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Journal of the Acoustical Society of America

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Jun 1974

Volume 55, Issue 6, pp. 1123-1361

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Acoustic reflection from elastic spheres. I. Steady‐state signals

Werner G. Neubauer, Richard H. Vogt, and Louis R. Dragonette

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1123-1129 (1974); (7 pages) | Cited 11 times

Online Publication Date: 12 Aug 2005

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Measurements are made of the acoustic reflected pressure from aluminum and tungsten‐carbide spheres for ka values between 5 and 20. Only the farfield monostatic case is considered. Experimental values are compared to a harmonic‐wave solution. Excellent agreement is observed when the wave speeds in the sphere material are adjusted by an amount smaller than the known uncertainty in the wave‐speed values in the solids. The position of rapid changes in the reflection solution with ka is found to be very sensitive to shear‐wave speed and insensitive to longitudinal‐wave speed. The sensitivity to ambient temperature of the position of a selected minimum in the reflection solution is examined computationally for an aluminum sphere. A shift in the value of ka at which a minimum is calculated is also observed experimentally. Long pulses are used to approximate steady‐state conditions and agreement with the steady‐state theory shows that this approximation is adequate.

Acoustic reflection from elastic spheres and rigid spheres and spheroids. II. Transient analysis

Louis R. Dragonette, Richard H. Vogt, Lawrence Flax, and Werner G. Neubauer

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1130-1137 (1974); (8 pages) | Cited 7 times

Online Publication Date: 12 Aug 2005

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Curves relating the reflected acoustic pressures to frequency for a rigid sphere and spheroid and for elastic spheres of aluminum, brass, and tungsten carbide in water are obtained. Experimental measurements using single short acoustic pulseforms are compared with theory. Excellent agreement is obtained for the limited ranges of ka over which the experiments were done. Only the case of monostatic reflection is considered.

Wave propagation in elastic rings and helical coils of small pitch

D. W. Haines, N. Chang, and C. H. Huang

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1138-1143 (1974); (6 pages)

Online Publication Date: 12 Aug 2005

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The problem of harmonic waves propagating around an elastic ring is formulated in generalized plane stress and solved. Three dispersion curves can be described. The wavenumber of the first branch is always real, but the second and third possess segments of real, imaginary, and complex wavenumbers. The third branch has a narrow range at low frequencies, for which the phase and group velocities are of opposite sign. As the wavelengths become progressively shorter, the dispersion curves approach their counterparts for straight bars. The solution is also valid for helical coils of small pitch and, when converted to plane strain, for similar waves in cylindrical shells and cylinders.

Acoustic waves from an impulsive source in a fluid‐filled borehole

W. L. Roever, J. H. Rosenbaum, and T. F. Vining

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1144-1157 (1974); (14 pages) | Cited 9 times

Online Publication Date: 12 Aug 2005

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Acoustic waves generated by an impulsive source in a fluid‐filled borehole have been experimentally measured and theoretically analyzed by means of modal and ray‐type expansions. Outstanding features of the response are obtained in closed‐form expressions, which are leading terms of asymptotic series. For source and detector near the borehole axis, the first refracted P‐arrival decays approximately as 1/(z log2 z), where z is the nondimensional axial source‐to‐detector distance. The first refracted S‐arrival is much larger for moderate z, but decays as 1/z2. The relation between the S‐arrival and “pseudo‐Rayleigh” wave is discussed on the basis of modal theory; a simple description of the “tube wave” in terms of integrals of Airy functions is presented. In the radial‐ray picture, the borehole axis is a caustic, where rays are subjected to a 90° phase shift; for the pulse problem, the waveform is replaced by its Hibert transform. The simple theoretical expressions agree with the results of model studies. For source and detector located off the borehole axis, the observed signal is more complicated. This can be ascribed to the fact that a number of circumferential modes can enter into the description of the response.

