Showing papers in "Journal of the Acoustical Society of America in 1961"

Critical Bandwidth and the Frequency Coordinates of the Basilar Membrane

Abstract: Masked audiograms were used to measure critical bandwidth. On the assumption that critical bands represent equal distances on the basilar membrane and that critical bandwidth increases exponentially with distance from the helicotrema, functions were derived which (1) relate critical bandwidth to frequency and to position on the basilar membrane and (2) relate position of maximum amplitude to frequency. The functions are consistent with Bekesy's optical observations and Mayer's psychophysical data. The frequency‐position function is f = A (10ax − 1). The coefficient a is numerically identical with the coefficient in the exponential function fitting Bekesy's elasticity data. Functions of this form fit data from seven other species and the values of the coefficient a seem related to their respective elasticity, functions The interpretation of critical bandwidth as the frequency interval over which the cochlea sums power is supported by data of Mayer, and the hypothesis that critical bands represent equal dis...

Pulse Superposition Method for Measuring Ultrasonic Wave Velocities in Solids

Abstract: The frequently used pulse method of measuring ultrasonic wave velocities in solids involves a high‐frequency quartz crystal transducer cemented to one end of a specimen having parallel end faces. The phase shift for waves reflected from the transducer must be considered for highest accuracy. It is shown that combining several measurements of phase delay (at two frequencies differing by approximately 10%) with a theoretical analysis of the reflection phase angle makes possible a determination of velocity to within one part in 5000 for round trip delays greater than 5 μsec. Indirectly, the approximate thickness of the cement bond between transducer and specimen can be determined. The advantages of the method for making measurements as a function of temperature or pressure are discussed.

Sound Waves in Deformed Perfectly Elastic Materials. Acoustoelastic Effect

Abstract: The general equations for a small displacement superimposed on a finite deformation of a perfectly elastic material of arbitrary symmetry are derived anew. These equations are the basis of an analysis of plane waves of small amplitude propagating in an initially deformed and stressed elastic material. Certain restrictions on the energy function of finite elasticity theory are determined. These restrictions, which provide necessary and sufficient conditions that a homogeneously deformed material admit plane waves, are then compared with other restrictions obtained from themostatic equilibrium considerations. Compatibility conditions, which are necessary and sufficient that data on sound wave propagation in elastic materials be compatible with classical elasticity theory upon suitable assignment of the material symmetry, are derived. Finally, it is shown how the variation of sound speeds with initial stress and the measured magnitude of the acoustoelastic effect can be used to determine the third‐order elas...

Transient Performance of a Piezoelectric Transducer

Abstract: The methods of transform calculus are used to solve several problems in which the transient response of a piezoelectric transducer is of interest. The electrical signal produced by a step function of force is derived, both for open‐circuit and resistive loading at the electrical terminals, and the mechanical signal produced by a voltage step is also discussed. The analyses are performed for both the plate transducer in compressional thickness vibration and the bar in compressional length vibration, and the important differences between the two transducers are discussed. The analyses commence with the fundamental piezoelectric equations, and solutions are found which represent successive time‐delayed reflections of the mechanical transient between the end faces of the transducer. The results are also discussed with reference to the exact transmission‐line electrical equivalent circuits of the transducers, whose development is outlined briefly. Simple equivalent circuits which do not involve lines are descr...

On the Edgetone

Abstract: The feedback mechanism of classical low‐speed edgetones in which the action at the edge is interpreted as an acoustical source is developed in detail. A theoretical development indicating that the acoustic field is primarily due to the dipole associated with the fluctuating fluid force on the edge has been verified. It is the hydrodynamic field of the dipole which disturbs the jet, whose instability characteristics are shown to depend acutely on the Reynolds and Strouhal numbers, and the orifice‐edge distance. The gain criterion is developed in detail, it being shown how the eigenfrequencies (which can form no algebraic sequence) arise; the lower limit to the orifice‐edge distance is discussed, yielding an estimate of the “linear” instability of the stream. The amplitude of the established edgetone depends on the nonlinear behavior of large‐amplitude stream disturbances and the corresponding upper limit to the edge force proves to be in satisfactory agreement with measurements, thus yielding acceptable expressions for the sound pressure. Multiple tones and the circumstances of the hysteretic frequency jumps are discussed. The basic action depends only on Reynolds number for geometrically similar systems, while the sound power depends on the cube of the Mach number also.

