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Sep 1976

Volume 60, Issue 3, pp. 543-759

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Optical holography for the study of sound radiation from vibrating surfaces

Colin H. Hansen and David Alan Bies

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 543-555 (1976); (13 pages)

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Time‐averaged holography has been used to quantitatively investigate sound radiation from an edge‐clamped circular flat plate mounted in an infinite rigid baffle. For a particular mode of vibration, the plate response is measured using holography and the sound power radiated is measured in a reverberant room with the plate mounted in one of the room walls. From these measurements a radiation efficiency is determined. The theoretical plate responce is calculated using both classical and Mindlin–Timoshneko plate theory and is shown to agree well with experimental measurements. Radiated sound power is calculated for each mode of interest by solving the wave equation in oblate spheroidal coordinates at the plate surface. These calculations are verified by direct evaluation of the Rayleigh integral in the farfield. Good agreement is obtained between experimentally measured radiation efficiencies and theoretical predictions. Small discrepancies between theory and experiment are discussed.
Subject Classification: [43]20.55, [43]40.24, [43]35.65.
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43.20.+g General linear acoustics
43.40.+s Structural acoustics and vibration
43.35.-c Ultrasonics, quantum acoustics, and physical effects of sound

Scattering matrix for elastic waves. I. Theory

Vasundara Varatharajulu and Yih‐Hsing Pao

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 556-566 (1976); (11 pages) | Cited 12 times

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A matrix theory is developed for investigating the scattering of elastic waves in solids by an obstacle of arbitrary shape. The scattering matrix which depends only on the shape and nature of the obstacle relates the scattered field to any type of harmonic incident field. Expressions are obtained for the elements of the scattering matrix in the form of surface integrals around the boundary of the obstacle, which can be evaluated numerically. Using the principle of reciprocity and the conservation of energy, the scattering matrix is shown to be symmetric and unitary. These properties are essential to assure the accuracy of numerical calculations. Both two‐ and three‐dimensional problems are discussed, and the obstacle may be an elastic inclusion, a fluid inclusion, a cavity, or a rigid inclusion of arbitrary shape.
Subject Classification: [43]20.15, [43]20.30.
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43.20.+g General linear acoustics

Matrix theory of elastic wave scattering

P. C. Waterman

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 567-580 (1976); (14 pages) | Cited 21 times

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Upon invoking Huygen’s principle, matrix equations are obtained describing the scattering of waves by an obstacle of arbitrary shape immersed in an elastic medium. New relations are found connecting surface tractions with the divergence and curl of the displacement, and conservation laws are discussed. When mode conversion effects are arbitrarily suppressed by resetting appropriate matrix elements to zero, the equations reduce to a simultaneous description of acoustic and electromagnetic scattering by the obstacle at hand. Unification with acoustic/electromagnetics should provide useful guidelines in elasticity. Approximate numerical equality is shown to exist between certain of the scattering coefficients for hard and soft spheres. For penetrable spheres, explicit analytical results are found for the first time.
Subject Classification: [43]20.15, [43]20.30.
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43.20.+g General linear acoustics

On parametric source aperture factors

Mark B. Moffett and Robert H. Mellen

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 581-583 (1976); (3 pages) | Cited 2 times

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It is well known that the beam pattern of a parametric acoustic source whose difference frequency is generated largely within the nearfield of the primary beam includes a multiplicative aperture factor that can be important at large angles when ka≳1 (k is the difference frequency wave number, a is the aperture radius). Not so well known, however, is the fact that the same aperture factor arises in the case of a spherically spreading, conical primary beam of finite initial aperture. The importance of the aperture size in determining the off‐axis behavior of parametric sources is discussed.
Subject Classification: [43]25.35; [43]20.30; [43]30.75.
Show PACS
43.25.-x Nonlinear acoustics
43.20.+g General linear acoustics
92.10.Vz Underwater sound

Acoustic spectral analysis of three tornadoes

Roy T. Arnold, Henry E. Bass, and Lee N. Bolen

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 584-593 (1976); (10 pages)

