Volume 54, Issue 1, July 1973
Index of content:
- PROGRAM OF THE EIGHTY‐FIFTH MEETING OF THE ACOUSTICAL SOCIETY OF AMERICA
- Session A. Georg von Békésy Memorial Symposium: Cochlear Biophysics I
- Invited Papers
54(1973); http://dx.doi.org/10.1121/1.1913570View Description Hide Description
Review of past experimental and theoretical research leads to a statement of our present knowledge of cochlear mechanics. In particular, an attempt is made at a clear definition of the nature of cochlear waves. With the help of prominent examples, it is shown that neither experiments nor theory have ever been entirely correct but have supplemented and corrected each other mutually in steps of successive approximation. As the approximation has become closer, the steps have become smaller, but the process is still going on. During the Békésy era, the weight of research was on the fundamental properties of cochlear waves; now, the emphasis is on numerical values of such parameters as wavelength, damping, and nonlinearity. At the end of the presentation, some effects of the cochlear wave pattern on auditory neural excitation are discussed. Especially, it is shown how displacement and velocity responses can be separated by means of appropriate stimulus patterns.
54(1973); http://dx.doi.org/10.1121/1.1977824View Description Hide Description
Georg von Békésy's visual observation of the basilar‐membrane travelling wave showed a broad mechanical tuning, quite at variance with the sharp tuning from neural recordings. A few years ago, Johnstone and Boyle applied the Mössbauer technique to the basilar membrane and showed the tuning to be much sharper than previously thought. Our latest results show high‐frequency cutoffs of up to 340 dB per octave. Using a special Mössbauer source with an isomer shift to eliminate the 180° ambiguity of previous work, the phase shift has been shown to asymptote to π/2 lead at low frequencies, rotating approximately linearly with increasing frequency and finally asymptoting sharply to 3π lag at the tuning‐curve cutoff. The low‐frequency slope of about 12 to 24 dB/oct is apparently much less than the neural curves. However, the Mössbauer technique requires a higher sound level than used for neural threshold curve, and if neural curves are constructed with constant firing rates as a parameter, e.g., 50 impulses per second, so that comparable sound pressures are used, then they show a low‐frequency scope of around 36 dB/oct—not too different from the mechanical figure. Hence, taking into account a basilar membrane nonlinearity of the type found by Rhode, the neural and mechanical curves may be reconciled.
54(1973); http://dx.doi.org/10.1121/1.1977825View Description Hide Description
The Mössbauer technique has been applied to the measurement of vibration of the basilar membrane in the squirrel monkey's cochlea. Both steady‐state and transient responses have been recorded in the 7–8 kHz range of the cochlea. The steady‐state response indicates that the basilar membrane vibrates nonlinearly from frequencies of stimulation near or greater than the characteristic frequency. The nonlinearity can be observed at the lowest levels of stimulation, 70–80 dB SPL, for which measurements could be made. The nonlinearity extends to lower frequencies and the baslar‐membrane transfer function tends to broaden as SPL is increased. Rapid post‐mortem changes occur in the cochlea. The amplitude of the transfer ratio (basilar membrane/malleus) decreases 10–15 dB over a period of several hours, with a downward shift of 1.5–3 kHz in the characteristic frequency of the basilar membrane at a given location. The low‐frequency slope of the transfer ratio settles to 6 dB/oct by six hours after death. The slope of the phase of the transfer function increases as the characteristic frequency decreases. The transient response was studied using acoustic clicks of approximately 150 μsec in duration, presented in sequences of 100 000 to 400 000. The transient response has an early component which has a fast decay and a second component which has an extremely slow rate of decay and displays nonlinear behavior.
54(1973); http://dx.doi.org/10.1121/1.1977826View Description Hide Description
An up‐to‐date description of the relationships among stimulus‐related cochlear potentials and various mechanical events in the inner ear is presented. Of special interest is to consider (1) how well the mechanical tuning characteristics (amplitude and phase) of the basilar membrane are represented in cochlear microphonics and summating potentials, (2) what these potentials reveal about the mode of excitation of the two groups of sensory cells of the cochlea, and (3) how nonlinearities are reflected in the recorded electrical responses.
