Volume 39, Issue 6, June 1966

Connection between the Fay and Fubini Solutions for Plane Sound Waves of Finite Amplitude
View Description Hide DescriptionPlane, progressive, periodic sound waves of finite amplitude are considered. The well‐known solutions of Fay and Fubini are reviewed. At first glance, the two solutions seem contradictory, but, actually, each holds in a different region of the flow, the Fubini solution close to the source and the Fay solution rather far from the source. In the intermediate, or transition, region, neither solution is valid. A more general solution is obtained by using a method commonly employed for waves containing weak shocks. For distances up to the shock‐formation point, the general solution reduces exactly to the Fubini solution. For distances greater than about 3.5 shock‐formation lengths, the general solution is practically indistinguishable from the sawtooth solution, which, in turn, is the limiting form of Fay's solution for strong waves. The form of the general solution shows clearly how, in the transition region, the Fubini solution gives way to the sawtooth solution. The problem of an isolated cycle of an originally sinusoidal wave is also considered. Finally, some limitations on the weak‐shock method are discussed. In the periodic‐wave problem, the general solution is found to be inaccurate for distances greater than 1/α, approximately, where α is the small‐signal absorption coefficient. In Appendix A, a brief extension of the analysis to spherical and cylinrical waves is given.

Effects of Slow Steady Flow on a Pure‐Tone Sound Field
View Description Hide DescriptionThe effect of a slow steady flow of ideal fluid upon a superimposed pure‐tone sound field is examined, especially for effects upon the acoustic admittance vector. It is assumed that the total field is derivable from a scalar potential and that terms of second order in Mach number are negligible. Blokhintsev's transformation [NACA Tech. Mem. No. 1399(1956)] to a flowfree acoustic problem is shown to be awkward, except for rigid, nonporous boundaries, because of complications in the transformed boundary conditions. For one dimensional fields, it is shown that the steady flow has no direct effect on the acoustic admittance or the magnitudes of acoustic pressure and particle velocity. However the steady flow may affect the terminating admittance of a one dimensional field, and thereby become evident within that field. If the correct value of terminating admittance is used in the analysis, then a flowfree acoustic solution will yield correct values for the magnitudes of the true pressure and particle velocity and for both magnitude and phase of the true admittance at every point.

Auditory Intensity Perception and Neural Coding
View Description Hide DescriptionThreshold signal‐to masker ratios for three sinusoids (250, 1000, and 4000 Hz) presented in a masker of corresponding frequency set to various levels were gathered and are presented. The masker was either continuous or pulsed‐on‐only during both signal intervals. The block up‐and down, two‐interval, forced‐choice psychophysical procedure was used. The relation between the obtained thresholds, and (1) the level of the masker, (2) whether the masker was continuous or pulsed, (3) other previously reported data for noise signals and maskers are especially considered. A discussion of these data as reflecting auditory nerve activity, loudness adaptation, increase of uncertainty and/or, a “drifting filter” is offered.

Computerized Investigation of Threshold‐Decision Phenomenon
View Description Hide DescriptionThreshold determination within the framework of the block up‐and‐down, two‐interval, forced‐choice (BUDTIF) method has been investigated using a computerized Monte Carlo technique. Two aspects of the results are presented in preliminary fashion. (1) In a block up‐and‐down threshold‐estimating method, modifications that yield minimal variance within individual runs may not automatically be assumed to yield minimal variance between successive threshold estimates. (2) The optimal number of trials per block was the smallest that yields a valid solution depending on the target performance level; use of a memory of more than one block for level change decisions is not indicated.

Binaural Masking of Speech by Periodically Modulated Noise
View Description Hide DescriptionThe interference with intelligibility of monosyllabic words produced by continuous white noise, by modulated white noise, and by continuous speech (single talker) was studied during homophasic (N0S0) and antiphasic (NπS0) listening. Five signal‐to‐masker ratios, four modulation rates, and four magnitudes of modulation were used. Reception in the continuous noise was characterized by steeply sloping intelligibility functions and a 4.5‐dB masking‐level difference favoring antiphasic listening. Reception in modulated noise changed with the rate and depth of modulation. A 7‐dB modulation yielded intelligibility functions highly comparable to those for continuous noise having the same average level. By contrast, more extreme modulation (14, 21 dB, and complete interruption) produced better intelligibility under both homophasic and antiphasic conditions than did continuous noise. This effect was particularly great when noise was completely interrupted either 4 or 20 times/sec, under which circumstances intelligibility remained above in 80% in a speech‐to‐noise ratio of −24 dB. The advantage of antiphasic over homophasic listening, or masking‐level difference, was fairly similar for all conditions of modulated noise, averaging 3.9 dB. When the masking signal was a single competing talker, the antiphasic advantage dropped to 3.3 dB, and the intelligibility function did not duplicate any of the functions obtained in white noise, either continuous or modulated. Nonetheless, individual sets of conditions occurred where masking by speech and by modulated noise yielded equivalent performance, but the depth of modulation required for this equivalence varied with the speech‐to‐masker ratio being employed.

