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Journal of the Acoustical Society of America

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Dec 1962

Volume 34, Issue 12, pp. 1819-2005

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Frequency‐Correlation Functions of Frequency Responses in Rooms

M. R. Schroeder

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1819-1823 (1962); (5 pages) | Cited 14 times

Online Publication Date: 26 Jul 2005

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A mathematical study of the random interference of sound waves in large rooms requires statistical methods. “Statistical wave acoustics” is based on the random interference of many simultaneously excited normal modes of a room. In general, the random interference takes place for frequencies above 2000 (T60/V)½, where T60 is the reverberation time (in sec) and V is the volume (in m3) of the room. In the statistical theory, frequency responses between two points in a room are treated as random functions. The probability distributions, correlation functions, and “spectra” of these random functions are determined by physical parameters such as the distance between source and receiver, the volume and reverberation time of the room (or distribution of reverberation times), etc.
In this paper, correlation functions of frequency responses are derived for rooms with uniform reverberation time, and negligible direct sound transmission between source and receiver. Analytic formulas for the following frequency correlation functions are found: the autocorrelation functions of the real and imaginary parts, the modulus and the squared modulus of the frequency response, and the cross correlation function between real and imaginary parts of the frequency response.
The significance of these correlation functions in room acoustics is discussed. Measurement of the autocorrelation function of the real (or imaginary) part of the frequency response allows a precise determination of the distribution of reverberation times. The autocorrelation function of the modulus (or squared modulus) determines the required frequency shift in public address systems to improve their stability. For measurement of electroacoustic transducers in reverberation chambers, optimum bandwidths of noise or warble tones are obtained.

Binaural Detection of Single‐Frequency Signals in the Presence of Noise

Mark B. Gardner

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1824-1830 (1962); (7 pages) | Cited 1 time

Online Publication Date: 26 Jul 2005

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The effect of phase and pressure‐level differences on the detectability of single‐frequency signals in the presence of noise is presented for listening over of a binaural transmission system. During the several tests to be described, the two microphones were supported in free space both in the absence and in the presence of various approximations to an artificial head. The results indicate that over‐all detectability is a function of the combined binaural phase relationships of both signal and noise and of the monaural intensity relationship of the two signals at the ear having the higher signal to noise ratio. Some indication was found that phase differences may influence detectability to frequencies as high as 2000 cps. Pressure‐level differences, on the other hand, decrease in magnitude with decreasing frequency until only a small effect remains at 250 cps.

Evidence that the Lateral‐Line Organ Responds to Near‐Field Displacements of Sound Sources in Water

Gerard G. Harris and Willem A. van Bergeijk

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1831-1841 (1962); (11 pages) | Cited 2 times

Online Publication Date: 26 Jul 2005

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The lateral‐line organ of killifish is shown to be sensitive to a linear function of water displacements associated with the near‐field of sound sources, with the displacement probably being the most important factor rather than velocity or acceleration. The near‐field effect is discussed and is shown to be important not only for the lateral‐line organs but also for the acoustical and vestibular organs. It is emphasized that the near‐field effect introduces considerable complications into the study of the acoustico‐lateralis system, and is of conceptual importance for the theory of hearing and the study of schooling fish.

Energy‐Detection Model for Monaural Auditory Detection

Sheila M. Pfafflin and M. V. Mathews

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1842-1853 (1962); (12 pages) | Cited 2 times

Online Publication Date: 26 Jul 2005

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In the auditory detection of a sinusoidal signal in the presence of random noise, it has previously been demonstrated that the presence of a “pedestal” or background sinusoid of the same frequency and phase as the signal increases detectability. This increase was confirmed in a two‐interval forced choice experiment in which a 1000‐cps sinusoid was present in one of two 0.1‐sec intervals, and the noise plus pedestal were present in both intervals. Pedestals of moderate intensity in phase with the signal increased detectability. Pedestals in quadrature (90° out of phase) with the signal did not improve detectability. Very large pedestals decreased detectability irrespective of phase. A simple energy‐detection model was developed and its performance compared with the experimental results. The model consists of a bandpass filter, a square‐law element, and an integrator. The probability of correct detection varies with signal level in a manner similar to the auditory results. Detectability is improved by an in‐phase pedestal and approaches that of a correlation detector in the limit of infinite pedestal. Detectability is not improved by quadrate pedestals. The model can be modified to predict the decreasing detectability with large pedestals.

