Volume 53, Issue 2, February 1973

Acuity of the human sound localization response underwater
View Description Hide DescriptionMinimum Audible Angles (MMA) for divers were determined for 3.5 kHz, 6.5 kHz, and broad‐band white‐noise pulses having a duration of 100 msec, a rise‐decay time of 10 sec, and a repetition rate of 1/sec. In Expt. 1 six divers performed the right‐left discrimination with no training or feedback and the mean MAAs obtained were 21.5° for the 3.5‐kHz signal, 14.5° for the 6.5‐kHz signal, and 9.8° for the white‐noise signal. In Expt. 2 four of the original six divers were given feedback from their performance with the white‐noise signal at a single small angle. The mean MAAs obtained after training were 11.3° at 3.5 kHz, 11.5° at 6.5 kHz, and 7.3° with white noise. It was concluded that if one assumes that the MAA reflects the general level at which the binaural system operates then it seems likely that man will be an effective sound navigator in the water.

Problem of localization in the median plane: effect of pinnae cavity occlusion
View Description Hide DescriptionLocalization of sound sourcesoutside the median plane is influenced primarily by differences in head shadow and arrival time of the signal at the two ears of the observer. For sources located within this plane, localization is influenced primarily by the irregularities of the pinna. By progressively occluding these cavities, it is shown that localization ability decreases with increasing occlusion, that it is better for signals in the anterior than in the posterior sector of the median plane, and that high‐frequency signal content is more important than the low. A number of hypotheses regarding localization in the median plane are noted.

Interference and two‐tone inhibition
View Description Hide DescriptionSeveral experiments to determine the effects of two‐tone interaction in the cochlea are described. Nonlinear effects result when the cochlear partition is stimulated by a sinusoid whose frequency falls in a very narrow frequency band surrounding, but not including, the resonant frequency at the point under the recording electrode. These nonlinear effects are manifested as a negative shift in the dc potential accompanied by a partial or complete suppression of the cochlear microphonic potential to a second tone presented at the same time. This suppression is best seen in the first and second turns of the cochlea. Similar suppression effects accompanying a dc shift are obtained by artificially displacing the basilar membrane from its resting position by an asymmetrical change in hydrostatic pressure in the perilymph. The functional relations governing suppression were determined and the results compared with those obtained in two‐tone inhibition experiments in auditory nerve fibers. The results support the conclusion that inhibitory effects seen in nerve fibers, stimulated by two tones simultaneously, reflect mechanical events in the cochlear partition and subsequent changes in the effective stimulating waveform triggering the auditory nerve.

Multidimensional coding within the temporal microstructure of auditory displays
View Description Hide DescriptionThe feasibility of encoding multivariate information within the temporal microstructure of an auditory display is examined. Four pulse variables—ear of arrival, polarity, amplitude, and interpulse interval—were independently encoded pulse‐by‐pulse within auditory pulse trains. A fifth variable—conditional memory, representing the previous state of one of the variables—also served as an independent variable in combination with other variables. An informational constraint of up to 1 bit/pulse was imposed upon the combination of variables. Each variable was binary coded and constraints were imposed upon the combination of variables by means of a parity sum across variables. The accuracy of discrimination of a constant informational constraint falls with the number of variables contributing to the parity sum, and with the number of randomly manipulated variables outside of the parity sum. Excellent discrimination of the informational constraint was achieved for one condition with four independently controlled variables. Specific contributions of pulse variables were strikingly more discriminable than others.

An integrable model for the basilar membrane
View Description Hide DescriptionAssuming a logarithmic relationship between place and characteristic frequency, proportionality between the latter and phase velocity, and a loss factor independent of place, the wave equation for the basilar membrane displacement can be integrated analytically. The main theoretical results are as follows: (1) The low‐frequency phase slope equals approximately −Kω_{ r }(x), where K is a dimensionless constant and ω_{ r }(x) is the characteristic frequency at place x; (2) the asymptotic high‐frequency amplitude slope equals −6(K+1) dB/oct; (3) just above resonance the phase reaches a minimum value of about −K rad. The Rhode (1971) low‐frequency phase‐slope data yields K=27±3. The asymptotic high‐frequency amplitude slope should therefore be (168±18) dB/oct. Surprisingly, the great frequency selectivity of the cochlea as reflected in the large numerical value of the high‐frequency amplitude‐slope is not determined by hydromechanical losses, which primarily influence behavior, near resonance, but the constant K whose physical meaning is approximately “2π times the number of wavelengths” on the membrane for low frequencies. With the above value for K, the number of wavelengths becomes about five—considerably more than found by von Békésy. Nevertheless, it is interesting to note that the phase slopes and high‐frequency amplitude slopes of von Békésy (1960, pp. 446–463) are not inconsistent the light of the present theoretical calculations. If the membrane becomes stiffer at the high amplitudes at which von Békésy made his measurement, both phase and amplitude slopes would be decreased.

