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Journal of the Acoustical Society of America

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Dec 1975

Volume 58, Issue 6, pp. 1127-1335

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Optimal primary spectra for parametric transmitting arrays

James R. Clynch

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1127-1132 (1975); (6 pages)

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The use of more than two spectral components in the primary signal of a parametric endfire array is considered. Equations are developed for the spectra of N components which maximize the farfield SPL for shock‐free primaries in dispersionless media. Effects of the variation of attenuation with frequency are shown to have a considerable influence on the shape of the optimal spectra. For the case of attenuation proportional to the square of the frequency, the optimal spectra are functions only of the downshift ratio R and the number of components N, and not functions of the absolute value of the frequencies. The optimal spectra and waveforms for several sets of R and N values are shown. It is found that a 3‐dB increase over a two‐component primary can be obtained with three or four components for a wide range of downshift ratios. At extremely high primary powers, an increased tendency toward shock formation may negate this gain. Beamwidths were found to be essentially unaffected.
Subject Classification: 25.35; 60.10.
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43.25.-x Nonlinear acoustics
43.60.+d Acoustic signal processing

Finite‐amplitude standing waves within real cavities

Alan B. Coppens and James V. Sanders

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1133-1140 (1975); (8 pages) | Cited 8 times

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A three‐dimensional mathematical model for acoustical standing waves in lossy fluid‐filled cavities has been obtained which requires empirical values for the resonance frequencies fn and quality factors Qn (all measured in the linear acoustic régime) of the pertinent standing waves which the cavity can support. The nonlinear distortion of the observed pressure waveform depends strongly on the f’s and Q’s of those standing waves excited by harmonics of the driving frequency. The model is applicable to nonideal cavities if the deviations from idealized geometry and boundary conditions are small. It is restricted to small values of M (1+1/2 B/A) Q1 where M is the peak Mach number and Q1 the quality factor of the fundamental component of the driven standing wave, and B/A is the parameter of nonlinearity of the fluid. Comparisons between the model and experiment are made for a rectangular cavity driven in one‐ and two‐dimensional modes. Agreement is excellent except when there are degeneracies involving the predicted nonlinearly excited standing waves and other standing waves of the cavity. Small discrepancies appear to result from the coupling of energy from the nonlinearly excited standing wave into its degenerate neighbor.
Subject Classification: 25.25; 55.20.
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43.25.-x Nonlinear acoustics
43.55.+p Architectural acoustics

Parametric acoustic receiving array. I. Theory

James J. Truchard

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1141-1145 (1975); (5 pages)

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Closed‐form solutions are derived for several configurations of the parametric receiving array. First, the solution for the interaction of a high‐frequency spherical wave from a point source and a low‐frequency plane wave is obtained theoretically by using a two‐dimensional stationary phase solution of Westervelt’s scattering integral. The result is in turn used to generate the solution for parametric receiving arrays with various pump transducers, including a truncated line source, a rectangular piston, and a circular piston. In each case, the observer is assumed to be in the farfield of the pump transducer, but the result includes the effects of interaction in the nearfield of the pump transducer. The solution of the parametric receiving array with a point source pump and a truncated line receiver is also found. The theoretical solutions include the effects of misalignment of either the pump or receiving transducer.
Subject Classification; 25.35; 30.85.
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43.25.-x Nonlinear acoustics
92.10.Vz Underwater sound

Parametric acoustic receiving array. II. Experiment

James J. Truchard

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1146-1150 (1975); (5 pages) | Cited 1 time

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A series of experiments was conducted with a 48‐ft parametric receiving array at a pump frequency of 90 kHz. An omnidirectional transducer was used with either a rectangular or a square piston transducer. Each of the three transducers could be used as either pump or receiver, so that a variety of parametric receiving array configurations could be realized. The piston transducer could be independently rotated, to examine the effects of misalignment. Theoretical and experimental results are compared for the parametric receiving array with several transducer arrangements. With either the pump transducer or the receiver misaligned, the difference frequency beam pattern is asymmetrical and is the mirror image of the sum frequency beam pattern. The agreement between theory and experiment was excellent.
Subject Classification: 25.35; 30.85.
Show PACS
43.25.-x Nonlinear acoustics
92.10.Vz Underwater sound