- Session B. Underwater Acoustics I: Propagation
- Contributed Papers
54(1973); http://dx.doi.org/10.1121/1.1977827View Description Hide Description
Previous experiments in the South Pacific have shown that bottom features have a significant effect on sound channel propagation when observed at a bottom‐mounted hydrophone A comparison is made of a similar bottom‐mounted system with a hydrophone suspended at the sound channel axis in mid water using data obtained during the KIWI ONE Experiment along a 6000‐NM track from New Zealand to South America. The effect of the East Pacific Rise and the Louisville Ridge on the observed propagation loss from shots detonated at the sound channel axis is discussed.
54(1973); http://dx.doi.org/10.1121/1.1977828View Description Hide Description
Explosive sources were detonated at shallow depths in two long‐range deep ocean experiments. Signals were recorded from a shallow hydrophone in one experiment and from a SOFAR channel hydrophone in the other. The propagation was strongly influenced by subsurface sound channels. The shot arrival patterns determine the convergence zone locations and the sound velocity of the subsurface channel. Energy was detected which traveled more than 800 km through the subsurface channel.
54(1973); http://dx.doi.org/10.1121/1.1977829View Description Hide Description
Wide‐band signals received at long range in a SOFAR channel are distorted and dispersed during transmission. In addition to temporal dispersion explained by ray theory, there is frequency structure that is best explained by mode theory. Explicit prediction of the time‐frequency structure of the received waveform given the projected pressure pulse can be made for arbitrary sound‐velocity profiles by using the WKB approximation. The response of deep‐ocean sound channels to various pressure pulses including an impulse, an impulse pair, and a linear FM pulse has been investigated. It is shown that observed phenomena such as combined ray and mode propagation, and bubble pulse modulation of the spectrum, can be predicted by WKB mode theory.
54(1973); http://dx.doi.org/10.1121/1.1977830View Description Hide Description
In a recent ocean experiment, explosive sound sources at a depth of 18 m were used to measuresurface duct propagation loss at frequencies from 0.4 to 20.0 kHz, ranges from 1 to 32 kyd, and hydrophone depths from 6 to 180 m concurrently with detailed environmental sampling. These measurements were part of the experiment described in papers W4 and W5 at the 84th Meeting [J. Acoust. Soc. Amer. 53, 332(A) (1973)]. The investigation covered the low‐frequency cutoff due to leakage out of the duct and the high‐frequency rolloff due to surface scattering and attenuation. The explosive signals were recorded broad band and the surface duct arrivals were analyzed through filters. Three sets of these measurements using explosive sources were made alternately with four sets of similar measurements using towed projectors. Comparisons between the two types of measurements showed an overall agreement. Explosive sources in addition to towed projectors were used to partially alleviate the encountered dynamic effects of the mixed surface layer on underwater sound propagation loss. Results indicate that certain frequencies and hydrophone depths for each of the data sets gave less propagation loss than for other cases.
54(1973); http://dx.doi.org/10.1121/1.1977831View Description Hide Description
In both deep and shallow water the stratification of the medium quite often varies significantly with range as well as depth and thus affects the nature of acoustic transmission. In these cases a model of acoustic propagation should be able to accommodate the effect of such changes in the stratification of the ocean. A computer‐oriented procedure with its foundations in normal mode theory has been developed for problems of this type. Arbitrary changes in velocity profile, water depth, and bottom composition with range can be accommodated. The effect of mode conversion is included in the analysis. The theoretical procedure is discussed and the results are compared to values obtained from a deep‐water low‐frequency experiment for which the velocity profile changed significantly with range. [This work was supported by the Naval Ship Systems Command.]
54(1973); http://dx.doi.org/10.1121/1.1977832View Description Hide Description
We investigate the sound propagation in a deep ocean channel with an Epstein‐type velocity profile using the normal‐mode approach. Our treatment includes the effects of earth curvature, and the propagation of pulsed signals. The modes are obtained as the residues in a pole series arising from the Watson transformation. Intensity versus range curves over a curved earth are given both for phased and random modal sums. Dispersion curves for phase and group velocities of the modes are obtained. Arrival times in terms of the group velocities are shown to be inverted (the lowest‐order, closest‐to‐axis mode arrives last) in agreement with experiment, but in contrast to the predictions of a parabolic profile [P. Hirsch, J. Acoust. Soc. Amer. 38, 1018 (1965)]. Our Epstein parameters were chosen to reproduce an equivalent profile that applied to the long‐range propagation experiment in the southern ocean [A. C. Kibblewhite, R. N. Denham, and P. H. Barker, J. Acoust. Soc. Amer. 38, 629 (1965)]. [Supported in part by the Office of Naval Research.]