Threshold adaptation in normal listeners
View Description Hide DescriptionThreshold adaptation for 500, 1000, 2000, and 4000 Hz was studied with the Carhart, Rosenberg, and Owens tone decay tests using 40 normal‐hearing subjects. Differences in tone decay were evaluated for effects of experimental technique, frequency, hearing level and SPL of the stimuli. There were no significant differences between the results obtained with the three experimental conditions. Appreciable differences in the amount of decay (10 dB or greater) were shown only for 4000 Hz in terms of mean decay. Appreciable amounts of decay (to 25 dB) were found for 1000, 2000, and 4000 Hz in terms of individual test results. All frequency comparisons displayed significantly different ranking at the 0.05 level of confidence. As frequency increased in hertz, tone decay increased in decibels. Effects of hearing level and SPL of the stimuli were without statistical significance.

dBA attenuation of ear protectors
View Description Hide DescriptionThe adoption of dBA‐type hearing damage risk criteria and the consequent use of A‐weighted sound levels to identify areas of auditory hazard have created a need for a measure of the dBA attenuation of ear protectors. In Study 1, the dBA attenuation values of 30 ear protectors are calculated in 619 industrial noise spectra. It is found that the same ear protector may offer 20 dB more dBA attenuation to one noise than to another but that noises of like C‐A value are subjected to approximately the same dBA attenuation. Noises are therefore sorted into five classes according to C‐A value, and average dBA attenuation values for each class are calculated for each ear protector. This type of information makes it possible to select adequate ear protectors even though only the C‐ and A‐weighted sound levels of the noise environment are known. In Study 2, a simple procedure is developed for calculating the dBA attenuation values of any ear protector for the five C‐A classes defined in Study 1. The procedure incorporates correction factors which ensure that, for the average protector, the calculated dBA attenuation values are obtained in 90% of spectra.

Perceptual confusions between four‐dimensional sounds
View Description Hide DescriptionThe aim of this study was to determine the relative importance of source parameters (fundamental frequency and waveform) versus formant parameters (resonant frequency and number) in identifying meaningless complex sounds. Sixteen sounds were generated differing on four dimensions, each having two values. These were the source waveform, containing either all harmonics or odd harmonics only; the fundamental frequency, either 90 or 142 Hz, ratio=1.6; the number of formants, one or two; and the frequency of the formant(s) either low (600 Hz, or 600 and 1550 Hz) or high (940 Hz, or 940 and 2440 Hz) high/low ratio = 1.6. Twenty‐four listeners were trained to identify these sounds. The results show that fewer confusions were made between pairs of sounds (1) as the number of dimensions on which they differed increased, and (2) as the dimension (single or in combination) changed, from formant number to formant frequency region, to fundamental frequency, to source waveform. Listeners appear to make a generalized classification along a single dimension which seems to vary systematically with waveform complexity and periodicity.

The wolf in the cello
View Description Hide DescriptionThe occurrence of the wolfnote in the cello is shown by direct tonal analysis to be caused by the beating of two equally forced oscillations. The fundamental sinusoidal component of vibration of the string is shown to split at the wolfnote into a pair of oscillations separated by a frequency interval equal to that of the stuttering frequency of the wolfnote. In one of the two cellos investigated, higher partials up to the third are also split into pairs, their separation being the multiple of the harmonic number and the separation of the fundamental pair. Further evidence is obtained to support the interpretation of the wolf as beating between two equal forced vibrations from a frequency analysis of the bowed‐string vibration for different stopped string lengths. The frequencies of vibration of the string bear a close resemblance to those obtained in coupled electrical resonant circuits.

Elastic wave propagation in granular media
View Description Hide DescriptionSome measurements of the propagation of ultrasonic pulses through packs of spherical and nonspherical particles of different diameters are reported. The packings include evacuated and compressed media. The values of sonic velocitymeasured together with the measured bulk elastic properties of one such packing yield a reasonable value for Poisson's ratio, tending to 0.5 for the assembly. Increasing contact pressure between particles, or the presence of interstitial air affect the properties considerably.

Optical probing of ultrasonic diffraction in single crystal sodium chloride
View Description Hide DescriptionResults are presented of an experimental study of ultrasonicwavediffraction for the acoustical modes propagating along the [1̄1̄2], [11̄0], and [111] directions in single crystalsodium chloride. Laser beam optical probing in the Raman‐Nath regime was used to map the sound intensity distribution in the farfield of circular transducers. Calculations of the diffraction spread based on representation of the acoustic field by an angular spectrum of plane waves are in agreement with the experimental measurements. A simple method for estimating the diffraction spread based on the geometry of the inverse speed (slowness) surfaces is presented.

