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Showing papers in "Journal of the Acoustical Society of America in 1965"


Journal ArticleDOI
TL;DR: In this article, a new method of measuring reverberation time was described, which uses tone bursts (or filtered pistol shots) to excite the enclosure and a simple integral over the toneburst response of the enclosure yields, in a single measurement, the ensemble average of the decay curves that would be obtained with bandpass filtered noise as an excitation signal.
Abstract: A new method of measuring reverberation time is described. The method uses tone bursts (or filtered pistol shots) to excite the enclosure. A simple integral over the tone‐burst response of the enclosure yields, in a single measurement, the ensemble average of the decay curves that would be obtained with bandpass‐filtered noise as an excitation signal. The smooth decay curves resulting from the new method improve the accuracy of reverberation‐time measurements and facilitate the detection of nonexponential decays.

826 citations


Journal ArticleDOI
TL;DR: Evaluation of theories on the explanation of tonal consonance as the singular nature of tone intervals with frequency ratios corresponding with small integer numbers supports the hypothesis that the difference between consonant and dissonant intervals is related to beats of adjacent partials.
Abstract: Firstly, theories are reviewed on the explanation of tonal consonance as the singular nature of tone intervals with frequency ratios corresponding with small integer numbers. An evaluation of these explanations in the light of some experimental studies supports the hypothesis, as promoted by von Helmholtz, that the difference between consonant and dissonant intervals is related to beats of adjacent partials. This relation was studied more fully by experiments in which subjects had to judge simple‐tone intervals as a function of test frequency and interval width. The results may be considered as a modification of von Helmholtz's conception and indicate that, as a function of frequency, the transition range between consonant and dissonant intervals is related to critical bandwidth. Simple‐tone intervals are evaluated as consonant for frequency differences exceeding this bandwidth. whereas the most dissonant intervals correspond with frequency differences of about a quarter of this bandwidth. On the base of these results, some properties of consonant intervals consisting of complex tones are explained. To answer the question whether critical bandwidth also plays a role in music, the chords of two compositions (parts of a trio sonata of J. S. Bach and of a string quartet of A. Dvořak) were analyzed by computing interval distributions as a function of frequency and number of harmonics taken into account. The results strongly suggest that, indeed, critical bandwidth plays an important role in music: for a number of harmonics representative for musical instruments, the “density” of simultaneous partials alters as a function of frequency in the same way as critical bandwidth does.

747 citations


Journal ArticleDOI
TL;DR: Analysis of the responses to individual phonetic elements shows that the test can be useful for diagnostic study as well as for over‐all evaluation of communication systems.
Abstract: The development and evaluation of a new speech‐intelligibility test suitable for routine use by operational personnel in determining the performance level of speech‐communication systems is described. The format used is similar to that described for a rhyme test but makes use of a closed‐response set. An experiment was performed to determine the general reliability of the test materials when administered to U.S. Air Force enlisted personnel under a wide range of signal‐to‐noise ratios. Testing of 18 listeners over a period of 30 days showed that repeated exposure to the materials did not change the levels of average response in any appreciable way. Analysis of the responses to individual phonetic elements shows that the test can be useful for diagnostic study as well as for over‐all evaluation of communication systems. Talker differences that appeared during the experiment and the statistical reliability and sensitivity of the materials are analyzed and discussed.

419 citations


Journal ArticleDOI
TL;DR: In this paper, a ray-tracing method is proposed for computing the path of a wave from an exploding source in a shallow water with slowly varying depth, and the theory is applied to the study of the dispersion of waves from an explosive source in shallow water.
Abstract: A theory is presented that permits the extension of the method of normal modes to guided‐wave propagation in a medium with properties varying slowly with horizontal coordinates in addition to varying with the vertical coordinate. The principal assumption is the neglect of coupling between normal modes. It is predicted that different frequencies in different modes follow different horizontal paths. A ray‐tracing method is described for computing these paths. The theory is then applied to the study of the dispersion of waves from an explosive source in shallow water with slowly varying depth.