Multiple eigenvalues of sound‐absorbing circular and annular ducts

William E. Zorumski and Jean P. Mason

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1158-1165 (1974); (8 pages)

Online Publication Date: 12 Aug 2005

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Eigenvalue equations of the form D(λ)=0 are studied for acoustic modes in circular and annular ducts without flow. The ducts have locally reacting walls with arbitrary wall admittance. It is shown that circular duets may have double eigenvalues, or wall admittances where both D(λ) and D′(λ) are zero. These double eigenvalues are formed by the coalescence of the lowest‐order eigenfunction with some higher‐order eigenfunction. The eigenfunctions, or acoustic modes, associated with the double eigenvalues are found to be orthogonal to themselves so that the standard expansion formula for the acoustic field, which is obtained from a separation of variables analysis, is invalid. An alternate expansion formula for the acoustic field is derived. This alternate formula shows that the coalesced acoustic mode is linearly amplified by the transmission distance and exponentially attenuated at the expected rate. The expansion formula also reveals a new eigenfunction, or acoustic mode, which is exponentially attenuated the same rate as the coalesced eigenfunction. It is shown that annular ducts may have double eigenvalues for arbitrary values of one of the wall admittances. Annular ducts may also have triple eigenvalues, or selected values of the wall admittances, where D(λ), D′(λ), and D″(λ) are all zero. The associated triple eigenfunctions are shown to be self‐orthogonal. The expansion formula for the sound field in an annular duct with a triple eigenvalue shows a quadratically amplified acoustic mode, a new linearly amplified mode, and another new mode, all of which are exponentially attenuated at the same rate. Methods of calculating single eigenvalues by means of numerically integrating ordinary differential eigenvalue equations are given and discussed with regard to multiple eigenvalues. Results are presented showing double eigenvalues of circular and annular ducts and triple eigenvalues of annular ducts.

Nonlinear acoustic propagation in two‐dimensional ducts

Ali Hasan Nayfeh and Ming‐Shing Tsai

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1166-1172 (1974); (7 pages) | Cited 3 times

Online Publication Date: 12 Aug 2005

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The method of multiple scales is used to obtain a second‐order uniformly valid expansion for the nonlinear acoustic wave propagation in a two‐dimensional duct whose walls are treated with a nonlinear acoustic material. The wave propagation in the duct is characterized by the unsteady nonlinear Euler equations. The results show that nonlinear effects tend to flatten and broaden the absorption versus frequency curve, in qualitative agreement with the experimental observations. Moreover, the effect of the gas nonlinearity increases with increasing sound frequency, whereas the effect of the material nonlinearity decreases with increasing sound frequency.

Discrete tones of isolated airfoils

Christopher K. W. Tam

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1173-1177 (1974); (5 pages) | Cited 4 times

Online Publication Date: 12 Aug 2005

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Recent experimental measurements reveal that discrete tones are emitted by isolated airfoils under certain operating conditions. Arguments are presented that these tones are unrelated to vortex shedding processes as has been suggested. It is proposed that the tones are generated by a self‐excited feedback loop of aerodynamic origin. The loop consists of large‐scale unstable disturbances in the boundary layer and wake flow and the feedback acoustic waves. Quantitative deductions based on the feedback loop model compare favorably with experimental measurements. It is also found that the proposed model is consistent with the observed characteristic features associated with the discrete tone phenomenon.

Analysis of the effect of a Rossby wave on sound speed in the ocean

R. N. Baer and M. J. Jacobson

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1178-1189 (1974); (12 pages)

Online Publication Date: 12 Aug 2005

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The effects of an assumed Rossby wave on density, pressure, current, and sound speed are examined and analyzed. It is shown that the zeroth‐mode wave solution has only slight effect on sound speed, while the first‐mode solution is significant. A dispersion relation is developed, having as one solution an east‐west wavelength of 210 nautical miles and a period of 114 days, for parameters consistent with the Sargasso Sea area. This first‐mode solution predicts the gross behavior of observed sound speed versus depth variations, and provides striking agreement with measured curves of constant sound speed. The addition of a second‐mode solution to the first leads to a crossover of sound‐speed profiles in qualitative agreement with observations.

Underwater sound transducer beam control with reflectors

C. M. McKinney and R. H. Wallace

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1190-1196 (1974); (7 pages)

Online Publication Date: 12 Aug 2005

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Several underwater sound reflector‐transducer systems are described, and experimental data are presented to show the relationship between aperture size, near‐focal distance, depth of focus, beamwidth, minor lobe characteristics, and test distance for circular, parabolic, and elliptical converging reflectors. In addition, transducer systems using planar and diverging reflectors are described, and sets of experimental data are presented to demonstrate the beam formation characteristics of those systems.

