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Journal of the Acoustical Society of America

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Nov 1951

Volume 23, Issue 6, pp. 637-719


On the Dynamics of the Cochlea

Harvey Fletcher

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 637-645 (1951); (9 pages)

Online Publication Date: 18 Jun 2005

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This paper is concerned with the dynamical behavior of the cochlea. It is assumed that a length of the basilar membrane which is equal to its width at each position vibrates as a unit, and that the forces exerted upon it by adjacent units are negligible compared to that exerted by the difference in pressure in the scala vestibuli and scala tympani. The boundary conditions at the stapes end is simply that the pressure difference in the two canals is equal to P0 any desired pressure difference. However, at the helicotrema the pressure difference must be equal to that between the two ends of the capillary opening at the helicotrema.
Then from the fundamental hydrodynamical equations and the experimental constants obtained by Békésy it is shown that the speed of sound through the liquid of the inner ear may be considered infinite compared to the speed of the wave along the basilar membrane. In other words, the liquid may be considered incompressible so that the rate of liquid displacement at the oval window is equal to that at the round window, and is also equal to that produced by flexure of the basilar for frequencies above 200 cps. Below this frequency some of the liquid goes back and forth through the helicotrema.
With these assumptions, the following quantities were calculated from the fundamental dynamical equations and found to be in good agreement with the experimental results of Békésy; (a) displacement amplitudes and phases of the basilar membrane at different distances from the stapes and for different frequencies, (b) time for wave to travel from stapes to various distances from stapes, and (c) volume displacement, at various frequencies, per dyne difference of pressure at oval window and that at round window.

On the Threshold and Loudness of Repeated Bursts of Noise

Irwin Pollack

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 646-650 (1951); (5 pages)

Online Publication Date: 18 Jun 2005

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The loudness and threshold of an interrupted white noise (of constant sound‐time fraction) was studied over a wide range of interruption frequencies. White noise has the useful property that, when interrupted, no spectral changes result in the white noise spectrum (in the frequency range passed by a dynamic earphone). Both at the threshold and at equal‐loudness, less energy is needed for an interrupted noise than for a continuous noise. In many cases, an interrupted noise (sound‐time fraction of 0.45) sounds louder than a continuous noise of the same burst amplitude (but of greater energy). There is a broad minimum, in the intensity required at equal loudness, for interruption rates between 2–10 per second. A conceptual formulation to encompass the results is presented.

Sensitivity to Differences in Intensity between Repeated Bursts of Noise

Irwin Pollack

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 650-653 (1951); (4 pages)

Online Publication Date: 18 Jun 2005

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Thresholds for the detection of a decrement in noise intensity between repeated bursts of noise were determined as a function of the duration of the interval between successive bursts. The results indicate a critical duration (55 milliseconds) between successive noise bursts: (1) above which, the differential threshold is constant and independent of the interval between successive bursts and (2) below which, the differential threshold increases proportionately as the interval between successive bursts decreases. Since an equivalent critical interval has previously been obtained by several different independent measures of auditory persistence, the observed deterioration of differential sensitivity is interpreted in terms of the overlap or addition of auditory persistence with the direct effects of stimulation.

On the Measurement of the Loudness of White Noise

Irwin Pollack

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 654-657 (1951); (4 pages) | Cited 1 time

Online Publication Date: 18 Jun 2005

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Scales of loudness for complex sounds have usually been obtained by determining the equal‐loudness relation between the complex sound under investigation and a sound for which a scale of loudness is already available, e.g., a pure tone of 1000 cps. It is possible, however, to determine scales of loudness for complex sounds without appeal to pure tones or without extrapolation from pure‐tone data. This was done in the present experiment. Loudness measurements were carried out by several independent procedures for a 1000‐ cycle tone and for white noise. The agreement among the different procedures indicates satisfactory internal consistency among the several methods of determining loudness scales. A suggested scale of loudness for white noise, based upon all available data, is presented.

Pitch and Intensity

C. T. Morgan, W. R. Garner, and Robert Galambos

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 658-663 (1951); (6 pages) | Cited 1 time

Online Publication Date: 18 Jun 2005

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This paper presents data for changes of pitch with intensity for 18 ears, for frequencies from 125 cps to 8000 cps, and for intensities up to a loudness level of approximately 100 db. There are wide individual differences, but most observers show very small changes (less than 2 percent) of pitch with intensity. In general, as intensity is increased, pitch falls at low frequencies and rises at high frequencies. Two different methods of measuring pitch‐intensity changes showed no significant difference.