199 citations


Journal ArticleDOI
Emmanuel P. Papadakis1
TL;DR: In this paper, the grain size distributions and ultrasonic velocities in fine-grained specimens of several metals were determined and the experimental attenuation was in good quantitative as well as qualitative agreement with current theory.
Abstract: Ultrasonic‐attenuation measurements have been made on fine‐grained specimens of several metals. The grain‐size distributions and ultrasonic velocities in these metals were also determined. The experimental attenuation is in good quantitative as well as qualitative agreement with current theory. Nickel and three iron alloys, one 30% nickel reported previously, the second 12% chromium (type 416 stainless steel), and the third 17% chromium and 1% carbon (type 440‐C stainless steel), all gave good results. Brass also gave good results, but copper showed much twinning, which as yet is unaccounted for.

190 citations


Journal ArticleDOI
Karl D. Kryter1
TL;DR: The paper contains graphs of maximum sound‐pressure levels and durations of exposures that the NAS‐NRC CHABA Working Group believes would be tolerable and examples of the use of these graphs.
Abstract: The following document was prepared by NAS‐NRC CHABA Working Group 46. This group was asked to specify damage‐risk criteria for exposure to sound. The paper contains graphs of maximum sound‐pressure levels and durations of exposures that the Working Group believes would be tolerable and examples of the use of these graphs in addition to background information and a discussion of the rationale, assumptions, limitations, and general problems pertinent to the development and application of a damage‐risk criterion and related exposure contours.

185 citations


Journal ArticleDOI
TL;DR: A retrospective study of hearing in a female population exposed to weaving noise is described, finding an initial deterioration in the first 10–15 years of exposure, followed by a period of about 10– 15 years where deterioration attributable to noise is small.
Abstract: A retrospective study of hearing in a female population exposed to weaving noise is described. The noise is believed to have remained substantially unaltered over periods of exposure ranging from less than 1–52 years. The deterioration of hearing due to noise has been assumed to be estimated by the difference between the recorded hearing level and the expected hearing level from other published presybcusis data. Patterns of deterioration of hearing are described for various audiometric frequencies. The most conspicuous feature is an initial deterioration in the first 10–15 years of exposure, followed by a period of about 10–15 years where deterioration attributable to noise is small. Thereafter, after 20–25 years of exposure, further deterioration occurs, especially marked at 2000 cps. The possible distribution of noise‐induced threshold changes is briefly considered.

182 citations


Journal ArticleDOI
TL;DR: In this paper, a two-part study concerning the wave propagation of free harmonic waves in hollow and solid circular cylinders of transversely isotropic material is discussed on the basis of the linear theory of elasticity.
Abstract: A two‐part study concerning the wave propagation of free harmonic waves in hollow and solid circular cylinders of transversely isotropic material is discussed on the basis of the linear theory of elasticity. The three‐dimensional equations of elastodynamics are solved in terms of three displacement potentials, and the resulting frequency equation is discussed for several special cases.

176 citations


Journal ArticleDOI
TL;DR: Human evoked cortical responses to acoustic stimuli occurring within 150–170 msec after stimulus onset yielded input‐output functions fairly comparable with Stevens' power functions from psychophysical experiments.
Abstract: Human evoked cortical responses to acoustic stimuli occurring within 150–170 msec after stimulus onset yielded input‐output functions fairly comparable with Stevens' power functions from psychophysical experiments. The objective threshold and equal‐loudness contours thus obtained were both in fair agreement with the well‐known subjective measurements.

153 citations


Journal ArticleDOI
TL;DR: The Zwislocki theory of temporal summation was tested for vibrotactile sensitivity and suggested that glabrous skin contains at least two populations of mechanoreceptors, was confirmed by using contactors of varying size.
Abstract: The Zwislocki theory of temporal summation was tested for vibrotactile sensitivity. Vibrotactile thresholds were determined as a function of pulse repetition rate and pulse number for short pulses. Thresholds for various burst durations of sinusoidal signals were also determined. The results indicate that the theory is sufficient to predict vibrotactile thresholds for the temporal patterns used. An earlier finding, which suggested that glabrous skin contains at least two populations of mechanoreceptors, was confirmed by using contactors of varying size.

