Volume 63, Issue 2, February 1978

Sound radiation from an accelerated or decelerated sphere
View Description Hide DescriptionA careful review of the current literature has led to a more complete theoretical analysis of the sound radiation from an accelerated or decelerated sphere. The acoustic field has been calculated for an accelerated sphere in an arbitrary fluid medium, which shows the effect of the fluid density on the radiated soundpressure. The radiated soundpressure from an impulsively accelerated sphere has been compared with a finite acceleration case in order to emphasize the effect of the rate of change of velocity on the pressure waveform. Energy calculations have been made in both the time and frequency domains in order to identify the sources of radiated acoustic energy and the stored nearfield energy and also to demonstrate conclusively that the energy lost in the acceleration or deceleration is dissipated as sound.

Surface wave resonances in sound scattering from elastic cylinders
View Description Hide DescriptionIt is shown that the elastic‐type surface waves(Rayleigh wave, etc.) which enter in a description of sound scattering from elastic objects, exhibit resonances at the eigenfrequencies of the elastic body. These resonances can be interpreted in terms of Regge poles.

Theory of scattering by rigid bodies with thin liquid coatings
View Description Hide DescriptionA plane wave is incident on a rigid body which is partially or totally surrounded by a thin liquid coating whose (possibly variable) density and sound velocity differ from those of the ambient medium. By assuming the incident wavelength to be large compared with coating thickness, approximate expressions for the scattered field are obtained in integral form. By further assuming incident wavelength to be small compared with typical dimensions of the rigid body, the integrals are evaluated asymptotically and the scattered field is expressed in terms of contributions from certain scattering centers of the coating, viz., the specular point and points at which incident rays are perpendicular to the edge of the coating. As an example the method is applied to the problem of a partially coated sphere.

Radiated power and radiation loading of cylindrical surfaces with nonuniform velocity distributions
View Description Hide DescriptionA general approach is presented to evaluate the radiation loading and radiated power from a nonuniform harmonically vibrating surface on an infinite cylinder. The approach utilizes a combined Green’s function and Fourier integral technique to develop integral expressions for the generalized radiation impedance and power radiated from the surface. The general expressions are shown to reduce to previously developed expressions for several problems of interest, i.e., a uniformly vibrating band on a cylinder, a vibrating piston on a cylinder, and various circumferentially varying velocity distributions on a cylinder with no axial variation. Simplified integral expressions are then presented for a particular velocity distribution of interest. Although the integrals can be evaluated asymptotically, in general the integrals must be numerically integrated. Extensive numerical results are presented and discussed in order to illustrate the characteristics of the radiation loading and radiated power.

Design of a curved‐face parametric projector
View Description Hide DescriptionA transducer capable of penetrating marine sediments with multiple, rectangular beams which are broad (20°–30°) in one plane and narrow (2°–3°) in the other plane at frequencies of 10–20 kHz was desired. Transducer size constraints prohibited attaining such a beam conventionally; thus, parametric operation of a rectangular transducer was examined. A relatively high parametric source level of 190 dB r e 1 μPa at 1 m was also desired, and the resulting cavitation and acoustic intensity considerations dictated a curved‐face transducer design. Primary and parametric beam patterns and propagation data obtained for both a rectangular transducer and a curved‐face transducer confirmed the prediction techniques being employed. Parametric beam patterns in the broad plane exhibited minor lobes with the minor‐lobe structure of the curved‐face transducer beam less pronounced than that experienced with the rectangular transducer.Sound pressure levels and beam patternsmeasured for the curved‐face projector confirmed that a curved‐face transducer can be operated parametrically to produce high‐power, low‐frequency rectangular beams.

Nonlinear attenuation of an N wave propagating in a tube, including dissipation due to wall effects
View Description Hide DescriptionTheoretical computations are made for the variation of waveform of an N wave propagating in a circular tube. The change with distance of the slope of the straight‐line segment of the waveform at its axis crossing is calculated. Various assumptions are made in the calculation to isolate the separate contributions of weak‐shock theory and tube‐wall effects. The change in slope is as predicted by weak‐shock theory. The slope is affected by tube‐wall dissipation, but virtually unaffected by velocity dispersion. Measurements are reported pressure profiles of N waves at various distances in a tube. Experiments were done with several different gases. The agreement between theoretical and observed values is fairly good.