Some Effects of Interaural Phase Differences on the Perception of Pure Tones

W. R. Garner and M. Wertheimer

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 664-667 (1951); (4 pages) | Cited 1 time

Online Publication Date: 18 Jun 2005

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Fifty‐four naive observers were asked to report whether they could hear a difference between two successive tones which differed only in respect to which ear was leading in phase angle. They were not given specific suggestions to listen for a particular effect, but were later asked what they had heard. Two intensities, eight frequencies, and seven phase leads were used. The major conclusions from the results are: (1) All observers heard differences due to phase and identified the differences as localization, although for most the localization was in terms of which ear was stimulated rather than in terms of apparent localization of a sound source. (2) Pitch and loudness differences also occurred, but cannot be explained on the assumption that only one ear was effectively stimulated. (3) Measures of phase‐difference thresholds, upper frequency limits, and time‐difference thresholds show approximately the same results as are obtained with other methods.

Frequency Detection and Speech Formants

E. Peterson

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 668-674 (1951); (7 pages)

Online Publication Date: 18 Jun 2005

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This study is aimed primarily at evaluating the utility of axis‐crossing detectors in tracking speech formants. Detectors of the usual type are found subject to an error, fundamental in nature. To remove this source of error speech is modulated up in frequency as a single sideband before limiting and detecting processes are applied. Experimental results with this carrier type of detector on a small number of speech samples are presented, and compared with spectrograms.
Conclusions are that the average axis‐crossing rates cannot be trusted in general to follow specific formants, whether the speech is normal or differentiated. But when the formants are sufficiently localized by frequency selectivity, prospects of tracking the lower formants look promising.

The Intervalgram as a Visual Representation of Speech Sounds

S. H. Chang, G. E. Pihl, and J. Wiren

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 675-679 (1951); (5 pages)

Online Publication Date: 18 Jun 2005

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The points of zero crossing and the points of zero slope of the oscillograms of speech sounds are considered to contain the essential information for intelligibility. The intervals between zero crossings θ0, and the intervals between zero slopes θm, are plotted as points in rectangular coordinates. The ordinate of the dot is a function of θ (θ0 or θm), and the abscissa is a function of the time of occurrence t of the particular θ. The resulting intervalgram gives a half‐tone picture (consisting of dots) of speech sounds. The patterns may be proportioned to show either a detailed or general representation of the variation of the interval distribution. One type of pattern portrayed at the speech rate on a cathode‐ray oscilloscope with a screen of long persistence has been found quite similar in certain respects to the patterns obtained using the sound spectrograph as described in the book Visible Speech by Potter, Kopp, and Green. The equipment involved in obtaining the intervalgram, however, is much simpler.

Transformer Analogs of Diaphragms

B. B. Bauer

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 680-683 (1951); (4 pages)

Online Publication Date: 18 Jun 2005

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The use of the conventional analog for diaphragms in equivalent circuits often causes serious difficulties. The action of a diaphragm is shown to be analogous to that of a system of ideal transformers, each corresponding to an area of the diaphragm. The ancillary concept of “acoustical ground” analogy is introduced to facilitate synthesis of equivalent electrical circuits. The analysis includes equivalent circuit representations of a piston diaphragm, multiple diaphragms, diaphragms with subdivided sides, and articulated diaphragms, etc., together with examples. Simultaneous use of the transformer analogy of diaphragms and the transformer analogy of transducer couplings is treated in the Appendix.

Pulse Technique for the Reciprocity Calibration of Microphones

R. L. Terry and R. B. Watson

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 684-685 (1951); (2 pages) | Cited 1 time

Online Publication Date: 18 Jun 2005

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This paper describes a pulse technique which makes possible a free‐field reciprocity calibration of a microphone indoors, without recourse to an anechoic chamber. The method is limited to frequencies above the middle audio range by consideration of the room size and pulse spectrum. An experimental calibration of a microphone is included, and waveforms are presented which demonstrate the validity of the method.

Tentative Recommended Practice for Laboratory Measurement of Airborne‐Sound Transmission Loss of Building Floors and Walls

A. London

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 686-689 (1951); (4 pages)

Online Publication Date: 18 Jun 2005

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The American Society for Testing Materials recently promulgated the tentative recommended practice which is reproduced below with the permission of that Society. As far as is known this is the first successful tentative standard which has been adopted in the field of architectural acoustics in this country, even though standardization efforts along these lines go back to the late 1930's. This specification was prepared by Subcommittee VII on Sound Transmission of ASTM Committee E‐6 on Building Constructions. The chairman of the Subcommittee is Richard K. Cook, while members of the writing group were Albert London and William A. Jack.
Copies of the specification may be obtained from the ASTM at a cost of 25 cents each. The complete unabridged tentative is as follows (the “Society” referred to in the tentative is of course the American Society for Testing Materials).

Propagation of Sound in a Duct with Constrictions

U. Ingård and D. Pridmore‐Brown

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 689-694 (1951); (6 pages)

Online Publication Date: 18 Jun 2005

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The transmission of sound through a duct periodically loaded with constrictions (iris partitions) is studied. The attenuation as a function of frequency in such ducts both with hard and absorptive side walls is given. In the case of a hard‐walled duct the results of the analysis are presented in chart form. It is shown that by proper choice of side wall absorption and iris partitions a broad attenuation band can be obtained. Measured values of the attenuation are found to be in good agreement with the theory.