152 citations


Journal ArticleDOI
TL;DR: There are large individual differences in the minimum sensation level of primary tones for which combination tones appear, and for usual listening levels of speech and music, the ear's distortion is sufficiently low to avoid audible combination tones.
Abstract: Experiments were performed on the detectability threshold for combination tones, defined as the sensation level of primary tones for which combination tones become audible. Investigated were (1) detectability threshold for h−l with (h−l)<<(h+l), where h and l are the frequencies of the higher and lower primary tone, respectively; (2) detectability threshold for 200, 400, and 600 cps with 800+1000 and 800+1400 cps as primary tones; (3) audibility of combination tones for l = 1000 cps and h variable between 1000 and 3000 cps; (4) detectability threshold for the “missing fundamental” of ∑ n−210 cos 2 πnft, with f varying from 125 to 1000 cps. From the experimental data, we may conclude that (1) there are large individual differences in the minimum sensation level of primary tones for which combination tones appear; (2) for usual listening levels of speech and music, the ear's distortion is sufficiently low to avoid audible combination tones; (3) the same holds for the “missing fundamental,” so the fact that ...

Journal ArticleDOI
TL;DR: In this article, effective elastic coefficients for wave propagation obeying all of the classical symmetry relations βijkm=βkmij=βjikm=βijmk= … can be defined for crystals of any symmetry under positive or negative hydrostatic pressure.
Abstract: Effective elastic coefficients for wave propagation obeying all of the classical symmetry relations βijkm=βkmij=βjikm=βijmk= … can be defined for crystals of any symmetry under positive or negative hydrostatic pressure. For other states of stress, the full symmetry is lost, even in isotropic materials. The loss of the full symmetry commonly expected of elastic coefficients has a simple physical interpretation the case of uniaxial stress in an isotropic medium. A transverse wave propagates faster in the direction of tension than in the perpendicular direction because tension increases the restoring force for displacements associated with the former wave, just as in a stretched string. The difference in ρV2 for the two waves equals the tensile stress. Hence, the corresponding effective elastic coefficients, which would be equal under the classical symmetry, also differ by this same amount. In this paper, we define effective elastic coefficients and express them in terms of the stress, the deformation result...

Journal ArticleDOI
TL;DR: In this paper, a number of methods are described for increasing the sensitivity of a measuring technique that has proven to be particularly useful for determining 3rd-order moduli and other quantities from measured changes in ultrasonic delay times.
Abstract: A number of methods are described for increasing the sensitivity of a measuring technique that has proven to be particularly useful for determining 3rd‐order moduli and other quantities from measured changes in ultrasonic delay times [J. Acoust. Soc. Am. 33, 12 16(1961)]. Pulse cancellation, phase comparison, and methods involving either pulse position or frequency modulation have been examined. Two of the circuits developed are amenable to automatic frequency control, with precisions better than one part in 106.

Journal ArticleDOI
TL;DR: In this paper, the behavior of a masking transient that indicates that masking of a short signal pulse by a longer white noise burst is stronger at the beginning of the masker burst than later was investigated.
Abstract: The motivation of the research described was to investigate the behavior of a masking transient that indicates that masking of a short signal pulse by a longer white‐noise burst is stronger at the beginning of the masker burst than later. The threshold of signal pulses masked by masker bursts was measured as a function of different variables such as bandwidth and center frequency of the signal, delay between onset of masker and onset of signal, duration of signal and masker, level of masker, and repetition rate. The results reveal very little “overshoot” of the threshold of short pulses as a function of the ON time of the masker if the signal and the masker have the same or similar broad spectra. The overshoot increases up to 13 dB as the bandwidth of the signal decreases down to that of a tone. The size of the “overshoot” and the prior excitation seem to be related to each other. Taking this in account, the thresholds under different conditions can be calculated on the basis of detection models. The measured and the calculated values are in good agreement.