On Vowel Duration in English

Abstract: Average durations of 12 vowels of American English measured in bisyllabic nonsense utterances are reported. The vowels occurred in 14 symmetrical consonantal environments and the utterances were produced by three male talkers. The consonant environments consisted of the voiced and voiceless versions of three stop, one affricate, and three fricative consonant articulations. Four determinants of the characteristic durations of stressed vowels are identified and discussed. The hypothesis is advanced that the primary lengthening of vowels in English—that found in tense vowels and in vowels before voiced constants—is a part of the phonology of the language and is learned by speakers of the language, and that the secondary lengthening of vowels in English—that found in open vowels and in vowels before fricative constants—is a function of the articulatory process itself.

On the Properties of Voiceless Fricative Consonants

Abstract: According to an acoustical theory of speech production, the spectra of voiceless fricatives can be characterized by poles and zeros whose frequency locations are dependent on the vocal‐tract configuration and on the location of the source of excitation within the vocal tract. The locations of the important poles and zeros in the spectra of fricatives can be determined by a matching process whereby comparison spectra synthesized by electric circuits are matched against the spectra under analysis. This method has been used to determine the frequencies and bandwidths of the important poles and zeros for several versions of /f/, /s/, and /∫/. Based on these findings, a simplified electrical model is developed for the synthesis of voiceless fricatives. The model consists of a noise‐excited electric circuit characterized by a pole and a zero whose frequency locations can be varied. Stimuli generated by this model, both in isolation and in syllables, are presented to listeners for identification. The results of the listening tests are consistent with the data from the acoustic analyses and with the findings of other investigators.

Voice Level: Autophonic Scale, Perceived Loudness, and Effects of Sidetone

Abstract: The speaker's numerical estimation of his own vocal level, the autophonic response, was found to grow as the 1.1 power of the actual sound pressure produced. When listeners judged the loudness of another speaker's vocalization (the phoneme [a]), the exponent was 0.7. The disparity between these exponents suggests that the speaker does not rely solely upon his perception of loudness in judging his own relative vocal level. The minor role played by loudness in the autophonic judgment is further demonstrated by the fact that the form and exponent of the subjective scale for autophonic responses remain relatively invariant under wide changes in auditory feedback.The power laws governing the autophonic response (exponent 1.1) and loudness (exponent 0.6) were used to predict successfully the outcome of cross‐modality comparisons in which subjects tried to match their vocal level to sounds of various intensities presented either by loudspeaker or by earphone. The slope of the matching function, relating the criterion SPL to the vocal SPL in log‐log coordinates, is given by the ratio of the two exponents.Unless the speaker tries deliberately to hold a constant level, the amount of sidetone gain with which the voice is fed back to the ears alters the voice level. The degree to which the speaker lowers his voice when the sidetone is increased is also predicted by the exponents governing the autophonic scale and the loudness scale.

Auditory Masking and the Critical Band

Abstract: Masked audiograms were studied as a function of the bandwidth, level, and frequency of a masking noise. In a reverse procedure, audiograms were determined when a movable, narrow, and approximately rectangular band of noise was used as signal in the presence of one or more masking tones. In both cases changes in the masked audiograms as a function of bandwidth made it possible to measure critical bandwidth. When masked audiograms were studied as a function of level, discontinuous changes in their height and shape occurred when the masking stimulus reached a certain “transition” level. If masking noises of subcritical or critical width were used, the growth of masking with level contained a discontinuity at a level of the masking stimulus equal to about 50 db SL. An abrupt change in the shape of the masked audiograms occurred at the same level. The change of shape when a pure tone was the masking stimulus consisted in the appearance of a “notch” one critical bandwidth above the frequency of the masking tone. Findings associated with the bandwidth parameter suggest interpretations of the critical band and of masking. The changes occurring at the transition level may indicate the threshold of the inner haircells.