Perception of Steady and Intermittent Sounds with Alternating Noise‐Burst Stimuli

Willard R. Thurlow and Anita E. Marten

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1853-1858 (1962); (6 pages)

Online Publication Date: 26 Jul 2005

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Bursts of high‐pass filtered thermal noise coming from two different sources in space were alternated in time (with no time gap between bursts). Separation angles between sources from 5 to 50 deg were used, and alternation rates from 2 to 14 per sec. Duration of bursts was also varied. Subjects indicated for each sound perceived whether it was steady or intermittent, and where it was located.
When the angle between sources is small, some subjects may hear only one continuous sound, provided that the repetition rate is relatively high. More commonly, however, our subjects tend to hear one steady sound and one intermittent sound when the separation angle between sources is small; they tend to hear this pattern at wider separation angles when the duration of one of the stimuli is short. When one of the bursts has short duration, and sources are separated by 30 to 50 deg, it appears to many subjects that the short burst is markedly displaced in location. For wider angles of separation between sources, and various conditions of duration, many subjects can also hear a third steady sound between the other two. Occurrence of this latter sound has especially interesting implications for a theory of sound‐localization mechanisms.

Crest and Extremal Statistics of a Square‐Law‐Derived Random Process

T. I. Smits, D. A. Smith, and R. F. Lambert

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1859-1864 (1962); (6 pages)

Online Publication Date: 26 Jul 2005

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Theoretical analysis of the crest and extremal statistics of a square‐law‐derived random process is presented. The differences between the crest and the extremal statistics, particularly the bandwidth dependence of the latter, are illustrated for the Gaussian‐derived case. The theory is applied to the statistical response of a uniform bar in tension. Particular attention is paid to the crest distributions which deviate from the integrated Rayleigh distributions in a predictable way at large amplitudes of vibration. Experimental distributions obtained from the strain response of a uniform bar forced in its fundamental mode by band‐limited Gaussian white‐noise signals are in excellent agreement with calculated values.

Analysis of Nasal Consonants

Osamu Fujimura

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1865-1875 (1962); (11 pages) | Cited 6 times

Online Publication Date: 26 Jul 2005

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The sound spectra of nasal murmurs in various vowel contexts have been studied by use of an analysis‐by‐synthesis scheme. The acoustic characteristics are described in terms of format‐antiformant distributions (pole‐zero locations of the transfer function for the articulatory system) in the frequency domain. It is shown that the location of the antiformant characterizes the murmur of each consonant within the class. The spectral structures are discussed with reference to the articulatory features, and acoustical interpretations of the observed characteristics of the formants and antiformant are given. Also suggested is the existence of certain gross spectral features that are characteristic of nasals as a class.

Perception of Two‐Component Noise Bursts

K. N. Stevens, T. T. Sandel, and A. S. House

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1876-1878 (1962); (3 pages)

Online Publication Date: 26 Jul 2005

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In a series of experiments, listeners were asked to make judgments of the relative duration, loudness, and stress associated with the components of stimuli consisting of sequences of two noise bursts. The over‐all duration of each stimulus was the same, and the two components were given various relative intensities and durations. All response sets demonstrate marked asymmetry, particularly those requiring a judgment of the stress pattern of the sequence.

Bonding Methods and a Bonding Clamp for Ultrasonic Measurements

Paul F. Sullivan

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1879-1882 (1962); (4 pages)

Online Publication Date: 26 Jul 2005

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The results of an experimental investigation into the techniques of coupling the transducer to the specimen in making ultrasonic measurements are presented. Two major couplants, glycerine and phenyl salicylate, were subjected to tests. As a result of these tests, a bonding clamp was developed that greatly increased the reproducibility and accuracy of the measurements.

Measurement of Small Values of Electromechanical‐Coupling Coefficient in Piezoelectric Transducers

Kimio Shibayama

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1883-1886 (1962); (4 pages) | Cited 1 time

Online Publication Date: 26 Jul 2005

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The electromechanical‐coupling coefficient of a piezoelectric transducer k is usually derived from the difference between resonance and antiresonance frequencies for a particular mode. However, if the mechanical Q of the transducer Qm is low, i.e., k2Qm < 2, this relationship breaks down. The region k <20% and 100 <Qm <1000 has been analyzed and the resulting formulas processed by computer. The final data are presented in graphical form, making it possible to derive accurate values of k and Q from observations of the magnitudes and frequencies of the impedance maximum and minimum.

