Volume 33, Issue 10, October 1961
Index of content:
33(1961); http://dx.doi.org/10.1121/1.1908417View Description Hide Description
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.
33(1961); http://dx.doi.org/10.1121/1.1908419View Description Hide Description
For the diffraction of electromagnetic waves from a standing sound wave, the amplitudes of the first diffraction order are calculated from Born's approximation. If the wavelength of the electromagnetic signal is made comparable to the acoustic wavelength, the first diffraction order vanishes periodically with increasing width of the sound beam because of a destructive interference of scatteredwaves. The sound‐perturbed medium becomes also slightly anisotropic. The diffraction of microwaves by a standing sound wave in oil is measured as a function of sound frequency and polarization of the electromagnetic wave.
33(1961); http://dx.doi.org/10.1121/1.1908421View Description Hide Description
Frequency equations of simple axisymmetric axial shear and simple axisymmetric radial vibrations were obtained for a soft elastic cylinder with a hard, thin, elastic skin. The soft core is treated on the basis of the three‐dimensional exact equations of elasticity while the thin skin is regarded as a membrane. Numerical frequencies for the first several modes for various values of the skin thickness were tabulated and their implications discussed.
33(1961); http://dx.doi.org/10.1121/1.1908423View Description Hide Description
The transient behavior of shock mountings disturbed by steplike displacements that invoke large departures of mount stiffness from linearity is described theoretically and compared with the behavior of an ideally linear mounting. The influence of mount damping upon the transient motion of the mounted item is discussed in detail.
For the majority of step rise times considered, a mount that softens upon compression and is not heavily damped is shown to reduce both the acceleration and displacement experienced by the mounted item below the values observed for a linear mounting or, as is normally the case in practice, a mount that stiffens upon compression. The reduction in acceleration can be comparable with 10 db for quite a wide range of step rise times. It is frequently the magnitude of the acceleration to which the likelihood of damage to the contents of the mounted item may be related.
33(1961); http://dx.doi.org/10.1121/1.1908425View Description Hide Description
Dynamic shear compliance measurements on a vulcanized natural rubber stock have been carried out from 50 to 5000 cps as a function of static elongation in the range 0–400%. Above 300% elongation several very large resonance dispersions appear in the region 1000–2000 cps, but at lower elongations no such resonances are observed. The appearance of mechanical resonancedispersion thus coincides with the development of oriented crystallinity in the stretched rubber as shown from x‐ray diffraction data. On the other hand, the magnitudes of the dispersions decrease with increasing elongation above 300% whereas x‐ray measurements indicate the amount or extent of crystallinity increases with stretching above 300% elongation. The resonances thus clearly decrease as the crystallinity becomes more perfect or more extensive and hence appear to reflect the imperfections of the crystalline regions formed by elongation rather than the crystallinity itself. Observed changes in the compliance spectrum with time at each elongation also favor this view. Broad retardation dispersions were observed when the rubber was allowed to contract back to elongations below 300% after long times above 300%. These are tentatively ascribed to an extended amorphous state in which the rubber molecules are kept partially extended by very small randomly oriented crystalline regions which persist for some time after retraction. Another interesting feature of the results is an apparent correlation between the percent crystallinity determined from x‐ray diffraction and the reciprocal of the general level of storage compliance 1/J′ at frequencies well below or well above the dispersion region.
33(1961); http://dx.doi.org/10.1121/1.1908427View Description Hide Description
Because of the many resonances, plates have an extremely small driving‐point impedance, add accurate measurements are difficult to perform. Some of the fundamental difficulties that accompany such measurements are illustrated by experimental results. Measurements performed with thin, rectangular plates show that the asymptotic laws of vibration and sound radiation predict, within the range of experimental error, the characteristic impedance and the sound radiation of plates. The theoretical prediction that damping would have no appreciable effect on either the characteristic impedance or the background level of the radiated soundpressure was found to be accurate.