Scattering of plane wave by infinite semicylindrical bosses with random radii on a plane surface
View Description Hide DescriptionThis paper covers both theoretical and experimental phases of the subject of scattering of a plane wave incident on infinite semicylindrical bosses of random radii with periodic spacing. The probability density function of the radius of a semicylinder is assumed to be uniform, and the spacing between the centers of adjacent bosses is maintained constant. The spacing is so selected as to make the shadow effects negligible for the angles of incidence considered in this paper. The scalar form of the Helmholtz integral formulation was employed, although some of the inherent assumptions are invalid, owing to discontinuities in the surface. A comparison of the lobe structure (scintillation) of the experimental and theoretical angular acoustic‐intensity scatterpatterns, in particular, the main specular lobe, shows a reasonable agreement with the additional inference about the weakness of the assumption of the model material being rigid.

Pressure radiations from an infinite two‐layered elastic plate with point and shear force excitations
View Description Hide DescriptionPressure radiations generated from a two‐layered elastic plate by time‐varying point and shear forces are obtained analytically. The plate made of two different isotropic and homogeneous materials of uniform thickness is bounded on one side by a fluid medium and another side by a vacuum. Both the fluid and the plate are assumed to be infinite in extent. The effects of transverse shears and rotary inertias in both layers are included in the equations governing the plate motion. The solution is obtained with the aid of Hankel transforms for spatial coordinate and Laplace transform for time variable. “Saddle‐point” technique is used to carry out the inverse Hankel transform for farfield radiations. Numerical results for pressures generated by time‐harmonic point or shear force are presented.

Propagation of acceleration waves in a binary nonreacting mixture
View Description Hide DescriptionIn this work, the behavior of acceleration waves in a two‐constituent mixture is examined. This examination is based on a purely mechanical theory that does not consider reactions. Each of the constituents is assumed to behave in a quasielastic manner, and no restriction is placed on the amplitude of the waves.

Acoustic propagation in waveguides with sinusoidal walls
View Description Hide DescriptionThe propagation of acoustic waves through a plane waveguide consisting of two rigid sinusoidal walls is examined analytically. It is found that the phase difference between the walls, the wall wavenumber, and the mode number strongly influence both the form of the disturbances generated by the walls, and the conditions under which these disturbances become very large.

Velocity‐dependent reflection, refraction, and scattering of elastic shear waves in the presence of a lubricating layer
View Description Hide DescriptionWave‐scattering problems involving moving media should take into account the effect of the boundary layers at the sliding interfaces. A recent paper by Graham and Graham [J. Acoust. Soc. Amer. 46, 169–175 (1969)], although restricted to acoustical waves, is indicative of the difficulties involved. Presently we consider shear waves in moving elastic media, having a viscous (Newtonian) fluid layer separating the sliding interfaces. The mean velocity profile in the viscous medium is prescribed by the solution of the relevant Navier‐Stokes equation and is unaffected by the perturbations. For the mean velocity profiles encountered between parallel planes and between concentric cylinders, solutions for shear waves are obtained in terms of Bessel functions. Various limiting cases are investigated.

Integral equation formulation of dynamic acoustic fluid‐elastic solid interaction problems
View Description Hide DescriptionThe interaction of waves traveling in an acoustic medium with an elastic obstacle (or vice versa) is studied by a formulation which has been useful in previous acoustic and elastic wave scattering problems. This formulation is based on an integral equation representation of wave problems and has the advantage of involving only boundary (i.e., interface) values of the unknowns, thus reducing the dimensionality of the problem. A simple example of plane wave scattering is included as an illustration for both time harmonic and transient cases as well as a spherical radiation problem to indicate the use of the procedure in a curvilinear geometry. Emphasis is on the method of approach and no new results are obtained.

Focusing of stress waves in an elastic sphere
View Description Hide DescriptionThis paper concerns the effect of focusing upon the strains in an elastic sphere excited by spherically symmetric surface loading. The analysis is carried out on the basis of the solution to the corresponding boundary‐initial value problem. This solution, which is found with the aid of the Laplace transform, is given in a form well suited to assessing the consequences of roughness in the loading.

Babinet's principle for elastic waves
View Description Hide DescriptionBabinet's principle for elastic waves gives a relationship between the displacement fields due to complementary diffracting screens. The relationship has been derived using the seismic representation theorem as the starting point. The relationship for rigid complementary screens, for stress‐free complementary screens, and for mixed rigid‐stress‐free complementary screens in each case has the same form. In deriving the relationship it is necessary to assume that the “jumps” across the complementary screens are the same as those that would exist when both complementary screens are present. This assumption has been tested in a seismic modeling experiment that utilized both stress‐free and rigid screens. The experiments show that the assumption is valid within the accuracy of the experiment and, consequently, that Babinet's principle for elastic waves is valid to the same degree of accuracy.

Geometrical theory for flexure waves in shells
View Description Hide DescriptionThe paper presents a formulation of geometrical theory for transverse flexure waves propagating in thin shells. The dynamic equations correspond to the states of vibration with large values of the index of variation (Bolotin). The basic equations of geometrical optics (the eikonal equation, the Fresnel equation, and the energy conservation law) are obtained for shells with arbitrary (smooth) metrics. Their applications are illustrated with the examples of sphere and ellipsoid of rotation.