Mechanism of Interaction between Vibrations and Heat Transfer

R. M. Fand

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1887-1894 (1962); (8 pages)

Online Publication Date: 26 Jul 2005

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Several different hypotheses have been proposed in the literature to explain the physical mechanism whereby transverse vibrations increase the rate of heat transfer by free convection from horizontal cylinders. The present paper contains a discussion of the validity of these hypotheses in the light of recent experimental data.

Vibrations of an Infinite, Monoclinic Crystal Plate at High Frequencies and Long Wavelengths

R. K. Kaul and R. D. Mindlin

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1895-1901 (1962); (7 pages) | Cited 2 times

Online Publication Date: 26 Jul 2005

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An asymptotic solution of the frequency equation of an infinite, monoclinic crystal plate is derived. Formulas are given which describe the variation of frequency with wavelength at high frequencies and long wavelengths.

Frequency Spectrum of a Monoclinic Crystal Plate

R. K. Kaul and R. D. Mindlin

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1902-1910 (1962); (9 pages) | Cited 2 times

Online Publication Date: 26 Jul 2005

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A sketch is constructed of the branches of Ekstein's frequency equation for an infinite, monoclinic crystal plate. The sketch is for the AT cut of quartz and covers a wide range of frequencies and propagation constants. The real, imaginary, and complex segments of the branches are included.

Extensional Vibrations of Thin Quartz Disks

A. G. Lubowe and R. D. Mindlin

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1911-1918 (1962); (8 pages)

Online Publication Date: 26 Jul 2005

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A general solution is given for the contour modes of vibration of circular crystal disks of certain elastic symmetries. The solution is applicable to three cuts of quartz, for which the frequencies of fourteen modes are computed.

Experimental Determination of Compressional Velocity for the Bottom Layer by the Dispersion Method

P. A. Barakos

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1919-1926 (1962); (8 pages) | Cited 1 time

Online Publication Date: 26 Jul 2005

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Pressure waves, generated different points along radial runs on the continental shelf and slope south of Long Island by 1‐1b explosions of TNT, were received by hydrophones connected by sea cables to a fixed station in the ocean. An extensive analysis of the dispersion phenomenon in the water wave covering five radial courses within a 150‐mile radius of the receiving station was made. Nearly 500 charges were examined in this analysis, and the “seasonal” effect upon dispersion was investigated. In general, for shallow water the received pressure wave displays certain features that are characteristic of the depth of the water, the velocity‐depth contour in the water, the range, and the structure of the bottom. Dispersion in the water wave was also observed in a surface channel formed in moderately deep water. The observed dispersion phenomena were studied quantitatively, and the data were interpreted in terms of the bottom structure. Two‐ and three‐layer liquid models were employed to interpret the experimental results. An expression is presented that relates all the parameters pertinent to the dispersion phenomenon.

Variation of Array Performance with Respect to Statistical Phase Fluctuations

J. L. Brown, Jr.

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1927-1928 (1962); (2 pages)

Online Publication Date: 26 Jul 2005

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The effect of phase fluctuations on the mean‐square time‐averaged output of a discrete linear array is considered under the assumption that the fluctuations are governed by a Gaussian joint‐probability density function. In particular, a closed‐form expression is derived for the variance of the array output over the ensemble of phase variations.

Theoretical Analysis of the Scattering of Short Acoustic Pulses by a Thin‐Walled Metallic Cylinder in Water

C. W. Horton, W. R. King, and K. J. Diercks

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1929-1932 (1962); (4 pages) | Cited 1 time

Online Publication Date: 26 Jul 2005

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A theoretical analysis given of the scattering of plane acoustic waves by a thin‐walled metallic cylinder in water. It is shown that a surface wave of low attenuation is propagated around the cylinder as a flexural vibration and that this wave acts as the “creeping” wave discussed by Franz. The phase velocity of this wave depends on frequency so that one must use group velocity for short pulses. Theoretical calculations are compared with experimental measurements made on an aluminum and a brass cylinder of wall thickness 0.094 in. and o.d. 5.475 in. over a frequency range of 70 to 130 kc/sec. The theoretical curve of the velocity of pulses around the aluminum cylinder shows a frequency dependence that agrees with the experimental curve, but the magnitude of the theoretical value of the velocity is 10% too low. It is not possible to excite these waves in the brass cylinder with the present experimental arrangement.