33(1961); http://dx.doi.org/10.1121/1.1908429View Description Hide Description
This report treats the free and forced vibrations of infinitely long, thick and thin cylindrical shells surrounded by water. Exact elasticity theory is used to treat unpressurized shells and an approximate shell theory is employed to treat the effects of static pressure, internal fluid, and structural damping. Comparisons are made between the results of the exact and approximate theories.
33(1961); http://dx.doi.org/10.1121/1.1908431View Description Hide Description
Spectra of sound‐pressure amplitude versus frequency in the range 1.1 to 2.4 kc have been obtained at regular intervals in shallow (10 ft) water during two periods of extended observation. The acoustical data have been presented in the form of contour diagrams of sound‐pressure amplitude versus frequency and time as coordinates and compared with water conditions.
The form of the contour diagrams permits differentiation between field‐structure variation and variation in attenuation although differentiation between the associated processes has not been possible. Temporal variation in the vertical sound‐velocity profile produced only small changes in the gross features of the field structure, as inferred from the contour diagram, for up to the first three modes of propagation. For frequencies above 1.6 kc (i.e., when three or four modes were stimulated) the variations in field structure were prominent. Attempts have been made, with little success, to explain periods when the received signal was strongly attenuated in terms of vertical sound‐velocity structure.
33(1961); http://dx.doi.org/10.1121/1.1908433View Description Hide Description
Frequency spectra of the underwater noise produced by cavitating submerged water jets were determined experimentally for nozzle diameters from to , efflux velocities from 40 to 175 ft/sec, and ambient pressures up to 2 atm. When cavitation is barely incipient, the rms sound pressure varies with differences in the manner of handling the water prior to a run; this variation of sound pressure is presumably due to changes in the nuclei content of the water. When, however, the cavitation index is sufficiently small, cavitation is well advanced, and then the radiated sound is independent of the manner of treating the water. For this condition a simple relation is found to exist among the noise spectra when they are plotted as dimensionless functions of those physical quantities which determine the flow.
33(1961); http://dx.doi.org/10.1121/1.1908435View Description Hide Description
Piezoelectricceramic 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 piezoelectricproperties 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 (k 33∼0.64 compared to 0.365) and therefore offers higher transducer bandwidth.
33(1961); http://dx.doi.org/10.1121/1.1908437View Description Hide Description
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 Békésy's optical observations and Mayer's psychophysical data. The frequency‐position function is . The coefficient a is numerically identical with the coefficient in the exponential function fitting Békésy'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 distances on the basilar membrane is strengthened, one critical band corresponding to one millimeter. Problems for cochlear theory are posed (1) by the apparent equivalence of critical bandwidth, the derivative of the frequency‐position function, and the frequency interval over which spatial integration takes place, and (2) by the proportionality of these three at a given point to the compliance at that point.
33(1961); http://dx.doi.org/10.1121/1.1908439View Description Hide Description
The perception of sounds characterized by a moving resonance was investigated a series of experiments. Stimuli were generated by exciting a tuned circuit with a short train of pulses of repetition rate 100/sec. The resonant frequency of the tuned circuit was changed in a piecewise linear manner over a 500‐cps range. Subjects matched the test stimuli by adjusting the resonant frequency of a fixed (i.e., nonvarying in time) resonant circuit until the test and comparison stimuli were judged to be most alike. Results indicate a strong tendency for subjects to adjust the frequency of the fixed resonant circuit until it is close to the terminal resonant frequency of the time‐varying circuit. This tendency depended to some extent on the direction and rate of the frequency change in the test stimulus. The implications of the results for auditory theory and speech perception are discussed briefly.