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Three sound recordings of tornadoes have been spectrally analyzed over the frequency interval between 100 and 2000 Hz. The low‐frequency analysis was limited by the response of the microphones used for the recordings; the upper frequency limit was imposed both the microphone response and the low‐signal level. One recording was made by James Cramer of a tornado which passed through Clay Center, Kansas on 25 September 1973. A second recording was made by Richard Allen Lindley of a tornado that passed through Guin, Alabama on 3 April 1974, and a third recording was made by Tom Bittman of a tornado which damaged his home in Tulsa, Oklahoma on 8 June 1974. All of the recordings are of low quality and the audio information required major spectral corrections, but the data analysis does indicate that the audio emissions from the tornadoes decrease in intensity as a function of increasing frequency. An attempt has been made to correlate the data with real (and conjectured) physical characteristics of the tornadoes and attendent atmospheric phenomena. It is clear to us from an objective analysis (and the more difficult subjective evaluation of the recordings) that identification of tornadoes based on acoustic emissions is possible . A study of tornadic sounds can not only provide a new tool for gaining insight into electrical and mechanical disturbances within a tornadic storm, but will also allow acoustic detection of a tornadic storm. A study of the change in intensity of the sounds emitted by the approaching Guin storm at both high and low frequencies suggests that noises generated by the high‐speed winds of the principal tornado vortex as its base scoured the ground might be discerned from noises generated by the winds of one or more smaller vortices moving around the tornado, and/or electrical discharges aloft.
Subject Classification: [43]28.45, [43]28.65.
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43.28.+h Aeroacoustics and atmospheric sound

A near‐wake model for the aerodynamic pressures exerted on singing trailing edges

William K. Blake

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 594-598 (1976); (5 pages)

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Periodic vortex streets are formed in the wakes of blunted trailing edges on airfoils and struts. The pressures generated on the shedding struts by the vortices in these wakes are periodic in time with a frequency that is set by the shedding rate for the vortices. A simple analytical formulation is derived to relate wake‐induced pressures to the characteristics of the wake near the edge. The chordwise distribution and magnitude of the pressure is shown as a function of the circulation of shed vortices, as well as the formation distance and the spacing of the vortices in the street. Predictions from the theory are compared to some recent measurements which were obtained in the wakes downstream of different trailing edges. These measurements were made at Reynolds numbers, based on trailing edge thickness, on the order of 104 to 105.
Subject Classification: [43]28.65; [43]50.55.
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43.28.+h Aeroacoustics and atmospheric sound
43.50.+y Noise: its effects and control

Vortex‐shedding noise from oscillating cylinders

T. E. Burton and R. D. Blevins

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 599-606 (1976); (8 pages)

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The theory of sound radiation from cylinders vibrating in resonance with vortex shedding is extended to consider the effects of vibration amplitude and mode shape. Farfield intensity and total radiated power are expressed as functions of given structural and flow parameters. Closed form solutions for intensity are obtained when cylinder vibration velocity is either much smaller than or comparable to mean flow velocity.
Subject Classification: [43]28.65, [43]40.26, [43]50.55.
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43.28.+h Aeroacoustics and atmospheric sound
43.40.+s Structural acoustics and vibration
43.50.+y Noise: its effects and control

Resolution performance of Doppler ultrasound flowmeters

James M. Griffith, William R. Brody, and Lester Goodman

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 607-610 (1976); (4 pages)

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Ultrasonic Doppler flowmeters can simultaneously obtain spatial and velocity distribution patterns of flow in a blood vessel. The factors fixing spatial and velocity resolution, however, must be determined if optimum utilization is to be realized. The parameters influencing spatial resolution have been described in the literature, but velocity resolution has received relatively little attention. This paper demonstrates analytically how optimum velocity resolution can be derived with a simple mathematical model and presents experimental data to verify theory. In addition, a ’’resolution product’’ is offered which characterizes pulsed Doppler flowmeters. This product shows explicitly the necessary compromise between position and velocity resolution for a given instrument.
Subject Classification: [43]28.60, [43]28.20; [43]80.70; [43]35.80.
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43.28.+h Aeroacoustics and atmospheric sound
43.80.-n Bioacoustics
43.35.-c Ultrasonics, quantum acoustics, and physical effects of sound