Statistics of normal mode amplitudes in a random ocean. I. Theory
View Description Hide DescriptionA statistical theory of acoustic propagation in a model random ocean, valid in the limit of low acoustic frequency, is presented. A random internal‐wave model gives sound‐speed fluctuations δc (r,z,t) about a deterministic profile ? (z). Using normal modes of ? (z) as a basis, the theory gives quantitative estimates of statistical moments of the mode amplitudes ψ_{ n }(r,t), which are randomly coupled via δc. Invoking a quasistatic approximation, the theory treats time as a parameter. From any initial (r=0) distribution of modal powers ‖ψ_{ n }‖^{2}, the evolution of their averages to an equilibrium is predicted by ’’coupled power’’ equations. The theory makes similar predictions for average fluctuations of the modal powers about their means. In the equilibrium limit, the theory gives the full probability distribution of the ψ_{ n }.

Sound velocity–density relations in sea‐floor sediments and rocks
View Description Hide DescriptionIn studies in underwater acoustics,geophysics, and geology, the relations between soundvelocity and density allow assignment of approximate values of density to sediment and rock layers of the earth’s crust and mantle, given a seismicmeasurement of velocity. In the past, single curves of velocity versus density represented all sediment and rock types. A large amount of recent data from the Deep Sea Drilling Project (DSDP), and reflection and refraction measurements of soundvelocity, allow construction of separate velocity–density curves for the principal marine sediment and rock types. The paper uses carefully selected data from laboratory and i n s i t umeasurements to present empirical sound velocity–density relations (in the form of regression curves and equations) in terrigenous silt clays, turbidites, and shale, in calcareous materials (sediments, chalk, and limestone), and in siliceous materials (sediments, porcelanite, and chert); a published curve for DSDP basalts is included. Speculative curves are presented for composite sections of basalt and sediments. These velocity–density relations, with seismicmeasurements of velocity, should be useful in assigning approximate densities to sea‐floor sediment and rock layers for studies in marine geophysics, and in forming geoacoustic models of the sea floor for underwater acoustic studies.

Characterization and simulation of underwater acoustic signals reflected from the sea surface
View Description Hide DescriptionThe properties of underwater acoustic signals scattered in the forward direction by the sea surface have been analyzed statistically. It is shown that the energy of the scattered signal is described adequately by a beta distribution. The beta parameters (α, β) can be estimated using ensemble estimates of the mean and variance of the normalized scatteredenergies. The mean scatteredenergy in turn can be related to the surface roughness parameter g=4πσsinϑ/λ, where σ is the rms surface wave height, ϑ is the grazing angle, and λ is the acoustic wavelength. For a wind driven, rough surface, the acoustic frequency and grazing angle were varied to obtain values of g from 0.5 to 1.4. The structural changes of pulses reflected by the surface are also treated statistically by means of a linear autoregressive model. It is shown that models of relatively low order (e.g., first or second, thus containing few parameters) provide a fairly complete description of forward‐scattered signals. The converse problem of using these models to simulate data having the appropriate statistical properties is also discussed and examples are given.

Signal speed in long‐range propagation
View Description Hide DescriptionThe speed of acoustic signals traveling from a large number of explosive sources in the Northeast Pacific and North Atlantic oceans has been measured and compared with the predictions of ray theory. Signal speed is defined here as the horizontal source‐to‐receiver range divided by the time from source detonation to the earliest detection of the signal at the receiver. The ray‐tracing predictions show that signal speed may vary by as much as 1% or more; changes of 15 m/s may occur within a 1.8‐km range interval. The nature of the signal‐speed‐versus‐range curve depends on the sound‐velocity profile and the source and receiver depths. The measurements show that the predicted features, in particular the regular fluctuation of signal speed, are readily observed.