54(1973); http://dx.doi.org/10.1121/1.1977833View Description Hide Description
Large thermal fluctuations associated with internal tidal waves can lead to highly asymmetric wave profiles having the characteristics of internal tidal bores. An acoustic wave propagated through a medium in which such a phenomenon is in progress can undergo amplitude variations exceeding 30 dB. Synoptic time and space series of environmental and acoustic data are obtained from sensor arrays fixed in space, in shallow water off southern California. The acoustic source radiates CW pulses every 3 sec at 30 kHz to a fixed hydrophone 150 m away. Time series are obtained of temperature from vertical thermistor space arrays, and wave height is obtained from a wave staff and water motion obtained using EM current meters. A sampling interval of 3 sec was used. The large‐scale acoustic amplitude fluctuations are investigated using acoustic ray techniques while the small‐scale events are looked at from the statistical point of view.
Beam Displacements for Media with Monotonic Sound‐Speed Profiles with Discontinuous and with Continuous First Derivatives54(1973); http://dx.doi.org/10.1121/1.1977834View Description Hide Description
A ray representation for some of the diffraction phenomena encountered in underwater sound propagation in media with nonmonotonic sound‐speed profiles [E. Murphy, J. Davis, and J. Doutt, J. Acoust. Soc. Amer. 50, 101 (A) (1971)] leads to beam displacements that remove the sensitivity or pathology of ordinary ray analysis when first derivatives of the sound‐speed profile are discontinuous. In this modified ray theory,diffraction phenomena take the form of frequency‐dependent beam displacements for rays with vertexes near the sound‐speed profile extremum. Unlike ordinary ray theory results, modified range‐versus‐source‐angle curves are well‐behaved (continuous derivatives). The analysis has been extended to monotonic profiles with discontinuous and continuous derivatives; the analysis is somewhat more complicated than for the nonmonotonic extremum examples. Here also, beam displacements remove some of the pathology in the range‐versus‐source‐angle curves. For the smooth monotonic profiles there are displacements if the curvature of the profile is too great. For the profile with discontinuous gradients there can be oscillations in the range‐versus‐source‐angle curves.
54(1973); http://dx.doi.org/10.1121/1.1977835View Description Hide Description
If the sound‐speed profile is obtained by Cubic Spline interpolation, the intensity calculations become very accurate; for instance, the problem of false caustics does not arise. However, the ray equations need to be solved numerically, as theoreticalsolutions do not exist for a cubic. This idea has been applied to both range‐independent and range‐dependent ray tracing. Some numerical differential equation solvers are compared with regard to computer time and accuracy. A special test method, for the range‐dependent case, that makes use of complex function theory checks ray and intensity calculations. Some computer results are shown.
Regression Analysis for Averaged Decay Laws for Energy versus Range in Some Winter and Summer Mediterranean Shallow Water Sound Transmission Data54(1973); http://dx.doi.org/10.1121/1.1977836View Description Hide Description
Shallow water broad‐band sound transmission data from a SACLANT Centre Mediterranean program have been analyzed, in 20 frequency bands, for evidence for various decay laws for the variation of sound energy with range. The data, averaged over depth, show surprisingly smooth, reproducible variations with range. For example, exponents in power‐law regression analysis of winter data (with volume attenuation removed) are close to the often‐predicted power with standard deviations often less than 1 dB. There is evidence, at lower frequencies, depending on sea bottom, for a range interval with better propagation (perhaps cylindrical spreading) prior to the power region [see D. E. Weston, J. Sound Vibration 18, 271–287 (1971)] with a more complicated frequency dependence than idealized arguments would suggest. The pertinent aspect of the appearance of various forms of range dependence is the range interval over which they occur; prediction schemes require these limits to arrive at absolute levels. Convincing evidence for various decay laws can be found; however, the range limits may show such complicated dependence on frequency, location, and season that no useful prediction scheme will follow from such a study.
54(1973); http://dx.doi.org/10.1121/1.1977837View Description Hide Description
In the design or operation of sonar systems it is required to know under what conditions optimum performance can be achieved. The subject of this paper is a technique which should be useful in dealing with one term in the sonar equation, namely, transmission loss. Since the amount of energy lost depends on many parameters (e.g., the sound‐speed profile, source and receiver depths, frequency, bottom loss, etc.), the process of determining the optimum mix of these parameters is cumbersome even if a validated transmission loss model is available. The approach utilizes the Fast Field Program (FFP) to generate transmission loss values for typical sound‐speed profiles of the major ocean areas. It is assumed that at a sufficiently large range the mean propagation loss is represented by where r is horizontal range and α is Thorp's attenuation coefficient. The constant A is then determined from a linear least‐squares fit between this expression and the FFP values. The FFP is rerun for various combinations of the input parameters and the value of A are then combined to form a collection of nomograms which display the dependence of the mean transmission loss upon the input parameters. This work supported by the Chief of Naval Material.]