Averaged sound transmission in range‐dependent channels

P. W. Smith, Jr.

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1197-1204 (1974); (8 pages) | Cited 3 times

Online Publication Date: 12 Aug 2005

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We derive an integral formula as an estimate of the averaged, steady‐state transmission ratio for two points in a channel whose environmental parameters vary slowly with range. We base the derivation on the theory of ray acoustics with lossy specular reflection from the boundaries. The averaging eliminates all but gradual changes with range of the transmission loss (TL); dependence on the depth of each point is retained. Detailed tracing of ray paths over many cycles is not required. Numerical results for an isogradient channel with constant bottom slope are exhibited, and an appendix contains modal interpretation of the general formulation.

Direct measurement of surface‐scatter channel coherence by impulse probing

J. G. Zornig and J. F. McDonald

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1205-1211 (1974); (7 pages)

Online Publication Date: 12 Aug 2005

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A method of studying the statistical properties of the random time‐varying surface‐scatter channel using ultrasonic scale modelling and using a novel digital‐probing system is discussed. Measurements of the coherent transfer function of such channels are presented and are shown to be in minor disagreement with existing theoretical predictions. Various mechanisms to explain this disagreement are explored leading to the tentative conclusion that a violation of the Kirchhoff condition is probably responsible for the effect observed.

Rayleigh‐wave reflection from groove and step discontinuities

Hang‐Sheng Tuan and Robert C. M. Li

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1212-1217 (1974); (6 pages) | Cited 17 times

Online Publication Date: 12 Aug 2005

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In an important new class of signal‐processing devices using elastic surface waves, the reflection of a Rayleigh wave from grooves is a key feature. In the present paper, a boundary‐perturbation technique is employed to determine the reflection of a Rayleigh wave from either a shallow groove or a low step in the surface of an isotropic elastic half‐space. Comparison with available experimental data for the case of the rectangular groove and step yields excellent agreement.

Ultrasonic holography free from phase turbulence

Mitsuhiro Ueda, Takuso Sato, and Osamu Ikeda

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1218-1224 (1974); (7 pages)

Online Publication Date: 12 Aug 2005

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It is well known in the field of ultrasonic holography that the formation of a hologram is affected seriously by the presence of turbulence inside the medium in which ultrasonic waves propagate; especially in case of large phase turbulence, it becomes almost impossible to reconstruct the image from the hologram. In this paper, a principle of a new method of reducing the effect of the fluctuation on the detected hologram by using a stochastic processing of the signal is proposed. The basic idea is to estimate the mean values of the phase and the amplitude of the ultrasonic signal separately and then combine these two averaged values to get the ultrasonic signal which would be obtained in the absence of turbulence. By constructing models of a turbulent medium, the effect of this processing is studied and the result of computer simulation which demonstrates the usefulness of this method is presented. In addition, such usefulness is shown by the experimental result obtained by using a device which was constructed to verify the principle.

Fundamental‐frequency approximation methods

Harry Herman and Robert P. Kirchner

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1225-1231 (1974); (7 pages)

Online Publication Date: 12 Aug 2005

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The vibration of a sandwich plate is used, as an illustrative problem, to evaluate the effectiveness of some methods of obtaining one‐term approximations for the lowest eigenvalue of coupled systems. It is shown that, in using a method of weighted residuals, the boundary conditions satisfied by both the trial and the weighting function play significant roles in the accuracy of the eigenvalue. Moreover, the desired boundary conditions for the weighting function may differ from those of the trial function, so that the Galerkin method, in which the trial function and weighting function coincide, may not be the best method to use. In addition, it is shown that the values of some physical parameters may play a critical role in the accuracy obtained with a given trial function. It is demonstrated that good approximations of the fundamental frequency are obtainable upon uncoupling a set of differential equations, but uncoupling may lead to non‐self‐adjoint boundary conditions, in which case the weighting function should satisfy boundary conditions which are adjoint to those of the trial function. Attention is also called to a method, due to Lanczos, which does not require a choice of trial or weighting functions, is insensitive to the form in which the problem is stated, appears to require less effort for a given degree of accuracy, and is applicable to non‐self‐adjoint as well as self‐adjoint systems.

Natural vibrations of systems of elastically connected Timoshenko beams

S.S. Rao

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1232-1237 (1974); (6 pages) | Cited 1 time

Online Publication Date: 12 Aug 2005

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The differential equations governing the flexural vibrations of systems of elastically connected parallel bars are derived considering the effects of rotary inertia and shear deformation. These equations are solved to find the natural frequencies and mode shapes of particular three‐ and two‐beam systems. For the two‐beam system, the present results are compared with the available experimental values.