Transitions, Glides, and Diphthongs

Abstract: The study deals with the formant movements associated with transitions, glides, and diphthongs in spoken American English. The transitional characteristics associated with all initial and final consonant phonemes were studied in a large sample of utterances. The rate of change of the transition from a consonant hub to the steady state vowel formant position and conversely was investigated for vowels which are commonly considered monophthongs. It is assumed that such changes are cues for the perception of the consonants rather than linguistically significant components of the vocalic nucleus. The rate of change associated with syllable nuclei commonly perceived as diphthongs, [ɑɪ], [ɔɪ], [ɑᴜ] was investigated and compared with the changes due to consonant transitions in monophthongs. Criteria are suggested by which the formant movements due to transitions may be distinguished from movements that have linguistic signalling value within the syllable nucleus.

Operating characteristics, signal detectability, and the method of free response

Abstract: The method of free response refers to the following listening situation. Against a background of noise, a weak signal is presented several times in a long (2‐min) observation interval. The temporal intervals between the presentations of the tones are randomly distributed; consequently, the listener does not know when a tone will occur, and he does not know how many tones will be presented. From one series of observation intervals to the next, the listener is instructed to adopt various criteria and to press the single response‐key each time he “hears a tone.” The problem consists in the determination of a procedure that allows the total number of yes responses to be partitioned meaningfully between “hits” and “false alarms.” A model is developed in which the measurable quantity, rate of response, is related to the “hit rate” and to the “false‐alarm rate.” Although the criterion adopted by the listener cannot be directly evaluated, the use of a wide range of criteria makes it possible to estimate the detectability ds of the signal. Two experiments are described, and the results support the model.

Effect of Anoxia on Cochlear Potentials

Abstract: The anterior inferior cerebellar artery of guinea pigs was occluded, thereby interrupting the blood supply to the cochlea. Durations of occlusion ranged from 1 through 60 min. Cochlear microphonics, summating potential, action potential, and endocochlear potential were recorded before, during, and subsequent to occlusion. The differential effect of anoxia on the various potentials was observed, as well as the appearance of the large negative dc potential in scala media as anoxia progressed. For the brief occlusion durations, the amplitudes of all potentials except cochlear microphonics became greater than normal soon after the blood supply returned. Even for the longer anoxic intervals, the summating potential and the endocochlear potential exhibited super‐normality during the recovery process.

Theory of Rectified Diffusion of Mass into Gas Bubbles

Abstract: The problem considered is the behavior of a gas bubble in a liquid saturated with dissolved gas when oscillating pressures are imposed on the system. This situation is encountered in experiments on cavitation and in the propagation of sonic and ultrasonic waves in liquids. Since gas diffuses into the bubble during the expansion half-cycle in which the pressure drops below its mean value, and diffuses out of the bubble during the compression half-cycle in which the pressure rises above its mean value, there is no net transfer of mass into or out of the bubble in first order. There is, however, in second order a net inflow of gas into the bubble which is called rectified diffusion. The equations which determine the system include the equation of state of the gas in the bubble, the equation of motion for the bubble boundary in the liquid, and the equation for the diffusion of dissolved gas in the liquid. In the solution presented here, the acoustic approximation is made; that is, the amplitude of the pressure oscillation is taken to be small. It is also assumed that the gas in the bubble remains isothermal throughout the oscillations; this assumption is valid provided the oscillation frequency is not too high. Under these conditions one finds for the mean rate of gas flow into the bubble the expression (dm/dt) = (8π/3)D C_∞ R_0 (ΔP/P_0)^2 where D is the diffusivity of the dissolved gas in the liquid, C_∞ is the equilibrium dissolved gas concentration for the mean ambient pressure P_0, R_0 is the mean radius of the bubble, and ΔP is the amplitude of the acoustic pressure oscillations. It may be remarked that the most important contribution to the rectification effect comes from the convection contribution to the diffusion process.

Reduction of Speech Spectra by Analysis‐by‐Synthesis Techniques

Abstract: Procedures are described for reducing the speech wave to a specification in terms of the time‐varying vocal‐tract resonances and source characteristics. The basic method, which has been called analysis by synthesis, involves the comparison of speech spectra with a series of spectra that are synthesized within the analyzer. Each comparison spectrum is generated according to a set of rules based on an acoustical theory of speech production. The result of the analysis of each input spectrum is a set of parameters that describes the synthesized spectrum providing the best match. In one version of the method convergence, towards the best match is controlled by the experimenter; in another version convergence to a match is accomplished automatically without the intervention of the experimenter. All the operations have been programmed on a general‐purpose digital computer and have been applied to the analysis of vowels and some consonants. The advantages of the analysis techniques are discussed.