Calculation of the effect of internal waves on oceanic sound transmission

Stanley M. Flatté and Frederick D. Tappert

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1151-1159 (1975); (9 pages) | Cited 11 times

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The signal received by a hydrophone in the ocean many kilometers from a steady sound source fluctuates dramatically due to variations of the speed of sound in sea water. By inserting an empirical model of internal‐wave‐generated sound‐speed variations into an acoustic‐transmission computer code, we have shown that internal waves cause significant variations in sound transmission at 100 Hz, comparable in size and frequency to the variations observed in field experiments. We have also studied the usefulness of vertical hydrophone arrays.
Subject Classification: 30.25, 30.82; 28.60.
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92.10.Vz Underwater sound
43.28.+h Aeroacoustics and atmospheric sound

Cavitation dynamics: II. Free pulsations and models for cavitation bubbles

H. G. Flynn

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1160-1170 (1975); (11 pages) | Cited 15 times

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A mathematical formalism developed for investigating the dynamics of cavitation bubbles has been used to obtain numerical solutions describing the behavior of bubbles of different initial radii that are damped by heat conduction, viscosity, and compressibility. Calculations have been made to determine two measures of damping, the maximum temperatures, the maximum pressures, and the resonance frequencies of bubbles set into pulsations by a pressure pulse. In general, these quantities are controlled by heat conduction and viscosity at small amplitudes and mainly by compressibility at large amplitudes of motion. One measure of damping—the energy dissipation modulus—has a peak at a well‐defined maximum radius. This peak serves to define a transition radius; for pulsations with amplitudes greater than this transition radius, the fraction of available energy dissipated in a cycle decreases and hence very large internal energy densities may occur. A second transition occurs at a radius called the critical radius; for pulsations with amplitudes greater than this critical radius, inertial forces control the collapse of a bubble and very large kinetic energy densities may occur in the liquid at the interface. The transition radius and the critical radius, which are functions of the initial size of a cavity, have been used to define a dynamical threshold for cavitation. In a motion where the maximum radius exceeds this proposed threshold, the characteristic phenomena of cavitation may be expected to appear. The dynamical threshold has in turn been used as the basis for models of cavitation bubbles useful in interpreting such phenomena.
Subject Classification: 30.70, 30.60.
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92.10.Vz Underwater sound
47.55.dp Cavitation and boiling

Range‐dependent normal modes in underwater sound propagation: Application to the wedge‐shaped ocean

R. D. Graves, Anton Nagl, H. Überall, and G. L. Zarur

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1171-1177 (1975); (7 pages) | Cited 6 times

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We use the adiabatic range variation method of Pierce and Milder to perform an approximate separation into normal modes of the wave equation for the problem of underwater sound propagation in an almost‐stratified under‐ocean channel with gradual range dependence of medium and boundaries. Our solution is illustrated by an application to the isovelocity ocean wedge with rigid ocean floor, and compared with the exact solution of Bradley and Hudimac. Even when mode coupling is neglected, good agreement is obtained for moderately large wedge angles.
Subject Classification: 30.20; 20.15, 20.40.
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92.10.Vz Underwater sound
43.20.+g General linear acoustics

Parabolic approximations for underwater sound propagation

Suzanne T. McDaniel

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1178-1185 (1975); (8 pages) | Cited 1 time

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Several alternative parabolic approximations to the reduced wave equation and their numerical solution are investigated for underwater acoustics applications. Parabolic approximations are derived by splitting the wave equation into transmitted and reflected components. An exact splitting operator is found, and further parabolic approximations for the transmitted fields are based on approximations to this operator. For the case of a range‐independent environment, the resulting parabolic approximations are compared with normal‐mode theory. The efficiency with which numerical results can be obtained is discussed, and an example of propagation from shallow to deep water is given.
Subject Classification: 30.20; 20.15, 20.40.
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92.10.Vz Underwater sound
43.20.+g General linear acoustics

Analysis technique for classifying wind‐ and ship‐generated noise characteristics

Anthony J. Perrone and Louis A. King

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1186-1189 (1975); (4 pages)