Axisymmetric vibrations of laminated composite cylindrical shells

Chang‐Tsan Sun and J. M. Whitney

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1238-1246 (1974); (9 pages) | Cited 1 time

Online Publication Date: 12 Aug 2005

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A refined theory of vibration of laminated composite thick shells is developed. The present theory includes the effects of transverse shear deformation, transverse normal stress and strain, rotary inertia, and higher‐order stiffness terms. Numerical results of natural frequencies under axisymmetric vibrations for graphite‐epoxy composites are evaluated and compared to results obtained from Flugge's theory. A significant difference between these two results is observed for shells having relatively large thickness‐to‐length ratio.

Spectrum of rotor noise caused by inlet guide vane wakes

Donald B. Hanson

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1247-1251 (1974); (5 pages)

Online Publication Date: 12 Aug 2005

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A blade loading model is formulated for the interaction of an axial‐flow fan rotor with turbulent wakes from inlet guide vanes. From this, the spectra of both the blade lift and the associated sound field are computed. The analysis and results arc similar to those in the analogous case treated previously by the author for a stator interacting with the wakes from an upstream rotor [D. B. Hanson, “Unified Analysis of Fan Stator Noise,” J. Acoust. Soc. Am. 54, 1571–1591 (1973)]. The turbulence in the wakes causes a smooth broad‐band spectrum component, while the spatially periodic portion of the wakes causes periodic components in the blade lift and sound field. The spectrum peaks do not exhibit bandspreading or “haystacking,” except for fans with inlet guide vane wakes which are wider than the gap between adjacent rotor blades.

Cochlear partition stiffness—a composite beam model

P. Allaire, S. Raynor, and M. Billone

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1252-1258 (1974); (7 pages) | Cited 2 times

Online Publication Date: 12 Aug 2005

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A mathematical model of the human cochlear partition is developed to investigate the partition's stiffness. To date, no experiment has been performed on the partition to determine the difference between the dynamic and the statically measured stiffness. Nonlinearities observed in the partition's dynamic motions and dynamic stiffness measurements on bone and muscle tissue indicate that previous investigations of the cochlear partitions's stiffness may not be adequate. In this study the cochlear partition is modeled by a series of composite beams whose stiffness is due to linear bending rigidity at normal amplitudes of motion. At larger amplitudes (in the nonlinear range near the threshold of pain), the model's stiffness is increased, owing to the nonlinear stretching of the basilar membrane. The model also includes the increase in stiffness, above the static stiffness, due to dynamic loading, as observed in the studies of bone and muscle tissue. The dynamic cochlear partition stiffness predicted by this model increases approximately by a factor of 100 from apex to base. Except near the stapes, the model's stiffness in the linear range at 100 Hz is approximately the same as measured statically. At 10 000 Hz the model's stiffness in the linear range is nearly twice as large as the statically measured value.

Lateralization and the binaural masking‐level difference

G. Bruce Henning

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1259-1262 (1974); (4 pages) | Cited 2 times

Online Publication Date: 12 Aug 2005

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Observers can readily detect interaural delays in certain complex waveforms even when the energy in the waveform is confined to high‐frequency regions. However, the detectability of such complex waveforms is not measurably dependent on interaural phase—that is, there is no masking‐level difference with high‐frequency signals in spite of the fact that interaural phase effects are readily observed as changes in the apparent location of the source of the signal.

Binaural interaction in cat and man. I. Signal detection and noise cross correlation

Susan A. Hoppe and Ted L. Langford

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1263-1265 (1974); (3 pages)

Online Publication Date: 12 Aug 2005

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See Also: Erratum

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Detection of diotic 500‐Hz tones partially masked by diotic and dichotic noise was studied in the cat and compared with similar detection data for man. The interaural correlation of the masker was varied by delaying the channel to one ear from 0 to 5 msec in steps of 1 msec. An avoidance response was used to measure detectability. The absolute sensitivity of the cat was less than that of man and smaller MLDs were found for the cat at each delay. The temporal interval over which the binaural system of the cat is able to effect a correlation between events occurring at the two ears was estimated to be smaller, while the critical band appears to be wider than in man.