Mechanism of the Middle Ear

Abstract: A mechanical model of the middle ear is obtained from anatomical observations. The differential equations for the model are solved, and the solutions are found in good agreement with the impedance of the ear at the tympanic membrane measured in many earn of fresh cadavers. Thus, the mechanism of the middle ear is clarified theoretically as well as experimentally. The ossicular chain loaded with the impedance of the cochlea is found to be the most important factor controlling the impedance of the tympanic membrane. The ossicular chain has two resonances: the lower one due to the malleoincudal body, and the higher due to the stapes. Thus, the ossicular chain keeps the reactance of the tympanic membrane near or at its resonances. The function of the air cavities behind the tympanic membrane is found to be similar to but less than that of the ossicular chain. The apparent pressure gain by the middle ear for the cochlea is measured. From these data the frequency characteristic of the ossicular chain the impedance of the stapes are calculated. Moreover, it is found experimentally as well as theoretically that the transmission of the middle ear is not only increased by a lower impedance of the tympanic membrane but also by a higher impedance; transmission is increased by the tympanic membrane vibrating as a rigid cone attached to the ossicular chain even though such attachment increases the impedance of the tympanic membrane.

Procedure for Calculating Loudness: Mark VI

Abstract: In order to improve the procedure for calculating the loudness of a complex sound, two changes have been made. (1) The equal loudness contours for bands of noise in a diffuse field have been approximated by straight lines in a log‐log plot. (2) The spacing of the contours have been altered to reflect the nonlinear growth that takes place in the loudness level of bands of noise when their width exceeds the critical bandwidth. The basic formula for the addition of loudness across frequency remains the same: the total loudness St is given by St = Sm + F(Σ S − Sm), where Sm is the loudest band and F has the values 0.3, 0.2, and 0.15 for octave, half‐octave, and third‐octave bands.The revised procedure has the advantages that it can be described more easily and it agrees better with the available measurements on loudness level.

Network Model of the Middle Ear

Abstract: The fine‐structure acoustic‐impedance curve of the ear obtained from normal humans in vivo is used to develop a network model of the middle ear. First a model representing the middle ear during stapedius muscle contraction is constructed, representing the middle ear with the stapes blocked. A further development adds a circuit corresponding to the input impedance of the cochlea as seen from the stapes. To decrease the influence of the eardrum itself, the eardrum was coated with collodion. Good agreement is found between the input impedance measured at the ear and calculated from the model over the range investigated, from 200 to 1800 cps. The effect of the collodion coating is investigated and the earlier model is modified to fit the input impedance of the uncoated ear. The agreement is not so good as in the case of coated drum. The reason is suggested to lie in the complicated motion of the uncoated eardrum, which could not be represented by the simple circuit of the model.

Mode Coupling Occurring in the Propagation of Elastic Pulses in Wires

Abstract: The propagation of elastic pulses in wires of circular cross section has been studied for conditions in which pulses having carrier frequencies ranging from 0.5 to 4.0 Mc were transmitted in wires having diameters between 0.1 and 0.2 cm. The pulses used in the experiments were shaped to have relatively narrow frequency spectra. At certain frequencies, herein called critical frequencies, pulses propagating in certain modes were observed to undergo pronounced distortion in which the peak amplitude of an affected pulse was reduced and the duration of the pulse was increased many times its original length. This pulse distortion associated with the presence of critical frequencies is shown to be caused by coupling between two modes of propagation. In agreement with predictions of the general theory of mode coupling, the critical frequencies are frequencies at which two modes of propagation have the same phase velocity.

Axisymmetric Modes of Vibration of Thin Spherical Shell

Abstract: In this paper we present a detailed study of the theory of free, axisymmetric vibrations of thin elastic spherical shell and demonstrate by experiment that the normal modes of vibration predicted by theory do exist. The theory, which is an expansion of an ancient study by Lamb, predicts the existence of two infinite sets of normal modes, one of which is bounded in frequency and the other unbounded. The first four modes in each set are identified by experiments on a small steel shell.