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An analysis technique is described that permits the classification of ambient noise sources (wind generated and shipping) without the need for information concerning the environment or shipping in the area of interest. Wind‐generated and ship‐generated ambient noise, or a combination of the two, can be classified by finding the zero‐axis crossing time of the autocorrelation function versus frequency of the long‐term (greater than two weeks) ambient noise time series for a given geographic area. Results obtained from the zero‐axis crossing times of the autocorrelation function of ambient noise level versus time (measured by omnidirectional hydrophones and processed through 1/3‐octave filters) are bounded by two distinct zero‐axis crossing times. Analysis of data from four widely separated geographic areas produces the same bounds, which suggests that they may be independent of area. In the region of the spectra where 1/3‐octave bands were highly correlated with wind speed, the decorrelation time (i.e., zero‐axis crossing) was found to range from 26 to 40 h. In the region of the spectra that was not wind correlated and, therefore, attributed to ship‐traffic noise, the decorrelation time was found to range from 4 to 8 h. For spectra that were composites of both noise sources, the decorrelation time ranged between 8 and 26 h. The observed correlation functions were fitted to a two‐term equation to aid in determining the decorrelation times for all values of the wind‐generated to ship‐generated noise‐level ratios. Each term of the equation (one being wind related and the other ship related) is a sinusoid whose decay parameter is equal to its corresponding mean value decorrelation time and whose sinusoidal period is four times that value.
Subject Classification: 30.70, 30.80.
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92.10.Vz Underwater sound

Multiple scattering by two cylinders

J. W. Young and J. C. Bertrand

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1190-1195 (1975); (6 pages) | Cited 8 times

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Theoretical calculations and experimental measurements of the backscattering of a plane acoustic wave by two parallel, rigid cylinders are presented. The effects of multiple scattering between cylinders are included in the calculations. Two methods of solution of the equations are discussed. Good agreement is found between theory and experiment. Multiple‐scattering calculations show the influence of the shadow of one cylinder upon the other. Variations in level of the interference peaks are correctly predicted.
Subject Classification: 30.30, 30.40; 20.30, 20.15.
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92.10.Vz Underwater sound
43.20.+g General linear acoustics

Acoustic wave propagation in a viscoelastic fluid undergoing a simple steady shearing motion

W. H. Schwarz

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1196-1203 (1975); (8 pages)

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The theory for the prediction of the absorption and dispersion of forced acoustic waves propagating through a viscoelastic fluid in a steady simple shearing motion is presented. The stress tensor is represented by an approximate constitutive equation for a simple fluid obtained by a functional expansion about the basic state of a motion with a constant‐stretching history. The linear terms are written as integrals, having kernels identified as shear and compressional relaxation functions. The absorption and dispersion depends on the direction of acoustic propagation relative to the shearing axis. Two cases are examined and the appropriate relaxation functions, or alternatively, the complex viscosity functions, obtained. These forms are compared to the shear relaxation functions obtained from shear oscillation experiments. The special case of acoustic wave propagation through a viscoelastic fluid, otherwise at rest, is considered and the results are compared to existing theories and experimental data.
Subject Classification: 35.50, 35.24.
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43.35.-c Ultrasonics, quantum acoustics, and physical effects of sound
43.35.Mr Acoustics of viscoelastic materials

Elastodynamic stress intensity factors for a crack in a layered composite

L. M. Keer, W. C. Luong, and J. D. Achenbach

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1204-1210 (1975); (7 pages)

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Elastodynamic stress intensity factors are computed for diffraction of antiplane shear waves by a crack in a layered composite. The crack is parallel to the layering. The problem is formulated by means of integral transforms, and reduced to the solution of a singular integral equation. The special case when the direction of the wave motion is perpendicular to the layering is studied numerically, and stress intensity factors are obtained for several values of frequency, material constants, and geometrical parameters.
Subject Classification: 40.55; 20.30.
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43.40.+s Structural acoustics and vibration
46.50.+a Fracture mechanics, fatigue and cracks
81.05.-t Specific materials: fabrication, treatment, testing, and analysis
43.20.+g General linear acoustics

Comparisons of variability in aircraft flyover noise measurements

Dwight E. Bishop

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1211-1221 (1975); (11 pages)