Intensity and frequency discrimination in one‐ and two‐interval paradigms

Walt Jesteadt and Robert C. Bilger

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1266-1276 (1974); (11 pages) | Cited 13 times

Online Publication Date: 12 Aug 2005

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Both intensity and frequency discrimination data were collected for the same four subjects using several psychophysical paradigms. No differences were observed that would indicate that frequency discrimination involves fundamentally different decision‐making processes than intensity discrimination. In both cases, performance in a two‐interval forced‐choice task exceeded performance in a yes‐no task by a factor greater than the generally predicted √2. Consistent individual differences were observed in frequency discrimination but not in intensity discrimination.

Localization of paired sound sources in the rat: small time differences

Jack B. Kelly

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1277-1284 (1974); (8 pages) | Cited 7 times

Online Publication Date: 12 Aug 2005

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Seventeen albino rats were trained to perform two sound‐localization tasks with single and paired sound sources. The conditioned suppression of a licking response was used as a behavioral measure. All animals were first trained to detect a change from a series of single clicks on the left to a series on the right. They were then given further training with paired clicks separated by a small time interval; the discrimination was between left‐right pairs and right‐left pairs. The intervals used were 0.5, 1.0 2.0, 4.0, 8.0, 16.0, 20.0, and 32.0 msec. Five animals were given further tests with smaller values using the method of constant stimuli. Additional values tested were 31, 62, 125, and 250 μsec. Transition from single clicks to paired clicks was good for values between 0.5 and 4.0 msec. An ability to discriminate paired clicks was easily demonstrated for values between 0.25 and 16.0 msec. The upper limit for discrimination was somewhere between 20.0 and 32.0 msec. The lower limit for discrimination was between 31 and 62μsec. These results were discussed in relation to the precedence effect in human hearing.

Equal aversion levels for pure tones and 1/3‐octave bands of noise

John A. Molino

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1285-1289 (1974); (5 pages)

Online Publication Date: 12 Aug 2005

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College students tapped rapidly on a telegraph key to reduce the intensity of a continuous acoustic stimulus presented through earphones. Failure to respond resulted in an intensity increase of 1 dB every 4 sec. A group of 14 students responded during 10‐min sessions to eight pure tones and eight 1/3‐octave bands of noise at octave frequencies from 63 Hz to 8 kHz. The average SPL maintained by the subjects became stable after about 5 min. The different asymptotic levels observed from 5–10 min were taken as a measure of equal aversion levels for the stimuli. Equal aversion levels were compared with other subjective weighting contours: equal loudness level, A‐weighted sound level, perceived noise level, etc. They were closest to an A‐weighted sound level of 80–85 dB.

Detection of interaural onset and offset disparities

David R. Perrott and Bernard J. Baars

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1290-1292 (1974); (3 pages) | Cited 1 time

Online Publication Date: 12 Aug 2005

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Interaural time difference thresholds for transient differences in signal onset and offset were examined. Lateralization of the acoustic image to either onset or offset transients was observed with signal pulses 1 and 10 msec in duration but not with longer pulses. Interaural difference thresholds for signal onset were observed with smaller time disparities than those obtained with signal offset transients. Both onset and offset transient thresholds were inversely related to signal duration and directly related to signal correlation.

Binaural masking level differences for pulse train signals of differing interaural correlation

Lawrence D. Pohlmann and Robert D. Sorkin

J. Acoust. Soc. Am. Volume 55, Issue 6, pp. 1293-1298 (1974); (6 pages)

Online Publication Date: 12 Aug 2005

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Binaural masking level differences (BMLDs) were obtained for pulse train signals in a 2IFC task in which the noise (Nπ) level was controlled by a PEST program. The signal in one channel was a random polarity (+1, −1) pulse train composed of 60 100‐μsec‐duration pulses with an interpulse period of 2 msec. Signal correlation was varied by modifying the signal in the contralateral channel. The correlation was varied by (a) randomly inverting some of the pulses, (b) randomly deleting some of the pulses, (c) deleting or inverting some of the pulses contingent on their polarity, or (d) delaying the pulses by an integral number of pulse periods. The data were compared to predictions generated from Osman's correlation model. Performance was found to be accurately predicted by the model for conditions (a), (b), and (d). Differences between the model and the data for condition (c) were explained in terms of changes in the monaural detectability of the contralateral signal.
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