Feedback and Psychophysical Variables in Signal Detection
View Description Hide Description144 observers, divided into eight groups of 18 each, were run in a two‐alternative, temporal, forced‐choice auditory‐signal‐detection task. At each of two signal intensities, four levels of information feedback were used. No feedback (NF); correct feedback on every trial (F100), on three‐fourths (F75), or half (F50) of the trials, with incorrect feedback on remaining trials. The results were that (a) NF and F100 led to higher probability of correct responding P(C) than either F75 or F50 for both signal intensities; (b) P(C) for NF was higher under the higher intensity but lower under the lower intensity than for F100; (c) on trials immediately following trials on which observer's response and feedback agreed, detection rates were higher and false‐alarm rates were lower than following disagreement trials, whereas these differences were close to zero for F50. It is argued that feedback leads the observer to change his criterion following disagreements. The effect of this variability is to depress the mean detectability index d′ of signal‐detectability theory.

Physiological Correlate of Tonal Masking
View Description Hide DescriptionA gross, slow potential that is differentially sensitive to the frequency of a tone burst was recorded from the region of the auditory nerve in the hamster. An experimental paradigm similar to that employed in psychological studies of tonal masking was used to measure neural‐response amplitude change in the presence of a second tone. The influence of one tone upon the other, as evidenced by the neural response, yielded functions similar to the masking curves generated by human listeners. Increases in the level of the signal required increases in the level of the masker in order to maintain the masking criterion. High‐tone maskers were seen to be less effective than low‐tone maskers. Masking was viewed as a preempting of neural activity by the secondary tone.

Superior‐Olivary Response Patterns to Monaural and Binaural Clicks
View Description Hide DescriptionThis study presents responses to dichotic clicks obtained from neurons of the medial superior‐olivary nucleus of anesthetized cats. The neurons described in this study evidenced interactive patterns to both time and intensity differences by changes in their probabilities of response and by shifts in their latency. These findings suggest a complex synaptic organization of neurons, some of which are responsive to large and some to small interaural time differences. The former neurons that show interactions to large time differences (ca. 10.0 msec) respond consistently to both monaural left and right clicks. Binaural clicks, however, significantly decrease the probability of firing in response to stimulation of the lagging ear. Some of the latter neurons that show interactions to small time differences (ca. 0–2.0 msec) fire only once, while others discharge twice to a monaural click; these single and double responders exhibit changes in latency and probability of their firings upon binaural stimulation and, in the case of the double responders, alterations in both spikes occur upon appropriate stimulation.

Interactions between Synchronous Neural Responses to Paired Acoustic Signals
View Description Hide DescriptionBrief tone pips were used as stimuli in two‐signal interference experiments to provide a basis for interpretation of intensity functions. Whole nerve action‐potential responses were recorded from the cochlea (guinea pig). Stimulation by a 6‐kcps pip interferes with the response to a 2‐kcps pip only when the latter reaches a magnitude (baseline peak measure) of 30–40μV, about 18 dB above a just detectable response. Interference depends more upon the strength of the 2 kcps pip than upon the strength of the 6‐kcps pip. The form of intensity functions for low‐frequency signals is dominated by a basal extension of excitatory region. Intensity functions for high‐frequency signals show less spatial change. The data suggest that there are two response modes for neural activity elicited by acoustic signals. For high‐frequency signals, synchrony of excitation depends upon envelope and there is little change in location of excitatory region along the cochlear partition with signal strength. For low‐frequency signals, synchrony depends upon the locations along the cochlear partition that exceed a critical amplitude, i.e., upon the velocity of the traveling wave. Broad‐band transient signals, such as clicks, may elicit neural activity in both response modes.

Electrophysiological Analog of the Interaural Time‐Intensity Trade
View Description Hide DescriptionVariations in the amplitude and polarity of evoked potentials with differences in intensity and arrival time of clicks delivered to the two ears were recorded from the superior‐olivary nucleus in cats with chronically implanted electrodes. An analog of the “time‐intensity” trade was seen in the cancellation of evoked potentials when time and intensity differences were opposed.