Interval of Time Uncertainty in Auditory Detection

Abstract: Three experiments were conducted to measure the decrement in performance that results from uncertainty in the time of onset of a signal presented against a continuous background of noise. The fixed‐interval observation experiment was employed. A light defined an observation interval for the listener during which the signal, a tone of 1000 cps, either was or was not presented [p(SN)=0.5]. The signal, when presented, started at an instant randomly selected within the observation interval. Thus, the listener was uncertain as to (1) whether or not the signal would occur in the observation interval, and (2) the onset time of the signal, if in fact the signal occurred. The interval of time uncertainty (ITU) during which the tone might start was systematically varied from one series of trials to the next, and the listener knew the duration of ITU in each series. After each observation interval, the listener indicated his confidence that a tone was presented by using a rating scale. Operating characteristics [p(y|SN) against p(y|N)] were plotted on normal‐normal coordinates, and measures of detectability were computed. The functional relation between the detectability index d, and the interval of time uncertainty is presented for each experiment.

Pitch Synchronous Analysis of Voiced Sounds

Abstract: A study of vowel sounds by means of a spectral analysis keyed synchronously to the voice pitch has been carried out. Spectra are obtained by Fourier analysis of individual pitch periods which were established by visual inspection of oscillogram. A digital computer served as the analyzer. The spectra are represented by a pattern of zeros and poles obtained by a process of successive approximation, again carried out by computer. The contributions from vocal tract and glottal source can be uniquely separated and examined. These results show that vowel sounds can be represented by a sequence of poles arising from the vocal tract and a sequence of zeros character the izglottal excitation. The frequencies of the vocal tract poles agreed with previous measurements, but the damping factors were not entirely consistent with earlier estimates. The zeros showed approximately uniform frequency spacing, particularly at high frequencies. A theoretical development indicated that this characteristic was to be expected from the known structure of the glottal excitation. The zero pattern was used to estimate the ratio of open‐to‐closed time for the glottis during voicing.

Bottom Reverberation for 530‐ and 1030‐cps Sound in Deep Water

Abstract: Bottom reverberation measurements were made during September, 1954, with 530‐ and 1030‐cps sound in 2100 fathom water near San Diego for ping durations of 0.1, 0.25, 0.5, 1.0, and 2.0 sec with omnidirectional sources and receivers. The data were analyzed by assuming that the returned sound consisted of both specularly and nonspecularly reflected sound, analogous to the regular and diffuse reflected light from Bristol board. At normal incidence the losses on reflection for the 530‐ and 1030‐cps sound were 19.5±2.5 db and 15.4±1.7 db, respectively. The other sound returning from the bottom as reverberation was assumed to be due to nonspecular reflections obeying Lambert's law of diffuse reflection. The reverberation level due to the nonspecular reflections was then analyzed to obtain the scattering constant μ of the bottom. A value of 10 logμ=−27 db was obtained for both the 530‐ and 1030‐cps sound. The curves computed for a sine squared dependence fit the data for grazing angles from 90° to 30°. A comparison with published values of other investigators indicates that for clays, muds, or fine grained sands there appears to be no significant frequency dependence over a range of seven octaves.

Effects of High Static Stress on the Piezoelectric Properties of Transducer Materials

Abstract: Piezoelectric ceramic elements in high‐power acoustic transducers are subjected to high static as well as dynamic stress. This is particularly true of well‐matched transducers operating in deep water, since the static stress in the piezoelectric element may be several times the water pressure. The present study was undertaken in an effort to determine the effects of static compressive stress on the piezoelectric properties of two commercial lead titanate zirconate compositions, PZT‐4 and PZT‐5, and of two barium‐titanate compositions, commercial Ceramic B (a barium calcium titanate), and the composition 88 wt% barium titanate, 12 wt% lead titanate (BaPb12Ti). The permanent effects of stress exposure, determined at zero stress after exposure to a given stress, were found to be more severe with stress parallel to the polar axis than with perpendicular stress, as expected. Under maintained stress, however, the effects of perpendicular stress are more severe. PZT‐4 and BaPb12Ti, generally better suited for use as radiating transducers, show effects dependent upon exposure time but independent of the number of stress cycles. Ceramic B and PZT‐5 show effects dependent upon the number of stress cycles and less dependent upon the total period of stress exposure. Of the compositions tested, PZT‐4 and BaPb12Ti were least affected by high static stress, suffering relatively little from exposure to stress as high as 15 000 psi. Of these two compositions. PZT‐4 has markedly higher coupling (k33∼0.64 compared to 0.365) and therefore offers higher transducer bandwidth.