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Data from controlled flight testing conducted for 11 aircraft noise certification programs under FAA FAR 36 show typical standard deviations for sets of EPNL and PNL values ranging from 0.8 to 1.4 dB. Much greater variability was found in the noise levels measured near the approach path to runway 21R at Detroit Metropolitan Airport during two ten‐day periods of routine operations. EPNL, SEL, and maximum A‐level data, classified in jet aircraft groups by number of engines (regardless of type), showed typical standard deviations ranging from 3.8 to 4.9 dB at the different ground measuring points. Correlation of the Detroit noise data with slant distance gave moderately high correlation coefficients, with 95% prediction intervals about the regression lines varying from ±5.4 to ±9.5 dB. The regression lines show quite good agreement, particularly in slope, with generalized noise level versus distance curves often used for noise exposure calculations. Correlations between different noise measures were high, as expected. However, prediction intervals about the regression lines were sizable, indicating distinct possibilities for occasional sizable errors in estimating one noise measure from another when analyzing aircraft flyover noise signals.
Subject Classification: 50.50, 50.55.
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43.50.+y Noise: its effects and control

Measurement of freeway noise and community response

M. A. Jenkins and Juergen Pahl

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1222-1231 (1975); (10 pages)

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Personal interviews were conducted with 562 freeway‐proximal residents and 134 residents in control neighborhoods. Five factor‐analyzed scales were used to measure community response to freeway noise in terms of (1) subjective reactions and (2) behavioral interruptions due to noise. The social survey allowed for spontaneously mentioned and directly elicited responses. Noise exposure was measured by an Environmental Noise Classifier; one representative noise sample was taken for every residence, and L10, L50, L90, NPL, and TNI were computed. These noise measures correlated highly with each other, except TNI, and none of the measures demonstrated superiority over the others as a predictor of community response. Community response was analyzed as a function of noise level, and all response scales increased with increasing noise levels; for example, freeway noise was reported by 50% as the main cause of dissatisfaction, by 13% as main cause for complaints, by 25% as the reason for wanting to move, and by 43% as the reason for awakening at night. Noise levels correlated 0.99 with mean annoyance ratings for groups of residents within specified noise strata, and 0.31 for ratings based on individual annoyance scores.
Subject Classification: 50.70, 50.50, 50.20, 50.75.
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43.50.+y Noise: its effects and control

Noise and sleep: A literature review and a proposed criterion for assessing effect

Jerome S. Lukas

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1232-1242 (1975); (11 pages) | Cited 1 time

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A brief discussion of human sleep is followed by presentation of data describing the variables that appear to affect human responsiveness to noise during sleep. Results from several studies that were conducted in different laboratories and that used several types of noises, age groups, and sexes are then combined to show that when EPNdB units are used as the measure of noise intensity, the correlation coefficient between intensity and the probability of no disturbance of sleep is −0.86. It is suggested also that a coefficient of similar magnitude would be obtained if units of EdBA were used. Some implications of these data are then exemplified.
Subject Classification: 50.70, 50.75.
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43.50.+y Noise: its effects and control

Clustering of volume reverberation spectra: An application of correspondence analysis

Paul T. McElroy and Woollcott Smith

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1243-1256 (1975); (14 pages)

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Correspondence analysis has been applied to 34 spectral curves of volume reverberation to cluster the spectra into groups. The clustering is compared with an earlier grouping of the spectra based on the cross‐standard‐deviation matrix with essentially similar results. However, the correspondence analysis technique has a number of clear‐cut advantages: (1) the clustering is quickly displayed in a two‐dimensional plot; (2) eigenvectors computed in the analysis are spectral curves which are characteristic of extremum environments in the data set (we call them volume reverberation environments and discuss their possible indentification with preponderant fish species); (3) those frequencies which most directly serve as indicators of a particular cluster of spectra are identified; and (4) the examination of the relationship of environmental parameters and the factor scores computed in the analysis provide a basis for extrapolation of the spectra to their appearance in unmeasured conditions. The volume reverberation spectra (known as column strengths) are chosen as a particular example of the application of correspondence analysis; we believe it is broadly applicable to the problem of identifying and classifying spectra in many disciplines. As an aid to the reader in understanding the technique, we have summarized the governing equations of correspondence analysis and given a geometrical interpretation relating the original spectra, eigenvectors, and factor scores.
Subject Classification: 60.20; 30.40.
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43.60.+d Acoustic signal processing
92.10.Vz Underwater sound