Acoustic sidebands from cw sources towed at long ranges in the deep ocean
View Description Hide DescriptionThree cw sources (9.8, 110, and 262 Hz) were towed at approximately 7 knots along a great circle track from Antigua, W.I., to the Grand Banks of Newfoundland. Acoustic data from each were recorded on a bottom‐mounted hydrophone near Antigua, providing source‐to‐receiver distances of from 100 to 2800 km. High‐resolution spectral analysis centered at each frequency showed that while no acoustic sidebands were discernible at 9.8 Hz, they were observable over the entire track for both the higher frequencies. Except for expected statistical fluctuations, the upper and lower sidebands were of equal amplitude and symmetrically placed about the carrier frequency. In regions of strong convergence zone activity the sideband level displayed similar peak‐to‐null variation to those of the carrier, although the peak‐to‐null ratio was smaller than for the carrier. Detailed environmental data were available only near the sources. A high degree of correlation was observed between the sideband levels and the wave and swell heights when the sources were towed through a storm which occurred some 2000 km from the receiver. Sideband levels computed from the single bounce sinusoidal surface theory of Roderick and Cron [J. Acoust. Soc. Am. 48, 759–766 (1970)] using swell amplitude data at the sources agreed well with the measured levels for both frequencies during the stormy period. The separation of the sidebands in frequency from the carrier was the same for both source frequencies, was not affected by the convergence zone behavior of the sideband levels, and decreased as the sources approached and transited the stormy area.

Observations of the propagation of very short ultrasonic pulses and their reflection by small targets
View Description Hide DescriptionThe field of a circular ultrasonic transducer emitting a single‐cycle pulse into water has been observed using a specially constructed small (150 μm) wide‐band receiving probe and a compact stroboscopic schlieren system. The theoretically predicted plane‐wave and diffracted edge‐wave components of the field have been resolved. Good agreement with the theory for a pistonlike source is obtained, except in a region less than 1.5 transducer radii from the transducer. The output of the transducer used in the transmit–receive mode to detect small targets has been measured and the results are in accord with a time‐domain principle of reciprocity between transmission and reception. Implications of the results for field plotting and for the location and characterization of small targets are considered.

Ray theory for wide classes of sound‐speed profiles with two‐dimensional variation
View Description Hide DescriptionThis paper presents closed‐form ray‐path and travel‐time equations using solutions of the eikonal equation for wide classes of sound‐speed profiles which vary with range as well as depth. The geometric intensity equation is also given. In the past, ray theory for two‐dimensional sound‐speed variation has been treated mainly by numerical methods. Closed‐form solutions have been available for only a few profiles of a simple form. In this paper the sound‐speed profile is expressed in terms of x and y of a transformed coordinate system in which x and y are functions of depth and range. This transformation and sound‐speed function are such that the transformed eikonal equation reduces to a partial differential equation separable in x and y. The closed‐form ray equations are calculated in terms of x and y, then the results are converted to and presented in depth and range coordinates. The general characteristics of large classes of allowable transformations are presented. Five specific examples of allowable transformation are presented. Three different profile forms are treated in detail for the polar coordinate transformation. Numerical results, including ray diagrams, are presented for these three forms. These three numerical examples provide controls suitable for test cases testing approximate numerical ray‐trace methods.

High‐resolution cross‐sensor beamforming for a uniform line array
View Description Hide DescriptionThe methods of high‐resolution spectral analysis can be used for high‐resolution cross‐sensor beamforming for a uniform line array. In this paper two high‐resolution techniques (maximum entropy and discrete decomposition) are applied to the cross‐sensor field. Sample calculations illustrate the effectiveness of these methods in the case of a realistic multiwave acoustic field plus narrowband Gaussian noise.

A novel approach to digital beamforming
View Description Hide DescriptionFor many sonar applications, the sensor outputs of a hydrophone array are sampled at a rate significantly higher than that required for waveform reconstruction when digital beamforming is used. The reason for this is that the number of synchronous, or ’’natural,’’ beampointing directions is proportional to the beamformer input rate. This paper presents an implementation of a digital beamformer that achieves the desired synchronous beams while minimizing the sensor channel sampling rate requirement. The technique employs zero padding of sensor data followed by digital interpolation filters to achieve vernier beamformer delays. Interpolation filtering can be done either at the beamformer input or output to minimize processing requirements. The resulting structure realizes a hardware savings since both A/D converter and cable bandwith requirements can be traded off against digital processing complexity to achieve an optimal partitioning.

Alternate derivation of the generalized beam pattern
View Description Hide DescriptionA derivation of the generalized beam pattern associated with approximate solutions to the source extraction integral equation is presented which has a number of advantages over the author’s original treatment. Specifically it is more direct, makes fewer assumptions regarding the algorithm employed, and makes explicit some interesting relationships with the local nature of the basic field equation.