Experiment in Ferroelectric‐Tape Recording
View Description Hide DescriptionLongitudinal recording has been achieved on plastic tape coated with ferroelectric material. Reproduced levels were constant with frequency at the low end, but in the system used there was an upper frequency limit at about 1800 cps with a tape speed of 147 ips. On one of the media tested, the recordings decayed about 9 dB in 150 sec, at a humidity of 20%. Improvement of the high‐frequency limitation probably depends on better design of the reproducing head. More‐permanent recordings might be obtained with stronger recording fields, resulting in deeper penetration of the recording medium, or perhaps with the use of a material with more‐suitable characteristics.

Logarithmic Frequency Systems
View Description Hide DescriptionLogarithmic calibration of the range of audible frequencies serves both physical and musical acoustics. Logarithmic assessment of frequency intervals leaves open the choice for a log base, for divisive multipliers, and for some reference frequency serving tabulations of “acoustical logarithms.” Euler's binary‐log measure describes intervals in terms of fractions of an octave; the characteristic counts the octaves re the frequency standard and the mantissas are invariant with the tonal species. Different forms of binary systems, their transforms (especially duodecimal), and other log systems (common, natural, commatic, etc.) are discussed. The angular transform of 2^{ x }, representable as an exponential spiral (helix), portrays the periodic properties of frequencies as perceived by the musical ear in the octave system. Huygens used common logs and antilogs to compute cycles of 12 and 31; Mercator proved the merits of the cycle of 53 by natural logs; Sauveur invented the first acoustical log step scale. Lambert, DeProny, and Drobisch elaborated binary measures, while Ellis, Hornbostel, Young, and Husmann constructed tabulations.

Optical‐Fiber Ultrasonic Delay Lines
View Description Hide DescriptionThe ultrasonic pulse‐propagation characteristics of nonmetallic optical fibers were investigated the 10‐Mc/sec region. It was found that the lowest‐order longitudinal L(0,1) mode and the lowest torsional or T(0) mode could be propagated, using piezoelectric transducers. The L(0,1) mode was propagated through single fibers as well as flexible bundles of fibers. The T(0) mode was propagated through single fibers. The attenuation was of the order of 0.1 dB/μsec in fused silica fibers of 75 μ diam, and about three times greater in clad glass fibers of the same diameter. In very‐short‐fiber lines, many echoes were observed and the end‐face geometry was not critical. In flexible‐fiber bundles with epoxy fused ends, no echoes were seen owing to the high attenuation of the epoxy, which was greater than 10 dB/mm of coated length. Dispersion was negligible in the single‐fiber lines and flexible fiber bundles, but severe in rigid, fully fused fiber‐optic bundles that behaved essentially as solid rods. There was no significant difference in the ultrasonic behavior of optically coherent and noncoherent flexible‐fiber bundles of short length. Flexible fiber‐optic bundles with fused ends appear to retain the simple acoustic‐mode structure of the single fiber. Various multiple‐fiber arrays are considered in parallel and series grouping and with different input‐output configurations. A multiple‐delay generator using a combination of glass and fused silica fibers of different lengths is described. Further applications are discussed.

New Method for the Measurement of Ultrasonic Attenuation in Solids at High Temperatures
View Description Hide DescriptionThe specimen under test is in the form of a rod with plane parallel ends. A thin annular groove is worked in the rod at about one‐third of its length. A transmitting‐receiving quartz crystal delivers ultrasonic pulses to the rod at its remote end. The pulse heights of the reflections from the constriction and the other end are measured on a cathode‐ray oscillograph. Assuming a plane‐wave propagation, a formula is derived to calculate the attenuation constant of the short portion of the rod in terms of the mentioned pulse heights. The obtained formula is independent of the length or attenuation of the long portion of the rod. This enables one to heat the short portion while the long portion is cooled, thus overcoming the difficulties of matching usually met with in high‐temperature measurements between a quartztransducer and specimen. The method is applied to measure the attenuation of longitudinal waves in pure aluminum at temperatures up to 700°K for frequencies of 3 and 5 Mc/sec, respectively. The results indicate a thermally activated internal friction whose value agrees with that previously obtained by Kâ at a frequency of 1 cps.

