from the sound source.

Forced oscillations of a separated shear layer with application to cavity flow‐tone effects
View Description Hide DescriptionWaveboundary conditions near the point of separation at a sharp edge are carefully examined, with new insights being derived for some common flow‐tone situations. Application of the continuity of velocity principle enables the amplitude and phase of the instabilitywave to be related to the acoustic driving wave phasor. Likewise, continuity of shear stress leads to a mathematical dependence of shear layer dynamics on upstream wall boundary layer parameters. Some surprising results: (1) An instabilitywave driven near the point of separation is found to move initially at half the velocity expected from linear theory. (2) Although resonator‐controlled flow tones operate at levels above the nonlinear saturation point for shear layer instability, they can exist only for shear layers that would otherwise be highly unstable. Some longstanding mysteries cleared up: (1) Why unflanged resonators (e.g., coke bottles) resist excitation by flow at grazing incidence. (2) Why flow‐tone spectra are nearly pure sine waves, even for multimode cavity systems.

Sound propagation through parallel jets exhausting from ducts
View Description Hide DescriptionThe method of matched asymptotic expansions is employed to construct the solution for the propagation of sound through parallel jets which exit from long ducts and are surrounded by a uniform parallel stream. Parts of the duct walls are lined with acoustically absorbent material. The small parameter for the expansion is the ratio of the inner jet thickness to the acoustic wavelength. The problem is further simplified when we impose the condition that the speed of the outer stream, which accounts for the forward motion speed of the ducts, is much smaller than the speeds of the jets. This condition is valid during landing and takeoff operations. Farfield pressure distributions are obtained for the case in which the inner jet is much faster than the outer jet and the case in which the two jets are the same.

Single mode transmission and acoustic backscattering measurements in a laboratory waveguide
View Description Hide DescriptionOur purpose was to make ’’farfield’’ sound scattering measurements in a limited space. We used a thick waveguide, about 35 acoustic wavelengths deep, and excited it in the first mode. The waveguide had pressure release surfaces on the top and bottom. To excite and receive in the first mode, we used a vertical array that was amplitude shaded to match the eigenfunction of the first mode. Experimental measurements verified that 90% of the energy was in the first mode. A pair of omnidirectional transducers were used as a probe transmitter and receiver to calibrate the system for scattering measurements. At 220 kHz, 24‐cm depth, and 100‐cm range, the cross section of the scattering region was about 6 cm high. At this range the first Fresnel zone was 10 cm wide. Scattering measurements of the target strength of a steel sphere, diameter 0.8 cm, gave −54±1 dB compared to −54 dB theoretical target strength.

Backscattering cross sections of live fish: PDF and aspect
View Description Hide DescriptionThe probability density function (PDF) of the peaks of the envelopes of sonarecho from live fish were measured at beam aspect. The measurements were made at 220 kHz and in a waveguide. The fish was the common shiner (N o t r o p i s c o r n u t u s) and was about 120 mm (about 18 acoustic wavelengths) long. The PDF of the echoes was approximately Rayleigh when the fish was moving gently. The backscattering cross section equaled 4.2×10^{−5} m^{2}. Transformation of the PDF’s to a target strength display in decibels displaced the maximum of the PDF to the target strength equaling 10 log_{10} (σ_{bs}/A _{0})+3 dB where σ_{bs} is the mean backscattering cross section and A _{0}=1 m^{2}. The target strengths of the common shiner (120 mm) and the mummechog (F u n d u l u s h e t e r o c l i t u s, 100 mm) were measured as a function of aspect angle. Comparison of the experimental measurements and Love’s empirical target strengths for any aspect showed that the measured target strengths at broadside aspect were about the same and the target strengths at other aspect angles were several decibels less than Love’s values. Linear arrays of point scatterers were chosen to match the gross aspect dependence of the target strengths of the fish. The lengths of the arrays were 6.5 mm for the common shiner and 16.5 mm for the mummechog. These lengths were less than the lengths of the corresponding fish’s swim bladders.

Surface‐duct propagation: An evaluation of models of the effects of surface roughness
View Description Hide DescriptionThe results of 25 measurements of acoustic propagation to a range of 6 km in the ocean mixed layer, at frequencies of 4, 8, and 16 kHz, are summarized and compared with a number of propagation models. Within the mixed layer , the acoustic energies have considerable variability and are usually 10 to 20 dB less than the prediction of normal‐mode theory for a perfectly reflecting surface (the shortfall increases with frequency). At 8 kHz, the (negative) correlation of acoustic energy with surface roughness (χ) is highly significant. The frequency dependence of the average data is similar to that predicted by the long‐range version of the AMOS model but different to that predicted by the Baker model. At 16 kHz, the average energy is about 7 dB less than spherical spreading minus absoption; the cause of this attenuation is unexplained. Below the mixed layer (in the ’’shadow zone’’), the measured energies also have considerable variability. They are usually 10 to 15 dB greater than the predictions of normal‐mode theory and decrease with frequency less rapidly than does the AMOS model. The measured ratios of below‐duct to in‐duct energies tend to increase with χ/λ; whereas, the Helmholtz–Kirchhoff theory of surface scattering predicts that, for values of χ/λ that correspond to the experimental values, the ratio should be a constant.