Tympanic membrane perforations in cats: Configurations of losses with and without ear canal extensions
View Description Hide DescriptionIn cat, a small tympanic membrane (TM) perforation produces a low‐frequency loss—in terms of sound pressure changes (ΔSP) in front of the TM r e a 10‐μV round window cochlear microphonic (RW CM) —that varies inversely with frequency at a rate of 12 dB/octave with a surgically shortened external auditory meatus (EAM). Losses were determined at the outer opening (ΔSP_{00}) and at the TM (ΔSP_{TM}) of four artificial EAM’s of various lengths, volumes, and leakiness. In the low‐frequency region, a leaky EAM produced a flat loss. In the midfrequency region, the flatness of losses was attributable to (1) the length of the EAM and (2) the location at which the loss was determined. EAM volume was not related to the configuration of the loss. Losses, under all conditions, were always identical in shape and magnitude for the open and closed systems. Clinically, hearing losses due to TM perforations are essentially frequency independent, especially in the low frequencies. The relation between voltage changes (ΔV) across the transducer and losses with different EAM’s suggests that the discrepency between audiometric results and CM losses—at least in the high and midfrequencies—may be due to the use of precalibrated SPL’s in clinical audiometry.

Auditory‐nerve response from cats raised in a low‐noise chamber
View Description Hide DescriptionA litter of four cats, born and raised in a soundproofed chamber, was studied in an attempt to determine which, if any, features of the auditory‐nerve response from routinely available cats might be due to the chronic effects of noise exposure. Two features of routine‐normal response were especially suspect in this regard: (1) a ’’notch’’ in the distribution of single‐unit thresholds centered at characteristic frequencies (CF’s) near 3 kHz and (2) a compression of the distribution of rates of spontaneous discharge for units with CF above 10 kHz. A third feature of response in routine animals was the presence of a small number (roughly 10%) of units with virtually no spontaneous discharge and very high thresholds, sometimes 80 dB less sensitive than high‐spontaneous units of similar CF. In the data from chamber‐raised animals, the high‐spontaneous units showed exceptionally low thresholds at all CF regions, however, there were signs of the midfrequency notch in the threshold distribution of at least two of these animals. The compression of the spontaneous rate distribution was not seen in any of the three most sensitive animals. The data suggest that there is a significant amount of ’’normal pathology’’ in the high‐CF units from routine animals. Low‐spontaneous, high‐threshold units were present in all four chamber‐raised ears with the same characteristics as in routine animals (exceptionally narrow tuning curves and exceptionally low maximum discharge rates) and at roughly the same percentage of the unit sample. A class of units with medium spontaneous rates and intermediate thresholds could also be identified. The possible significance of a classification of auditory‐nerve units according to spontaneous rate is discussed.

Categorical perception—phenomenon or epiphenomenon: Evidence from experiments in the perception of melodic musical intervals
View Description Hide DescriptionCategorical perception was investigated in a series of experiments on the perception of melodic musical intervals (sequential frequency ratios). When procedures equivalent to those typically used in speech‐perception experiments were employed, (i.e., determination of identification and discrimination functions for stimuli separated by equal physical increments), musical intervals were perceived categorically by trained musicians. When a variable‐step‐size (adaptive) discrimination procedure was used, evidence of categorical perception (in the form of smaller interval‐width DL’s for ratios at identification category boundaries than for ratios within categories), although present initially, largely disappeared after subjects had reached asymptotic performance. However, equal‐step‐size discrimination functions obtained after observers had reached asymptotic performance in the adaptive paradigm were not substantially different from those initially obtained. The results of other experiments imply that this dependence of categorical perception on procedure may be related to differences in stimulus uncertainty between the procedures. An experiment on the perception of melodicintervals by musically untrained observers showed no evidence for the existence of ’’natural’’ categories for musical intervals.

Temporal integration of tone glides
View Description Hide DescriptionTemporal integration of rising and falling tone glides against a 50–2800‐Hz background of noise at a sound pressure level of 60 dB r e 20 μPa was studied in two experiments. Glides were in the frequency ranges 200–700 Hz and 1200–1700 Hz for durations of 5–120 ms. Results indicate an asymmetry in the detectability of rising and falling glides of short duration, with rising glides detected at lower signal intensities in both frequency ranges. These effects are discussed in terms of differences in pattern of frequency analysis of identical, but temporally reversed, waveforms.