Journal ArticleDOI
TL;DR: The study suggests that a vowel is coded in short‐term memory, not as a unit, but as a set of values that are more likely to be forgotten than the correct value on the place dimension.
Abstract: Errors in short‐term recall of six English vowels (I, e, ae, U, ʌ, ɑ) were tabulated and related to several distinctive‐feature systems. Vowels were embedded in two contexts: /l[ ]k/ and /z[ ]k/. Subjects were instructed to copy items as they were presented, followed by recall of the entire list of (six) items. Perceptual errors were excluded from the recall error matrix by scoring for recall only correctly copied items. The rank‐order frequency of different intrusions in recall of each presented vowel was almost perfectly predicted by a conventional phonetic analysis in two dimensions: place of articulation (front, back) and openness of the vocal tract (narrow, medium, and wide). The error matrix also supported the assumptions that the values of openness are ordered in short‐term memory and that the correct value on the openness dimension is more likely to be forgotten than the correct value on the place dimension. The study suggests that a vowel is coded in short‐term memory, not as a unit, but as a set of two distinctive features, each of which may be forgotten independently.

Journal ArticleDOI
TL;DR: In this article, an empirical evaluation of attenuation in sea water in the frequency range of 354-3540 cps has been conducted, where the receiving elements were located near the axis of the so-far channel.
Abstract: An experiment was conducted to provide an empirical evaluation of attenuation in sea water in the frequency range of 354–3540 cps. Recordings were made of solar shots detonated every 5 miles along a 500‐mile track. The receiving elements were located near the axis of the sofar channel. An analysis is outlined both in terms of received energy spectrum and transmission loss as a function of range. The experimental data have been statistically fitted by least‐squares methods to a mathematical model of the form NW = H0+10 log R+aR, where H0 represents the transmission loss in excess of inverse first‐power spreading. These results have been combined with those from a subsequent experiment, conducted in the same geographical area, that extended the frequency coverage to 112 cps. The regression line fitting the joint set of coefficients to an upper limit of 1780 cps is given by a = 5.42×10−5 fkcps1.50 dB/yd. The present evaluation is compared with other results, and an apparent systematic anomaly is discussed.

Journal ArticleDOI
TL;DR: The results, especially those obtained when white noise with a frequency gap was the masker, lead to the hypothesis that the masking excitation appears almost instantane...
Abstract: The intention of the research described was twofold. One purpose was to investigate the difference between threshold curves for tones masked by bands of noise and the corresponding displacement curves obtained from models of the basilar membrane. The second object of investigation was the behavior of a strange masking transient which indicates that masking of a short signal pulse by a longer masker burst is stronger at the beginning of the masker burst than later under certain circumstances, but that under other conditions masking remains constant during the total duration of the masker. The threshold of signal pulses masked by masker bursts was measured as a function of different variables such as bandwidth and center frequency of masker, delay between onset of masker and onset of signal, duration of signal, and spectrum shape of masker. The results, especially those obtained when white noise with a frequency gap was the masker, lead to the hypothesis that the masking excitation appears almost instantaneously. This hypothesis was tested and accepted on the basis of loudness judgments comparing equally long tone pulses and white‐noise pulses of very short and long duration. The conclusion that excitation occurs almost instantaneously, taken together with the known relationship between the masking effect of white noise and that of narrow‐band noise, is construed to mean that a complex spatial inhibition in the nervous system may not be responsible for the narrow sensitivity curve; in fact, a sharp mechanical filter could account for the findings.

Journal ArticleDOI
TL;DR: In this article, a kinetic theory description of sound propagation in a simple gas is presented and the results are in very close agreement with experiment through all values of Knudsen number.
Abstract: A kinetic theory description of sound propagation in a simple gas is presented. The results are in very close agreement with experiment through all values of Knudsen number.