Crossing rate statistics for finite bandwidth or modulated multipath signals
View Description Hide DescriptionIn a previous paper [P. N. Mikhalevsky, J. Acoust. Soc. Am. 66, 751–762 (1979)] the first‐order statistics of finite bandwidth and/or modulated multipath acoustic signals are investigated. In this paper the crossing rate statistics of such signals are analyzed. It is shown that source bandwidth and modulation increase the phase crossing rate while leaving the amplitude crossing rate unchanged. Data acquired by the Woods Hole Oceanographic Institution and data from the CASE experiment conducted in the Pacific in 1973 are compared with theoretical predictions with very favorable results. The Woods Hole data were previously analyzed [I. Dyer and G. W. Shepard, J. Acoust. Soc. Am. 61, 937–942 (1977)]. Their consistent overprediction of the ratio of amplitude to phase crossing rates is explained when modulation effects are accounted for.

Fiber optic pressure sensor
View Description Hide DescriptionWe propose a new transduction mechanism for fiber opticpressure sensing: pressure‐induced microbending, which produces excess optical attenuation in the fiber. A simple bending transducer has been used to determine the response of a step‐index multimode fiber to changes in applied pressure. The potential (low frequency) acoustic sensitivity of such a transducer, calculated from this measured response, is approximately 100 μPa into a 1‐Hz detection bandwidth.

Flexural–extensional behavior of composite piezoelectric circular plates
View Description Hide DescriptionA plate‐type theory is developed for the flexural‐extensional vibratory response and static voltage deformation of heterogeneous piezoelectric circular transducer elements. Known results for homogeneous disks and bimorphs are shown to be special cases of the theory. Application is made to the design of simply supported metal‐piezoceramic unimorph disks, and thin piezoceramic bimorph benders possessing metallic electrodes of non‐negligible thickness.

Band‐limited power flow into enclosures. II
View Description Hide DescriptionIn the parent paper [J. Acoust. Soc. Am. 62, 906–911 (1977)] expressions were presented for band‐limited sound power flow into an enclosure in the low‐frequency regime where acoustic and structural modes are thinly scattered. Results for transmission by structural modes resonant below and within the frequency band of interest were given. The transmission was assumed to be to resonant acoustic modes of the enclosure. This addendum presents an additional expression for calculating power flow to nonresonant acoustic modes of the enclosure (modes resonant above and below the frequency band of interest) from structural modes resonant below, within, and above the band. If no resonant acoustic modes exist in a band, the new results can be used to predict the power inflow. If resonant acoustic modes do exist, the results can be used to increase the precision of the power inflow calculation. The procedure to be used in the calculation of the sound level in the enclosed space is presented.

Sound source above a rough absorbent plane
View Description Hide DescriptionThe scattering of sound from a steady simple source above a rough absorbent plane is treated in the context of the theory of geometrical acoustics. The roughness of the plane is described by a scalar parameter which defines the fraction of the reflected sound energy which is scattered randomly (Lambert’s Law), the remainder being reflected specularly (Snell’s Law). An image principle is derived; the specular image source is nondirectional and the random image source is directional.

Estimation of source motion from time delay and time compression measurements
View Description Hide DescriptionExpressions are derived for estimating the cross line‐of‐sight speed (CLSS) component of velocity from relative time compressions (RTC’s) and time delays. Theoretical expressions for the rms error in radial speed and CLSS are given and have been corroborated by simulation experiments. These expressions show the relative difficulty of estimating radial speed information as compared with CLSS.

Robust sequential detection of weak signals in undefined noise using acoustical arrays
View Description Hide DescriptionIn detection problems where the noise distribution may be unknown, employing nonlinear elements that precede the standard detector often significantly improves system performance in non‐Gaussian noise. However, in order to optimize the system to the noise conditions and, thereby, prevent degradation under Gaussian noise, the nonlinear elements should possess an inherent capability for adapting to the changing noise conditions. This paper presents a discrete formulation based on m‐interval partitioning for sequentially detecting weak signals in undefined noise. Partitioning requires knowledge of a small number of quantiles and related functions from the unknown noise distribution. The resultant detector is easily implemented and is adaptable to slowly changing noise conditions. Two examples are given that clearly show improved performance, over a wide class of noise distributions, for an array employing m‐interval partitioning compared with arrays employing linear correlators and sign detectors.