Measurements of the Scattering of Sound from Turbulence
View Description Hide DescriptionAn experiment was performed on the scattering of ultrasonicwaves (25 65 kc/sec) from the turbulence produced by the flow through a grid in a 6×f‐in. nozzle. The transmitter and receiver were of the solid dielectric, condenser type. The scattered signal was separated from the direct and reflected signals by a pulse technique. The intensity of scattered sound was measured at angles from 21.5° to 165° to obtain the differential scattering cross section. The 1‐in. mesh grid was heated to obtain scattering from both the velocity and temperature fluctuations. The results were compared with the formulas derived by Lighthill, Kraichnan, and Batchelor. [Proc. Cambridge Phil. Soc. 49 531–551 (1953); J. Acoust. Soc. Am. 25, 1096–1104(1953); in Symposium on Naval Hydrodynamics, F. S. Sherman, Ed. (National Academy of Science‐National Research Council, Washington, D.C., 1957), Publ. 515, pp. 409 430]. The general shapes of the curves predicted by the theory were obtained experimentally: the scattering was strongly in the forward angles, as was expected for high sound frequencies, with a minimum at 90°. The scattering from the velocity field displayed an additional minimum as 180° was approached, while the scalar field produced strong backscattering. Runs were taken at distances frown the grid to the center of the scattering volume of 5 and 22 in., and at Reynolds numbers of 4110–42 600, based on the grid mesh length.

Reflection of Plane Viscoelastic Waves from Plane Boundaries
View Description Hide DescriptionThe reflection of time‐harmonic plane dilatational or shear waves from the rigid or stressfree boundary of an “arbitrary” linearly viscoelastic half‐space is studied. Properties of general plane waves—i.e., plane waves whose amplitudes vary across their wavefronts—are used to determine the reflected dilatational and shear waves. In general, the reflected waves are general plane waves and there is a phase shift at the boundary. When certain specified conditions prevail, the reflected waves are attenuated only in their direction of propagation. Necessary and sufficient conditions on the material properties are derived for the existence of surface waves. It is shown that no surface waves can exist for certain viscoelastic materials. In general, surface waves are possible only for discrete incidence angles. However, for a special class of viscoelastic materials, which we call elasticlike, reflected surface waves may exist for a range of incidence angles greater than a specific critical angle. For the elasticlike materials, the phase shift at the boundary is the same as in the analogous elastic problem. In general, the phase velocities and reflected angles are functions of the incidence angle, the frequency, and material properties.

Parametric Solution of the Dispersion Relation for Guided Sound Propagation in Shallow Water
View Description Hide DescriptionThe normal‐mode dispersion relation for guided propagation in a liquid layer lying above an infinitely deep liquid bottom appears as a transcendental equation relating the angular frequency ω and the horizontal wavenumber k in Perkeris' classic solution. It is shown in this paper that this transcendental equation may be solved exactly in a parametric form for any given normal mode. Equations are derived and discussed. They give frequency, phase velocity, and group velocity in terms of a single parameter μ and mode number n.

Medium‐ and Far‐Field Expressions for Velocity Potential of Circular Plane Piston
View Description Hide DescriptionEquations developed by L. V. King [Can. J. Res. 11, 135–155 (1934)] can lead to useful expressions for the velocity potential of a circular plane piston, in an infinite rigid baffle, radiating into a dissipationless fluid. An exact series is derived, in negative powers of distance from the center of the piston face to the field point, with specific formulas for all coefficients. The first term is the Fraunhofer approximation. It is then shown that a much simpler series, with the same first term and with explicit coefficients, closely approximates the exact one, provided that the piston radius is at least a few acoustic wavelengths in size and that the field point, as viewed from the source, is at only a small angle from the beam axis. This approximate series always converges, and rapidly so for distances from just outside the near field to the remote regions governed accurately by the Fraunhofer expression. At any distance outside the near field, the angular range of validity includes almost all of the power radiated in the beam.

Forced Motions of an Encased Cylinder of Decreasing Thickness
View Description Hide DescriptionA hollow cylinder is encased in a thin elastic shell and subjected to a time harmonic pressure at the inner surface of the cylinder. Plane strain and axial symmetry are assumed. The material of the cylinder is incompressible in bulk and both elastic and viscoelastic behavior in shear are considered. The inner radius of the cylinder increases monotonically with time. The influence of loss of mass and stiffness on the forced motion of the system is considered. The oscillatory motion consists of the superposition of a maintained vibration and a transient term. The maintained vibration takes into account the loss of mass and stiffness in a quasistatic manner. For an encased viscoelastic cylinder, the transient term is damped rapidly. A bounded resonance effect occurs when the instantaneous frequency of the system passes through the value of the external forcing frequency.

Plastic Deformation in Random Vibration
View Description Hide DescriptionA randomly excited single‐degree‐of‐freedom oscillator in which an idealized form of plastic deformation can take place is studied. Through the use of an artificial process, statistics of this nonlinear, hysteretic system are deduced from linear system‐response statistics in two régimes of operation. The expected accumulated plastic deformation is found as a function of time and some other statistics derivable from the artificial process are indicated. A numerical example is given that illustrates the use of the method with low‐cycle fatigue data.