Detection of Auditory Sinusoids of Uncertain Frequency

Abstract: The decrease in the detectability of a gated sinusoidal signal in noise caused by deliberately introducing uncertainty about the signal's frequency is no greater than 3 db, even in an extreme condition of uncertainty. In this extreme condition the signal duration is 0.1 sec, and the signal frequency is varied between 500 and 4000 cps. This effect is not critically dependent on signal duration. Moreover, the observers not only detect the signal but display at least gross information about the frequency of the signal in the uncertain frequency conditions.Several models, suggested in previous studies, are considered. The magnitude of the decrease observed in the data falls far short of the predictions of these models. An interpretation suggested by the data is that the observers in a detection task, even when a signal of fixed frequency is used, are highly uncertain as to the exact physical parameters of the signal. Another way of stating this assumption is to say that the observer never tests for the presence or absence of a signal on the basis of one simple hypothesis. From this assumption we should expect little decrease in detectability from deliberately introducing frequency uncertainty. This interpretation would suggest the same result would be obtained if time were the major experimental variable.

Attenuation and Dispersion of Elastic Waves in a Cylindrical Bar

Abstract: The resonance method has been used to study the attenuation and dispersion of the first longitudinal mode of propagation and the dispersion of the first flexural mode of propagation of elastic waves in a cylindrical, aluminum alloy (24ST) rod. Q was found to decrease monotonically from 2.5×105 to 1.2×105 as the frequency increased from 0.84 to 100 kc. Longitudinal and flexural phase velocities are compared to Pochhammer‐Chree theory dispersion curves. Agreement of experimental and theoretical curves is within 0.3%. Similar agreement is obtained when normal flexural modes computed by a modified Timoshenko theory are compared to the experimental resonant frequencies. Measurements of torsional mode frequencies indicate dispersion does not exceed approximately 0.01% in the frequency range of approximately 0.5 to 100 kc.

Form of the Loudness Function in the Presence of Masking Noise

Abstract: It was established that the loudness of a 1000‐cps pure tone in the presence of random noise is given by ψ = k(In − I0n), where I is the pure tone intensity and I0 the threshold intensity of the pure tone in the presence of masking noise. The exponent n is approximately 0.27, and the value of k depends on the choice of units. This relation also holds when the only masking noise present is the physiological noise generated in the ears, and it thus describes the conventional loudness function.

Rayleigh Waves in a Porous, Elastic, Saturated Solid

Abstract: The equation for the velocity of propagation of Rayleigh‐type surface waves in a porous, elastic, saturated solid is derived and discussed. The inertia coupling between fluid and solid is neglected, and Darcy's coefficient is taken to be independent of frequency.

Phasor Analysis of the Stereophonic Phenomena

Abstract: An improved understanding of some stereophonic phenomena may be obtained by use of acoustical pressure phasors to portray sound pressure at the ears of the observer With the help of phasors it is possible to expand and modify certain conclusions of previous observers, and to validate some previously unpublished observations; stereophonic “law of sines” is derived The existence and location of “out‐of‐bounds” stereo‐phonic image is analyzed and verified The “allowed maximum out‐of‐phase ratio” is derived, together with the observation that this maximum is exceeded by certain microphone arrays The motion and elevation of the center image in stereophonic reproduction is observed and explained

Time vs Intensity in the Localization of Tones

Abstract: Subjects were asked to match the lateral position of one tone, the “signal,” by means of another, the “pointer.” The two tones were presented alternately. The experimenter selected a combination of interaural time and intensity differences for the signal, and the subject adjusted the interaural time difference for the pointer until it seemed to him to be in the same lateral position as the signal. Subjects having normal hearing perceived the signal in two places, one strongly affected by the difference of level at the two ears, the other almost wholly dependent upon the difference of time.