Encoding and pitch strength of complex tones

Joseph W. Hall, III and David R. Soderquist

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1257-1261 (1975); (5 pages) | Cited 2 times

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Pitch perception in the human was examined with respect to the level of neural analysis and pitch strength of various complex tones. In binaural conditions, three‐component complex stimuli were presented to each ear in such a way that if a central processor determined pitch from the combined information from the two ears, one pitch would be perceived. If the pitch processor attended to the information from each ear separately, two pitches would be perceived (corresponding to the fundamental at each ear). Two pitches were perceived and the importance of peripheral encoding for pitch perception was supported. Subjects judged the strength of monaurally and binaurally presented stimuli as a function of the spectral region of the frequency components, number of components per complex, and the spacing between components. Pitch strength was discussed in terms of recent theoretical models of pitch.
Subject Classification: 65.54, 65.56, 65.62.
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42.66.-p Physiological optics

Identification of random auditory waveforms

Irwin Pollack

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1262-1271 (1975); (10 pages)

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Listeners quickly learn to identify, apparently on an absolute basis, the ordering of a pair of sounds, where one sound is a specific random selection which is constant over successive observations, and where the other sound varies over successive observations. The accuracy of identification is not directly related to the uncertainty of the pool of possible waveforms. A wide range of sample durations and spectra characterize the identifiable pools. Increasing the predictability of the sequences does not improve identification accuracy. Listeners also can identify one of two selections from the same pool and can identify departures from a prototype which they have never heard. Since all random selections from the same pool have nearly identical long‐term average spectra, it is concluded that the listener must perform a short‐term, or running, spectrum analysis upon the signals.
Subject Classification: 65.22, 65.75, 65.68.
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42.66.-p Physiological optics

Perception of complex sounds: ’’Hidden auditory figures’’

Irwin Pollack

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1272-1279 (1975); (8 pages)

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Hidden auditory figures were generated by ORing the output of a bank of counters, driven by a high‐frequency periodic pulse train. The absolute detection, the relative discrimination, and the identification of hidden auditory figures of up to ten prime counts was examined. The crucial factor in detection and discrimination is the context in which the to‐be‐examined component is embedded. A given count may be nearly perfectly detectable if it is the smallest of the series of prime counts; that same count may be nearly undetectable if it is the largest of the series of prime counts. Within hidden auditory figures, the spread of interference is opposite in direction to most masking situations: High frequencies (represented by small counts) are more effective than low frequencies (represented by large counts). Many of the crucial details are to be found in the spectrum of these signals.
Subject Classification: 65.22, 65.56, 65.75.
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42.66.-p Physiological optics

Perception of voicing in English affricates and fricatives

Ronald A. Cole and William E. Cooper

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1280-1287 (1975); (8 pages) | Cited 2 times

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Two series of experiments were conducted to study the effects of consonant and vowel duration on the perception of the voiced–voiceless distinction for the English affricates [?] vs [?] and the fricatives [v] vs [f] and [z] vs [s]. The voiceless members of each pair of speech sounds were recorded by a male speaker in a CV environment with the vowel [a] ([?a], [fa}, and [sa]) and then duplicated a number of times. The frication of each syllable was then shortened in small steps by removing frication from just prior to the vowel and then closing the gap. Additional series were constructed by shortening the vowel duration of these syllables, and the resulting series were presented to listeners in randomized sequences for identification. The results of the first series of experiments showed that shortening the duration of frication for a voiceless affricate or fricative produced a change in the percept from voiceless to voiced (i.e., from [?a] to [?a], from [fa] to [va], and from [sa] to [za]). Whereas shortening the duration of frication produced a marked shift in the percept from voiceless to voiced, shortening the duration of the vowel produced only a weak effect, and the interaction between the two shortening effects was small. The small effect of vowel duration on perception of voicing for syllable‐initial affricates and fricatives was contrasted with the strong effects of vowel duration on voicing for fricatives in syllable‐final position observed in prior work, and this contrast was accounted for in terms of the perceptual processing required for CVC syllables in normal listening. In the second series of experiments, the frication of [sa] was shortened to produce a series of syllables ranging from [sa] to [za] to [‐a]. In selective adaptation tests, repeated presentation of these three syllables resulted in shifts in the listeners’ phonetic boundaries. Results of the selective adaptation experiment were compared to results of prior work using stop consonants.
Subject Classification: 70.30, 70.70.
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43.70.-h Speech production