Journal ArticleDOI
TL;DR: In this paper, a theoretical and experimental study of the influence of shear flow on the attenuation of sound in a lined duct is presented, and solutions of the linearized equations for acoustic wave propagation in flow, based upon both uniform and power-law models of the mean flow profile, are compared with attenuation measurements in a duct having two opposite side walls lined with a porous fiberglas® blanket.
Abstract: A theoretical and experimental study of the influence of shear flow on the attenuation of sound in a lined duct is presented. Both upstream and downstream propagation are considered. Solutions of the linearized equations for acoustic‐wave propagation in flow, based upon both uniform and power‐law models of the mean‐flow profile, are compared with attenuation measurements in a duct having two opposite side walls lined with a porous fiberglas® blanket for a frequency‐geometry range kδ⩽1 and midstream Mach numbers Ml<0.2. Here, k is the plane wavenumber and δ is the aerodynamic boundary‐layer thickness. Both profile models yield results in close agreement with experiments at low frequencies, kδ<0.1. For intermediate and high frequencies, 0.1

Journal ArticleDOI
TL;DR: A comparison was made between the digital spectra obtained for several speech sounds and those obtained with 50‐cps constant‐bandwidth analog filters, and within expected limits, the agreement was good.
Abstract: Digital spectral analysis offers certain advantages over analog techniques: (1) the equivalent bandwidth of the analysis can be varied easily and (2) complicated calibration procedures are not required. A real‐time analog‐to‐digital magnetic‐tape recording system, designed as part of future instrumentation that will record digitized noise or speech signals and calculate their spectra with special purpose computer, records 31 250 digitized analog time samples per second in a 9‐bit code. Currently, an IBM‐7094 data‐processing system is programmed to perform trapezoidal integration of the Fourier integral to obtain the spectrum of the digital recordings. The Fourier transform of a 16‐msec square pulse differed from the calculated values by less than 4% of the actual amplitudes in the frequency range 0–5000 cps. A comparison was made between the digital spectra obtained for several speech sounds and those obtained with 50‐cps constant‐bandwidth analog filters. Within expected limits, the agreement was good. T...

Journal ArticleDOI
TL;DR: In this article, a flat plate perpendicular to the jet axis, there being a hole in the plate of the same diameter as the jet orifice and concentric with the jet, and a ring whose plane was perpendicular to a jet axis and whose diameter was equal to that of the orifice was observed.
Abstract: Discrete‐frequency tones can be generated when objects obstruct the path of an axially symmetric jet. An experimental study of this phenomenon was conducted when the objects were (1) a flat plate perpendicular to the jet axis, there being a hole in the plate of the same diameter as the jet orifice and concentric with the jet, and (2) a ring whose plane was perpendicular to the jet axis and whose diameter was equal to that of the jet orifice. The tone from the former geometry is the hole tone and that from the latter, not previously observed, is the ring tone. The mechanism of tone generation appears to be very similar to that of the edge tone, although presently only qualitative explanations can be offered for certain aspects of the phenomena. The axially symmetric jet systems are sensitive to very weak acoustic reflections.

Journal ArticleDOI
TL;DR: A new method for measuring speech‐identification behavior is described and articulation functions under normal and degraded conditions are compared with analogous functions for more conventional‐speech audiometric materials.
Abstract: A new method for measuring speech‐identification behavior is described. Thirty closed‐message sets were constructed. Each set contained 10 synthetic sentences, representing 4 levels of approximation to a “real” sentence. Sentence length and informational content were controlled. Message identification under conditions of low‐pass filtering and periodic interruption was studied in 30 subjects. Performance varied systematically with informational content. Articulation functions under normal and degraded conditions are compared with analogous functions for more conventional‐speech audiometric materials. [This investigation was supported by National Institute of Neurological Diseases and Blindness, National Institutes of Health, Public Health Service, U. S. Department of Health, Education, and Welfare.]