Acoustic propagation in shallow water overlying a consolidated bottom

Frank Ingenito and Stephen N. Wolf

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 611-617 (1976); (7 pages) | Cited 3 times

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An experiment designed to measure normal mode amplitude functions and attenuation coefficients was conducted in shallow water on Campeche Bank off the Yucatan Peninsula. Measurements were made at two locations on the bank in water of about 30 m in depth over a bottom consisting of consolidated limestone having a measured and sound velocity of 1900 m/sec. Pulsed cw signals with frequencies of 400, 750, and 1500 Hz were used. Theoretical calculations of the mode amplitude functions using a fluid model of the bottom were found to agree well with the measurements. In order to reconcile the measured mode attenuation coefficients with theory, it was necessary to assume that the shear velocity of the bottom was 1000 m/sec. The latter is lower than the minimum sound velocity in the water column so that the generation of propagating shear waves in the bottom was the dominant attenuation mechanism. Significant differences in the measured mode attenuation coefficients at the two stations were explained by the deepening of the low velocity channel at the bottom of the water column.
Subject Classification: [43]30.20, [43]30.50.
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92.10.Vz Underwater sound

Acoustic estimates of fish density and scattering function

Miles L. Peterson, Clarence S. Clay, and Stephen B. Brandt

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 618-622 (1976); (5 pages) | Cited 2 times

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The amplitude of a sonar echo from a fish depends upon the species and size of the fish, acoustic wavelength, aspect, position of the fish in the sonar beam, range and backscattering cross section. We simplify the problem to a single species and size of fish, vertically downward echo sounding, single aspect, and nonoverlapping echoes. After removal of attenuation due to range and absorption two random functions remain. The position of the fish in the sonar beam is random and the scattering cross section for each trail is random. We assume that the fish have a uniform density (number/m3) and calculate the probability density function (PDF) for insonification and reception. We assume that the PDF of the envelope of the echo (excluding the variability of insonification and reception) has a Rayleigh PDF. Assuming two PDF’s are independent, we calculate the PDF of the echo envelopes wE(e). wE(e) depends upon the beamwidth of the sonar and the mean backscattering cross section. The theoretical PDF has the same shape as the measured PDF of echoes from alewife in Lake Michigan. We use the fit of the PDF’s to estimate the backscattering cross section and fish density. This calibrates the echo‐integration processing system. A profile of the density of alewife in Lake Michigan is shown.
Subject Classification: [43]30.40; [43]80.40.
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92.10.Vz Underwater sound
43.80.-n Bioacoustics

Improved acoustic viscosimeter technique

M. R. Fisch, R. P. Moeller, and E. F. Carome

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 623-625 (1976); (3 pages) | Cited 1 time

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An improved technique has been developed for studies of the shear viscosity of fluids. It utilizes an acoustic resonator as a four‐terminal electrical device; the resonator’s amplitude response may be determined directly and simply related to the fluid’s viscosity. The use of this technique is discussed briefly and data obtained in several fluids is presented.
Subject Classification: [43]35.10, [43]35.68; [43]85.52.
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43.35.-c Ultrasonics, quantum acoustics, and physical effects of sound
43.58.+z Acoustical measurements and instrumentation

Excitation, detection, and scattering of electroelastic surface waves via an integral equation approach

Harold A. Sabbagh and Thomas F. Krile

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 626-633 (1976); (8 pages)

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The problem of the excitation, detection, and scattering of electroelastic surface (Bleustein) waves is solved exactly by determining the charge distribution on the fingers of an interdigital transducer. The approach is to solve an integral equation, in the Fourier transform domain, that relates the charge density on the fingers to the electric potential of the fingers. The solution of the integral equation is accomplished by expanding the charge distribution in a series of pulses and then transforming the problem to a vector matrix,one which is readily handled by a computer. In this manner the charge distribution is determined for a variety of conditions.
Subject Classification: [43]35,54.
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43.35.-c Ultrasonics, quantum acoustics, and physical effects of sound