A Piezoelectric Method for Determining Young's Modulus and Its Temperature Dependence

H. E. Stauss, F. E. Martin, and D. S. Billington

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 695-696 (1951); (2 pages)

Online Publication Date: 18 Jun 2005

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A resonance method for determining Young's modulus in metals, based on support of the specimen at its central node for longitudinal vibrations, with the supporting rod articulating at its lower end with a piezoelectric crystal, has been developed. Utility of the method was extended by adapting it to measurement of changes in Young's modulus with temperature.

On the Relation between the Sound Fields Radiated and Diffracted by Plane Obstacles

Francis M. Wiener

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 697-700 (1951); (4 pages) | Cited 3 times

Online Publication Date: 18 Jun 2005

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In the past, acoustic diffraction and radiation problems have often been treated separately, although their intimate connection is clear from theory. In the case of plane piston radiators and plane rigid scatterers exposed to a perpendicularly incident plane wave, this connection becomes particularly simple and useful. It is easy to show that the radiated sound field is everywhere the same as the field scattered (diffracted) in the diffraction case, except for a factor of proportionality. It is also shown that the reaction of the medium on the radiator, as expressed by the mechanical radiation impedance, is equal to the force per unit incident pressure exerted on the same obstacle, held rigid as a scatterer, except for a factor of proportionality. By way of illustration, the foregoing principles are applied to the important case of the circular disk.

The Scattering of Sound from a Prolate Spheroid

R. D. Spence and Sara Granger

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 701-706 (1951); (6 pages) | Cited 11 times

Online Publication Date: 18 Jun 2005

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This paper presents the results of calculations of the scattering of a plane sound wave from a prolate spheroid. Scattering patterns are given for the major axis equal to λ/π, 2λ/π, 3λ/π, for the ratio of axes equal to 0.10, 0.20, 0.29, 0.37, and for the angle of incidence measured from the major axis equal to 0°, 30°, 60°, 90°.

Field and Impedance of an Oscillating Sphere in a Viscoelastic Medium with an Application to Biophysics

Hans L. Oestreicher

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 707-714 (1951); (8 pages) | Cited 24 times

Online Publication Date: 18 Jun 2005

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With an application to human tissue in view, a theoretical analysis of the behavior of mechanical vibrations in a medium with elastic, viscous, and relaxational properties is made. For this purpose, the equations of wave motion in a viscoelastic medium are discussed in general and solved for two problems, which are significant for the propagation and the transfer of vibrational energy: (1) energy propagation and absorption in plane waves, (2) field and impedance of an oscillating sphere.
The results show that the energy is propagated in two kinds of waves, the relative intensities of which change strongly with frequency: transverse waves, owing to the shear elasticity and viscosity, and compression (acoustical) waves, owing to the volume compressibility of the medium. A more detailed treatment is then accomplished for human muscle tissue by inserting the approximate values of its elastic constants into the general formulas, thus explaining the behavior in a frequency range from 0 up to several hundred kc.
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The Velocity of Sound at Reduced Pressures

P. W. Smith, Jr.

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 715-715 (1951); (1 page)

Online Publication Date: 18 Jun 2005

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Abstract Unavailable

Propagation of Sound in Carbon Dioxide at High Pressures

Glenn C. Werth

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 715-716 (1951); (2 pages)

Online Publication Date: 18 Jun 2005

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The Calculation of the Thermal Noise in Air

L. L. Boyarsky

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 716-716 (1951); (1 page)

Online Publication Date: 18 Jun 2005

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Physiological Demonstration of a Property of the Inner Ear Predicted by Békésy's Model

Karl Lowy

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 716-717 (1951); (2 pages)

Online Publication Date: 18 Jun 2005

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A Theory of the Action of the Cochlear Resonators

R. Guelke

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 717-719 (1951); (3 pages)

Online Publication Date: 18 Jun 2005

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The hypothesis is put forward that the mechanism of hearing may involve a building up of vibrations, and the damping of these vibrations when they reach a definite amplitude. This is able to explain the conversion of sound intensity reaching the ear into impulse frequency as measured on the nerve fibers. The hypothesis also reconciles the speed of response of the ear with the high pitch sensitivity and consequent sharpness of resonance of the aural resonators. A model is described which converts amplitudes into pulse frequencies by using a damping mechanism when a definite amplitude is reached.

C.I.D. Auditory Tests W‐1 and W‐2

R. W. Benson, H. Davis, C. E. Harrison, I. J. Hirsh, E. G. Reynolds, and S. R. Silverman

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 719-719 (1951); (1 page)

Online Publication Date: 18 Jun 2005

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Errata: The Theory of Steady Forces Caused by Sound Waves [J. Acoust. Soc. Am. 23, 312 (1951)]

P. J. Westervelt

J. Acoust. Soc. Am. Volume 23, Issue 6, pp. 719-719 (1951); (1 page) | Cited 1 time

Online Publication Date: 18 Jun 2005

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Abstract Unavailable
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