Journal ArticleDOI
TL;DR: By postulating that the recording electrode averages the output of many out‐of‐phase generators, several of the apparently rather anomalous behaviors of the SP and CM may be explained.
Abstract: This paper examines the effects of abandoning the assumption that the summating potential (SP) and cochlear microphonic (CM) commonly recorded from the cochlea are produced by single groups of in‐phase generators. It shows that, by postulating that the recording electrode averages the output of many out‐of‐phase generators, several of the apparently rather anomalous behaviors of the SP and CM may be explained. Included in this category is the behavior of the CM at very high intensities. A new mode of generation of the SP is suggested and some of its implications discussed. A semiquantitative argument is used to substantiate the claim that the mechanism of cancellation of out‐of‐phase components is adequate to account for those effects which have been attributed to it, and a concluding section deals briefly with some of the further implications of the model relating to other observed behaviors.

Journal ArticleDOI
TL;DR: Electrophysiological recordings made from the nerve to a piece of skin in vitro show that these two fibers are spontaneously active and are sensitive to water velocities in opposite directions, indicating that the origin of the spontaneous activity should not be Brownian motion of the cupula.
Abstract: In Xenopus laevis, the lateral‐line system may be considered as a single organ, containing about 20 000 hair cells, that is used to detect moving objects. From anatomical and neurophysiological evidence, it appears to be organized in groups of sensory buds, called stitches, which are directionally sensitive, probably to velocity. Each stitch is innervated by two large myelinated afferent fibers and by a few small myelinated and unmyelinated fibers, which may be efferent. Electrophysiological recordings made from a piece of skin in vitro show that the two large fibers are spontaneously active and sensitive to motion in opposite directions. The spontaneous activity in each fiber is independent of spontaneous activity in the other, indicating that the origin of spontaneous activity cannot be Brownian motion of the cupula. Interval histograms of spontaneous activity show an exponential tail for long intervals and a decrease in the number of small intervals. There is a characteristic absence of intervals less ...

Journal ArticleDOI
TL;DR: Comparison of the results of this experiment with those of previous experiments in which fixed‐amplitude tones were used, indicates little difference between the observers' abilities to discriminate frequencies of fixed‐ and random‐amPLitude tones at 1000 cps.
Abstract: The ability of human observers to discriminate frequencies of tones between 1000–15 000 cps was measured in a temporal two‐alternative forced‐choice discrimination experiment. On each trial, one of the test tones, selected at random, was attenuated by a random amount ranging from 8 to 20 dB in 2‐dB steps. Comparison of the results of this experiment with those of previous experiments in which fixed‐amplitude tones were used, indicates little difference between the observers' abilities to discriminate frequencies of fixed‐ and random‐amplitude tones at 1000 cps. Discrimination with random‐amplitude tones becomes relatively poorer, however, as frequency is increased. For example, the classical data show a frequency just‐noticeable difference (jnd) of 40 cps at 10 000 cps; in the present experiment, with random‐amplitude signals, the observers were unable to achieve 75% correct responses until ΔF was 300 cps.

Journal ArticleDOI
TL;DR: In this article, the exact frequency equations obtained in Part I [J. Acoust. Soc. Am. 37, 1016-1021 (1965)] are presented for hollow circular cylinders, and comparisons are made with an approximate shell theory developed previously.
Abstract: Numerical results to the exact frequency equations obtained in Part I [J. Acoust. Soc. Am. 37, 1016–1021 (1965)] are presented here for hollow circular cylinders, and comparisons are made with an approximate shell theory developed previously.