Vibrations of an infinite plate with a frequency independent Q

Michele Caputo

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 634-639 (1976); (6 pages) | Cited 7 times

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The dissipation in an elastic medium is represented by a dissipation mechanism which is similar to one used in an earlier paper [M. Caputo, Geophys. J. R. Astron. Soc. 13, 529–539 (1967)], but is simpler and has a frequency‐independent Q−1. The vibrations of a plate are studied by obtaining the eigenfrequencies, the amplitude of the displacement, the dispersion relation, the Q−1, the hysteresis cycle, and the yield stress.
Subject Classification: [43]40.24.
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43.40.+s Structural acoustics and vibration

Uniform spinning cable as a vibration absorber

O. L. Vance and J. H. Woodward

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 640-644 (1976); (5 pages)

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This paper presents an analysis of the free vibrations of a disk–cable system spinning freely about a fixed axis through the disk center. Secondly, it is shown how the cable can be used as a vibration absorber to reduce the effect of torsional disturbances on a rotating system.
Subject Classification: [43]40.22, [43]40.70.
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43.40.+s Structural acoustics and vibration

Alternative test method for evaluating impact noise

Theodore J. Schultz

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 645-655 (1976); (11 pages)

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The current method of measuring impact noise transmission involves the use of a standard hammer machine to produce a series of impact on the floor‐ceiling structure, and the measurement of the resulting noise produced in the room below. The method has been criticized on the ground that ratings based on the test data correlate poorly with the subjective judgments of people listening to real‐life impacts on the same floors. An alternative test method is proposed that uses a modified hammer machine whose internal impedance, intensity of impact, and striking frequency simulate those of real footfalls. The new method involves several changes from the present standard: short‐term rms impact sound levels are measured instead of long‐term rms levels; no normalization for the sound absorption of the receiving room is required; since the short‐term levels are higher than the long‐term levels usually measured, background noise is less of a problem than for the existing method. These proposed changes based on recent studies are expected to improve the correlation between test data and subjective judgments of floors.
Subject Classification: [43]55.80; [43]50.45.
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43.55.+p Architectural acoustics
43.50.+y Noise: its effects and control

The ac and dc components in lateral line microphonic potentials

J. R. Boston

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 656-664 (1976); (9 pages) | Cited 1 time

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Measurements of the microphonic potential from the lateral line sensory organs of killifish (Fundulus heteroclitus) are presented in this report. The potential consists of a dc shift and a dominant oscillatory component at twice the frequency of the stimulus, and it grows with the square of the stimulus at low amplitudes. An electrical circuit model of the microphonic is developed, assuming a simple quadratic nonlinearity in the electrical response of an individual hair cell as suggested by Flock. The model allows investigation of variable conductive or variable capacitive effects in microphonic generation, and the results obtained from the model are compared to the observed properties of the microphonic potentials. It is concluded that hair cell microphonics appear to be generated by a process involving current flow through a variable conductance, although capacitive effects of the hair cell are important in determining the waveform of the microphonic and its behavior as a function of frequency. A discrepancy between the observed low‐amplitude growth of the microphonic in killifish and the reported low‐amplitude growth of the microphonic in other acoustico‐lateralis preparations is also discussed.
Subject Classification: [43]65.28, [43]65.20, [43]65.40.
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42.66.-p Physiological optics

Light‐scattering heterodyne interferometer for vibration measurements in auditory organs

P. R. Dragsten, W. W. Webb, J. A. Paton, and R. R. Capranica

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 665-671 (1976); (7 pages) | Cited 5 times

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An interferometric optical heterodyne technique has been developed especially for vibrational amplitude and phase measurements on auditory organs of live animals. Laser light diffusely scattered from the vibrating structure is used for the measurement. Continuous calibration and feedback compensation systems were developed to cope with the problems of drift in interferometer alignment and small background movements. Vibrational amplitudes from below 0.1 Å to above 400 Å have been detected on the posterior tympanic membranes of live crickets.
Subject Classification: [43]65.20; [43]40.60; [43]35.65.
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42.66.-p Physiological optics
43.40.+s Structural acoustics and vibration
43.35.-c Ultrasonics, quantum acoustics, and physical effects of sound