A Comparison of Ray Theory, Modified Ray Theory, and Normal Mode Theory for a Deep Ocean Arbitrary Velocity Profile54(1973); http://dx.doi.org/10.1121/1.1977838View Description Hide Description
Modified ray theory [D. A. Sachs and A. Silbiger, J. Acoust. Soc. Amer. 49, 824 (1971)] can be used to calculate transmission loss near caustics and in shadow zones where ray theory fails. Normal mode theory is an approach that should work equally well in every region. For an arbitrary linear‐gradient profile, results of ray theory and modified ray theory have been compared near a convergence zone caustic. It was found that these two approaches do not always agree in the double arrival region associated with the caustic. Results from a normal mode program using finite difference methods for an arbitrary profile [A. V. Newman and F. Ingenito, NRL Memo. Rep. 2381 (1972)] will be compared where possible with the results from the above‐mentioned techniques. [Supported in part by ONR and DNA.]
54(1973); http://dx.doi.org/10.1121/1.1977839View Description Hide Description
With the current interest in low‐frequency wave propagation, it is highly desirable to know frequency‐dependent solutions of the reduced wave equation in at least a few idealized situations. For point sources in layered unbounded media with sound speeds satisfying [c″(z)/c(z)]′=0, we find approximate solutions with frequency (ω) dependence, . The leading term is the ray acoustics field, that is, t(x,y,z) is “travel time” and a(x,y,z) is “intensity.” The additional terms correct ray acoustics for finite frequency; for example, b(x,y,z) provides a measure signal distortion for brief signals. All our results are parameter‐less explicit functions of ω, x, y, z found without using rays, ray equations, or ray parameters.
- Session C. Shock and Vibration I: Vibration Data Analysis and Analysis Systems
- Invited Papers
54(1973); http://dx.doi.org/10.1121/1.1977840View Description Hide Description
This is a tutorial paper describing the fast Fourier transform and practical aspects of the digital computation of power density spectra using FFT. Discussed first is the relation of the discrete Fourier transform(DFT) to the Fourier integral. Then we describe an FFT algorithm, showing its computational saving over the naive calculation of the DFT. We then consider the estimation of the power density spectrum, describing briefly the indirect method (used before FFT) and then the direct method of power spectrum estimation via the periodgram estimate now commonly used. We continue with a discussion of bandwidth and stability of spectral estimates and how these properties are related to the time and frequency windows used to smooth the periodgram estimates. Finally, we consider briefly the estimation of cross spectra and coherency and discuss some of their properties.
54(1973); http://dx.doi.org/10.1121/1.1977841View Description Hide Description
Examples of applications of Fourier transforms are chosen from a variety of topics. Roughly, those topics can be classified in a few categories: problems that lead to partial differential equations and can be solved by certain methods of separation of variables; other problems that lead to ordinary differential equations or systems of such equations with constant coefficients, which are solved by subjecting the equations to Fourier analysis; and finally, many processes which become more intelligible to us if we study them not as functions of time but as functions of frequency. All these problems were previously attacked by standard Fourier analysis. Special emphasis is placed on pointing to the modifications brought about by the introduction of the fast Fourier transform. As far as physical subject matter is concerned, the applications are chosen largely from the field of ship design and ship operation.
54(1973); http://dx.doi.org/10.1121/1.1982232View Description Hide Description
The advantages of the Cooley‐Tukey technique for calculating the Fourier transform of a function were recognized immediately and universally; there is probably no other algorithm which was incorporated in program libraries so fast, and after only eight years it is now likely that there are no laboratories where current engineering work is being done that do not have an operational version of the fast Fourier transform. It would be reasonable to expect that this now universal ability to make the transform (and inverse transform) with great economy would have encouraged its widespread use and the development of new applications of this powerful technique. A cursory survey within the Aerospace Industry confirms that it is indeed being used widely, but suggests that the major use is the routine one of spectralanalysis, where the Fourier transform is an end product rather than a tool. This paper attempts to encourage the wider use of the fast Fourier transform by describing some additional applications from the experience of the authors and others at the author's home company, and from the experience of others whose comments have been solicited.