Journal ArticleDOI
TL;DR: In this article, the PB-50 lists were presented in a sound field against a background of spoken sentences, and test items came from a loudspeaker to one side of the subject and competing sentences from a second loudspeaker, on the opposite side.
Abstract: PB‐50 lists were presented in a sound field against a background of spoken sentences. Four signal‐to‐noise ratios plus one quiet condition were used. Test items came from a loudspeaker to one side of the subject and competing sentences from a second loudspeaker, on the opposite side. Sixteen normal hearers underwent both test and retest under one binaural and two monaural conditions. Discrimination functions for these conditions showed similar configurations, but were displaced from one another along the signal‐to‐noise axis. Head‐shadow effects caused poorer discrimination during monaural listening when test items come from the far side of the head. Monaural efficiency with the open ear facing the source of test items was almost as good as binaural efficiency. However, binaural performance here exhibited an advantage equal to approximately a 3‐dB shift in signal‐to‐noise ratio, despite the fact that the head‐shadow effect enhanced interference in the far ear by almost 13 dB. [Work supported by the Veterans' Administration and by the National Institute of Neurological Diseases and Blindness, National Institutes of Health, U. S. Department of Health, Education, and Welfare.]

Journal ArticleDOI
TL;DR: In this article, the elastic constants of silicon carbide polytype 6H have been measured by a resonance method and a double-pulse method, using a double resonance method.
Abstract: Elastic constants of silicon carbide polytype 6H have been measured by a resonance method and a double‐pulse method

Journal ArticleDOI
TL;DR: A pilot experiment revealed errors to be associated with (a) relative pattern complexity (large numbers of vibrators) and (b) high degree of communality (many elements in common).
Abstract: In an effort to supply widespread cutaneous stimulation and thus make possible systematic study of the limits of spatial discrimination through this channel, there has been devised a multiple contactor system permitting application of vibratory signals to 10 bodily loci simultaneously. Patterns comprising from 1 to 9 stimuli were presented in successive pairs, the subject's task being to report whether the patterns were perceived as “same” or “different.” Members of pairs were separated by 500 msec and burst duration was 200 msec. Two synchronized Western Union tape transmitters presented 20 programs of 50 pairs of patterns, 500 “same” and 500 “different” pairs being randomly intermixed in the 1000 presentations. A pilot experiment, in which many types of pattern changes were explored, revealed errors to be associated with (a) relative pattern complexity (large numbers of vibrators) and (b) high degree of communality (many elements in common). A formal experiment, involving a stratified sample with all combinations of numbers of loci and degrees of communality represented equally, verified the preliminary finding, and permitted, in addition, separation of the two factors apparently responsible. The relation between errors and communality, with number of stimulus positions held constant, proves to be an intimate one; confusions between patterns arise when there is relatively large overlap of elements in the patterns to be discriminated. A supplementary analysis, directed at whether particular receptive areas may be especially prone to error, shows no single locus, of the 10 employed, contributing to error production more than would be dictated by chance.

Journal ArticleDOI
TL;DR: In this article, it was shown that the amplitude response exhibits a downward jump while the driving frequency is being increased and an upward jump at a different frequency while the frequency was being decreased.
Abstract: The forced vibrations of stretched strings near their resonance frequencies exhibit several features that cannot be explained on the basis of the classical theory. As the driving frequency approaches resonance frequency, the increase in the amplitude of vibration of the string causes a change in its tension and the restoring force becomes nonlinear. Experiment shows that the amplitude response exhibits a downward jump while the driving frequency is being increased and an upward jump at a different frequency while the frequency is being decreased. Moreover, when the amplitude of vibration in the plane of the driving force reaches a certain critical value, which depends upon the magnitude of the driving force, the string acquires a component of motion in a direction normal to the plane of the string and the force. These phenomena are always observed in a more or less conspicuous manner, depending upon the magnitude of the force. When the restriction to infinitesimally small amplitudes of vibration (which is untenable near resonance) is removed, the motion of the string is governed by a pair of nonlinear, partial differential equations. Appropriate solutions of these equations show that the jump phenomena and the nonplanar vibration are the normal pattern of resonance behavior of stretched strings, however small the driving force may be. Response patterns and other results deduced from theory agree closely with those obtained from experiment.