Prestressed Electrodes for Spherical Transducers

E. A. Pence and R. E. Corwin

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1933-1935 (1962); (3 pages)

Online Publication Date: 26 Jul 2005

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The power‐handling capabilities of ceramic piezoelectric transducers in pulsed operation at low duty rate are limited by tensile rupture. Compressive bias has been used to increase the power‐handling capabilities of integral spheres; this mechanical bias has been applied by controlled nickel electroplating over the outer surface, such that the plated coating is under high tensile stress. Units formerly limited to 50 W/cm2 can now be operated at 200 W/cm3.

Acoustic Ambient Noise in the Ocean: Spectra and Sources

Gordon M. Wenz

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1936-1956 (1962); (21 pages) | Cited 56 times

Online Publication Date: 26 Jul 2005

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The results of recent ambient‐noise investigations, after appropriate processing, are compared on the basis of pressure spectra in the frequency band 1 cps to 20 kc. Several possible sources are discussed to determine the most probable origin of the observed noise. It is concluded that, in general, the ambient noise is a composite of at least three overlapping components: turbulent‐pressure fluctuations effective in the band 1 cps to 100 cps; wind‐dependent noise from bubbles and spray resulting, primarily, from surface agitation, 50 cps to 20 kc; and, in many areas, oceanic traffic, 10 cps to 1000 cps. Spectrum characteristics of each component and of the composite are shown. Additional sources, including those of intermittent and local effects, are also discussed. Guidelines for the estimation of noise levels are given.
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Erratum: Interaural Phase and the Absolute Threshold for Tone

K. J. Diercks and Lloyd A. Jeffress

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1957-1957 (1962); (1 page)

Online Publication Date: 26 Jul 2005

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Abstract Unavailable

Erratum: Influence on the Behavior of a Linear Dynamical System of Some Imposed Rapid Motions of Small Amplitude

John L. Bogdanoff

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1957-1957 (1962); (1 page)

Online Publication Date: 26 Jul 2005

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Abstract Unavailable

Phase Velocity of Plane Longitudinal Waves in Infinite Plates

K. J. Diercks, K. McCormack, and D. B. James

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1957-1958 (1962); (2 pages)

Online Publication Date: 26 Jul 2005

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Computed curves of the dimensionless phase velocity (c/cL) of plane longitudinal waves in infinite plates for values of the parameter ν (Poisson's ratio) from 0.25 to 0.40 are presented.

Equivalent Eulerian Boundary Conditions for Finite‐Amplitude Piston Radiation

Henry C. Kessler, Jr.

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1958-1959 (1962); (2 pages)

Online Publication Date: 26 Jul 2005

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A method is presented for replacing the Lagrangian boundary condition which occurs in the analysis of finite‐amplitude radiation from vibrating pistons by an approximately equivalent condition which permits the analysis to be carried out in Eulerian form.

Distribution of Response Crests in a Bimodal System

G. L. Park and R. F. Lambert

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1959-1960 (1962); (2 pages)

Online Publication Date: 26 Jul 2005

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The distribution of crests associated with a lightly coupled bimodal vibrating system under band‐limited white‐noise excitation has been calculated and measured. Measured crests of the strain response of a mass‐loaded cantilever beam, used as the bimodal system, follow the expected Rayleigh distribution to within experimental accuracy. Noteworthy is the result that crests of four times the rms strain are obtained using a bimodal configuration, and crests of five times the rms strain are obtained when the beam is vibrating in a unimodal configuration.

Relation between Strain and Velocity in Resonant Vibration

Stephen H. Crandall

J. Acoust. Soc. Am. Volume 34, Issue 12, pp. 1960-1961 (1962); (2 pages)

Online Publication Date: 26 Jul 2005

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In a recent paper Hunt examined the relation between strain and velocity in forced resonant motion for a wide variety of elastic bodies. He found that the maximum strain was always proportional to the ratio of the maximum vibratory velocity to the velocity of sound in the body and that the constant of proportionality appeared to be constrained to remain in a narrow range extending about an order of magnitude. Similar results were obtained independently by Ungar [see E. E. Ungar, “Maximum Stresses in Beams and Plates Vibrating at Resonance,” J. Eng. Ind. Trans. ASME 84B, 149–155 (1962)] for uniform beams and plates. In this note a similitude argument is used to establish the form of these results. It is also pointed out that because of both strain and velocity concentrations the range of possible values for the proportionality constant can be very much wider than the range found by Hunt.
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