Growth of loudness at 1000 and 3000 Hz

Rhona P. Hellman

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 672-679 (1976); (8 pages) | Cited 8 times

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Loudness growth at 1000 and 3000 Hz was measured directly by magnitude estimation and production, and indirectly by loudness matches between tone and wide‐band noise and by interfrequency matching. The outcome of the three series of experiments does not reveal any systematic difference in shape of the loudness curves at 1000 and 3000 Hz. To a first approximation, above about 30 dB SL the loudness functions at 1000 and 3000 Hz are power functions of sound pressure with an exponent close to the accepted ISO standard of 0.60 (0.30 re sound intensity). Below 30 dB SL both loudness curves become progressively steeper than a simple power function and approach the same limiting slope, re sound intensity, of unity. Consistent with Steven’s calculation system [J. Acoust. Soc. Am. 51, 575–601 (1972)], the data also show that loudness equality is achieved when a 3000‐Hz tone is about 8 dB below the SPL of a tone at 1000 Hz.
Subject Classification: [43]65.50, [43]65.75.
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42.66.-p Physiological optics

Identification of random auditory waveforms. III. Effect of interference

Irwin Pollack

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 680-686 (1976); (7 pages)

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The identification of specific random waveforms, imbedded within random interference, was examined. Backward interference (interference after the specific waveform) was more effective than forward interference (interference before the specific waveforms). The accuracy of identification with combined interference (interference before and after the specific waveforms) is approximated by an independence model of interference. Under the present test conditions, interference with the identification of specific random waveforms is interpreted to be more nearly related to the interruption of auditory processing than to the masking of signal audibility.
Subject Classification: [43]65.58, [43]65.75, [43]65.52.
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42.66.-p Physiological optics

Speech sound discrimination by monkeys and humans

J. M. Sinnott, M. D. Beecher, D. B. Moody, and W. C. Stebbins

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 687-695 (1976); (9 pages) | Cited 4 times

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Old World monkeys were trained with an operant conditioning technique to discriminate the natural speech sounds /ba/–/da/ and transferred to synthetic speech. Human and monkey difference thresholds for formant transitions were then compared along a seven‐step /ba/–/da/ continuum. Monkeys were not as sensitive as humans to differences in formant transition: the just noticeable difference for monkeys was about 320 Hz, and for humans, about 160 Hz. Although humans were more adept at intraphonemic discriminations than monkeys, their latencies to stimulus changes revealed evidence of ’’categorical perception’’ of the continuum: While latencies for the monkeys increased linearly as stimulus difference was decreased, human latencies were essentially constant for all interphonemic comparisons, but increased sharply for intraphonemic comparisons. We view these data as evidence for (a) similar sensory capacities in monkeys and humans, but (b) unique speech processing capacities in humans.
Subject Classification: [43]65.75; [43]70.30; [43]80.50.
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42.66.-p Physiological optics
43.70.-h Speech production
43.80.-n Bioacoustics

Comfortable effort level: An experimental variable

W. S. Brown, Jr., Thomas Murry, and David Hughes

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 696-699 (1976); (4 pages) | Cited 3 times

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It is not uncommon to read in speech studies that subjects were instructed to produce speech samples at a ’’comfortable effort level.’’ In many cases the experiments have made the assumption that this level of effort is more or less constant over repeated occurrences. The purpose of this study was to test the constancy of comfortable effort level in speakers’ utterances across experimental sessions. Sixteen speakers were recorded on each of five successive days while producing a series of vowels and phrases. The only instruction to the speakers was to repeat the utterances at a comfortable effort level. Measures of speaking fundamental frequency (SFF) and vocal intensity (SPL) were obtained from the recordings. Results indicate that variability in both SFF and SPL occurred in the utterances; in many cases (especially for SPL) this variability was considerable. These results suggest that experiments desiring constant vocal productions must be more specific in providing instructions to subjects since comfortable effort level can not be assumed to be constant from one experimental session to the next (especially from day to day).
Subject Classification: [43]70.40, [43]70.20.
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43.70.-h Speech production