A comparison of three schemes for filtering signals which have propagated through a random multipath medium
View Description Hide DescriptionThree filtering techniques that can be employed in the recovery of a signal after it has propagated through a nonrandom, distortionless, multipath channel have been studied. The generalization of these studies to the random medium situation is the objective of this paper. A fixed, omnidirectional source emits a signal which propagates through a multipath medium and is detected by an array of point receiving elements located at some arbitrary distance from the source. The medium is characterized by a set of attenuation and delay random variables associated with each of the multiple paths. In addition, the additive noise contributed by the medium is assumed to be negligible. The detected signals are then processed by delay filtering, matched filtering, or frequency‐inverse filtering. The criterion for comparison of these three schemes is the ratio of the standard deviation of the filtering scheme’s output time‐average power to the expected value of this power. It is found that under certain constraints this ratio is approximately independent of the delay statistics of the medium, and the duration and frequency of the input for the three filtering schemes. In addition, this ratio is approximately equal for delay and matched filtering and is √2 times greater for frequency‐inverse filtering.

Reconstruction of a reflectivity field from line integrals over circular paths
View Description Hide DescriptionWhen a broadband acoustic pulse is emitted from an omnidirectional source into a two‐dimensional reflecting medium and the resultant backscatteredechoes are recorded as a function of time at a point coinciding with the source, measurements of line integrals of the acoustic reflectivity are obtained over concentric arcs centered at the source point. Sufficient line‐integral data can be generated in this fashion, by translating the omnidirectional source–receiver point over a suitable aperture, to reconstruct the unknown reflectivity function. A closed‐form solution to this image reconstruction problem is derived, and on the basis of this solution, computerreconstructions of a point reflecting object from simulated echo data are presented. Finally, the closed‐form reconstruction formula is shown to be expressible as the sum of two terms, where the first term corresponds to a simple delay‐and‐sum operation applied to the echo data recorded over the aperture; the second term is new and represents a correction which is shown to provide a noticeable improvement in the temporal–spatial point spread function produced by conventional delay–sum processing alone.

Noise correlation functions for arbitrary receiver orientation and steering direction in vertically anisotropic, azimuthally isotropic noise fields
View Description Hide DescriptionA first approximation of array signal‐to‐noise gain for linear or planar arrays is obtained by assuming ideal sound transmission from source to receivers having zero time delay (unsteered elements) in the presence of two‐dimensional or three‐dimensional isotropic noise. The resulting noisecorrelation functions are the familiar J _{0} (x) and sin x/x. These functions are usually extended for computing the noisecorrelation functions for arbitrary receiver orientation steered to any direction and receiving any grade of signal transmission. A more general form of the noisecorrelation functions is available for any orientation of a pair of receivers with zero time delay in the presence of a vertically anisotropic, azimuthally isotropic noise field. The present paper treats noise correlation for an array of arbitrarily oriented receivers in the same environment. Furthermore, the generalized functions accommodate beamforming in any direction. Methods for simplifying noise gain computations are presented.

Differential electrical excitation of the auditory nerve
View Description Hide DescriptionThe multichannel cochlear prosthesis requires an electrode stimulus configuration which produces a stimulus field spatially localized to each electrode. In this paper, a three‐dimensional discrete resistancemodel of the cochlea was developed which exhibits electrical response properties similar to those observed during electrical stimulation of the cochlea. The model results suggest that the spatial attenuation of current within the cochlea varies greatly in magnitude, depending on the stimulus configuration. In addition, the model suggests that the spatial attenuation of current in both the auditory nerve fiber endings in the organ of Corti and in the myelinated fibers within the cochlear ground paths is different from the voltage attenuation in the scalar fluids. Therefore the efficacy with which a particular stimulus configuration differentially excites local terminal auditory nerve fiber populations cannot be deduced from scalar voltage measurements which have previously been recorded in the literature. Consequently physiological experiments were performed in the cat to measure the current distributions in the terminal nerve fiber region for monopolar and bipolar stimulation of the scala tympani, and also for stimulation between the scala tympani and the scala vestibuli. The mean length constants measured in the basal turn for these stimuli were found to be 12, 3, and 7.5 mm, respectively.

A model of lateral line microphonic response to high‐level stimuli
View Description Hide DescriptionThe electrical potential recorded from the lateral line canal organs of fish in response to a sinusoidal vibratory stimulus consists of a microphonic component with frequency twice that of the stimulus plus a dc shift. This paper describes the behavior of both components as functions of stimulus frequency (from 100 to 400 Hz) and amplitude. The microphonic decreases with frequency, while the dc shift increases, and the two components have different input‐output functions. An analytical model of hair cellelectrical properties with an asymmetric saturating nonlinear conductance is presented that describes the behavior of both the microphonic and the dc shift.