Linear estimation of nonstationary signals

Louis A. Liporace

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1288-1295 (1975); (8 pages) | Cited 5 times

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The efficacy of linear prediction for speech analysis depends upon the degree to which the speech signal is stationary within an analysis interval. For this reason the speech signal is usually divided into small intervals during each of which the signal is assumed to be stationary. The formulation described in this paper is aimed at accomodating the nonstationarity more automatically by allowing the linear estimate of the speech signal to be time varying.
Subject Classification: 70.40, 70.65.
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43.70.-h Speech production

Time‐frequency resolution experiment in speech analysis and synthesis

C. R. Patisaul and J. C. Hammett, Jr.

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1296-1307 (1975); (12 pages)

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This paper reports the results of a study of the perceptual consequences of the time and frequency resolution loss inherent in vocoded speech, and an evaluation of an adaptive resolution scheme. A cepstrum vocoder which adapted its time and frequency resolution according to the voiced–unvoiced nature of the input speech was computer simulated. Speech processed by the vocoder was subjectively evaluated and several tentative conclusions regarding time‐frequency resolution and speech quality were drawn. The results of the study suggest that (1) 20‐msec time resolution is adequate for vocoder applications, (2) adapting to better time resolution in unvoiced regions and regions of voiced–unvoiced and unvoiced–voiced transitions leads to improved speech quality in systems that do not normally maintain 20 msec or better time resolution, (3) frequency resolution may be reduced considerably in unvoiced and transition regions with no noticeable degradation in speech quality, and (4) time‐frequency resolution trading may occur in the speech perception process.
Subject Classification: 70.40, 70.55, 70.50.
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43.70.-h Speech production

Auditory intensity discrimination in the parakeet (Melopsittacus undulatus)

Robert J. Dooling and James C. Saunders

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1308-1310 (1975); (3 pages) | Cited 2 times

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Three parakeets were trained by a method of avoidance conditioning to respond to intensity differences in successsively occurring tone bursts. Intensity difference limens were obtained at six sensation levels of a 2.86 kHz tone. The relative intensity difference limens (ΔI) for the parakeet were larger than similarly reported measures for man and other mammals at all sensation levels tested. Calculations of the Weber fractions at each sensation level tested showed that Weber’s law holds for the parakeet at sensation levels above 50 dB.
Subject Classification: 80.50; 65.75, 65.50.
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43.80.-n Bioacoustics
42.66.-p Physiological optics

Equivalent circuit of a ceramic ring transducer operated in the dipole mode

Robert S. Gordon, Leonard Parad, and John L. Butler

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1311-1314 (1975); (4 pages) | Cited 4 times

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An equivalent circuit for a piezoelectric ring transducer excited in its dipole mode and its remaining odd‐order curcumferential extensional modes is derived. The analysis is accomplished by expressing the applied electric field excitation by a Fourier series and then combining solutions appropriately. The equivalent network presented here has a voltage–current terminal pair and a force–velocity terminal pair to each Fourier component which yield the transducer performance for the dipole and higher‐order modes.
Subject Classification: 85.52; 40.85.
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43.58.+z Acoustical measurements and instrumentation
43.40.+s Structural acoustics and vibration

Observation of acoustic layering and internal waves with a narrow‐beam 87.5‐kHz echo sounder

F. H. Fisher and E. D. Squier

J. Acoust. Soc. Am. Volume 58, Issue 6, pp. 1315-1317 (1975); (3 pages) | Cited 1 time

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Multiple thin layers have been observed from depths of 154 to 470 m with a narrow‐beam (±0.5° at 3 dB down) high resolution (0.6‐msec pulse) mounted on the bottom of FLIP. Layer reflection coefficients vary between −90 and −100 dB. The layers varied in depth sinusoidally about 5 m with a 22‐min period, indicating internal wave motion. Echo returns from the bottom at 770 fathoms indicated a reflection coefficient of −34 dB, in good agreement with earlier work at 75 kHz by Bezdek.
Subject Classification: 30.20, 30.82.
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92.10.Vz Underwater sound
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