An investigation of speaker height and weight identification

Norman J. Lass and Margaret Davis

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 700-703 (1976); (4 pages) | Cited 2 times

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The purpose of this investigation was to determine if listeners were capable of speaker height and weight identifications from recorded speech samples. A standard prose passage was recorded by 30 speakers, 15 females and 15 males. A master tape containing the randomly arranged recorded readings of all speakers was played to a group of 30 subjects for speaker height and weight identification purposes. All subjects participated in two experimental sessions. In one session they were asked to determine the height of each of the speakers on the tape, and in another session weight judgments were made. The order of presentation of the height and weight tasks was randomized so that 15 subjects made height judgments first while 15 subjects made weight judgments first. A multiple‐choice response sheet containing four choices for the judgment of height and weight for each speaker was provided. Results indicate that the subjects were capable, with slightly better than chance guessing accuracy, of identifying the heights of male and female speakers and the weights of male speakers when presented with only their recorded speech samples. Implications of these findings and suggestions for future research are discussed.
Subject Classification: [43]70.30.
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43.70.-h Speech production

The contribution of fundamental frequency and voice onset time to the /zi/‐/si/ distinction

Dominic W. Massaro and Michael M. Cohen

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 704-717 (1976); (14 pages) | Cited 5 times

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Functional measurement was utilized to study the acoustic cues that contribute to the perception of the voicing difference in /zi/ and /si/. Rather than simply varying the acoustic signal along a single dimension and observing the effect on perception, changes along two acoustic dimensions were covaried in a factorial manner. The time between the onset of the syllable and the onset of vocal‐cord vibration called voice onset time (VOT) was covaried with the fundamental frequency (F0). Observers were asked to indicate where each stimulus fell on a scale from /zi/ to /si/. The results showed that both VOT and F0 contribute to the perception of voicing. Sounds were judged as more /zi/‐like with decreases in VOT and with decreases in the F0. The frequency contour of F0 during the syllable had very little effect beyond that accounted for by the frequency of F0 at the onset of vocal‐cord vibration. Another experiment showed that the role of F0 could not be attributed to the possibility that there was less energy at the first formant with higher frequency values of F0. A quantitative model assuming that VOT and F0 are perceived independently provided a good description of the observed judgments.
Subject Classification: [43]70.30, [43]70.20, [43]70.70.
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43.70.-h Speech production

Some vocal distinctive features used by gelada monkeys

Bruce Richman

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 718-724 (1976); (7 pages) | Cited 7 times

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Recordings have been made of gelada monkeys freely vocalizing during normal social interchanges in captivity. Spectrographic analyses and perceptual evaluations of the recordings suggest that these primates produce a greater range of vocal distinctive contrasts than have been observed previously. In particular, evidence is presented which suggests that gelada monkeys are capable of producing three distinctive voice qualities, a wide range of vowel qualities, and a set of consonants that differ in manner of articulation (glides, a fricative, plosives, nasals) and in place of articulation (labial, postdental, velar).
Subject Classification: [43]70.40, [43]70.20; [43]80.50.
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43.70.-h Speech production
43.80.-n Bioacoustics

Jet drive mechanisms in edge tones and organ pipes

John W. Coltman

J. Acoust. Soc. Am. Volume 60, Issue 3, pp. 725-733 (1976); (9 pages) | Cited 15 times

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Measurements of the phases of free jet waves relative to an acoustic excitation, and of the pattern and time phase of the sound pressure produced by the same jet impinging on an edge, provide a consistent model for Stage I frequencies of edge tones and of an organ pipe with identical geometry. Both systems are explained entirely in terms of volume displacement of air by the jet. During edge‐tone oscillation, 180° of phase delay occur on the jet. Peak positive acoustic pressure on a given side of the edge occurs at the instant the jet profile crosses the edge and starts into that side. For the pipe, additional phase shifts occur that depend on the driving points for the jet current, the Q of the pipe, and the frequency of oscillation. Introduction of this additional phase shift yields an accurate prediction of the frequencies of a blown pipe and the blowing pressure at which mode jumps will occur.
Subject Classification: [43]75.60.
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43.75.+a Music and musical instruments
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