33(1961); http://dx.doi.org/10.1121/1.1908441View Description Hide Description
Typical methods for observing pitch changes with intensity for pure tones consist of varying the frequency of one tone of fixed intensity (the comparison tone) so as to match the pitch of a second tone of fixed frequency (the tone under test) when the latter is set at different intensities. Differences between the comparison and test‐tone frequencies, when equated in pitch under these conditions, are ascribed to their intensity differences and used as a measure of the pitch intensity shifts for the test tone. The comparison and test tones may differ in frequency, however, even when they are matched in pitch under equal intensity conditions. These frequency differences, called pitch‐matching errors, may be identical to those noted above for comparable conditions and consequently nullify the apparent pitch‐intensity shifts. This possibility was studied in two experiments which sought to reproduce the pitch intensity relationship as defined by the data of Stevens and Snow. In more than half the comparisons made under various frequency and intensity conditions, apparent pitch shifts for 50, 75, 100, 200, 400, 700, 1500, and 6000 cps were found to be not significantly different from pitch‐matching errors. When averaged, the remaining shifts followed the directions of Stevens' curves but were small (2% or less). Pitch‐intensity functions for the lower frequency tones were particularly variable and generally bore little relationship to Snow's functions for such tones.
33(1961); http://dx.doi.org/10.1121/1.1908443View Description Hide Description
Two experiments are reported regarding man's sensitivity to waterborne sound. The first study investigated the threshold sensitivity to tones of 250, 500, 1000, 1500, 2000, 3000, 4000, and 6000 cps and the attenuation due to the diver's hood. The second experiment obtained data on the “tolerance” to a high‐intensity tone of 1500 cps.
The sound‐pressure level needed to reach threshold in water is about 40–70 db higher than the MAP threshold in air. The greatest loss in sensitivity occurs in the regions of greatest air sensitivity. The diver's hood was found to provide about 20 db or more of attenuation of underwater sound at frequencies above 1000 cps.
The “tolerance” limits for hoodless divers is approximately 174 db re 0.0002 dyne/cm2. When wearing the hood divers were able to tolerate at least 180 db, the system's maximum output. Above 165 db all divers reported some distortion of the visual field.
33(1961); http://dx.doi.org/10.1121/1.1908445View Description Hide Description
Evidence from studies of tactual sensitivity indicates that transient suprathreshold stimuli presented simultaneously with and contralateral to test signals will mask such signals more effectively than do steady stimuli. The present report presents evidence that when pulsed masking sounds are presented simultaneously with pulsed auditory signals, two major effects are observed: First, a significantly greater amount of contralateral masking is obtained with the pulsed masker than with the steady masker, and, second, the pulsed masker is more effective in the monaural condition also. Furthermore, the masking effect of pulsed maskers increases with the increase of signal frequency, but not with increase of masker intensity. The frequency of the masker must be near that of the signal to be effective, and if pure‐tone maskers are used with pure‐tone signals, the masking effect shifts continuously to the localization effect as the signal frequency approaches the masker frequency. Some explanations of binaural and contralateral masking are discussed.
33(1961); http://dx.doi.org/10.1121/1.1908447View Description Hide Description
The following problem is examined theoretically: A pressure is applied to an open‐circuited bar of piezoelectricceramic; after steady‐state conditions have been achieved, an electrical resistanceR is connected between the electrodes and simultaneously the pressure is removed. General equations describing the subsequent current and energy dissipation in the resistor are developed, and examined in detail for a specific transducer of lead zirconate‐titanate ceramic. The general equation for current consists of a series of time‐delayed functions, signifying physically that a mechanical wave propagates through the transducer with successive reflections at the end faces, releasing strain energy originally stored in the material; this energy is then dissipated in electrical form in the resistance. The initial current h*s two components, an exponential function representing the discharge of energy stored in electrical form in the transducer capacitance C 0 (about 10% of the total stored energy), and a step function representing the release of energy stored in mechanical form (remaining 90%). If R is small the exponential function predominates, and has a time constant which is approximately RC 0; the stored electrical energy is released very rapidly, while the mechanical energy is released much more slowly. If R is large (of the order of 104 ohms), exponential function and step function are of comparable magnitudes, and the time constant of the exponential is modified by the mechanical impedance of the transducer.
33(1961); http://dx.doi.org/10.1121/1.1908449View Description Hide Description
This investigation reports acoustical differences found for drumheads made of Mylar plastic instead of the conventional calfskin. Two identical bassdrums and two identical field drums were fitted with heads of the two materials. A professional drummer was engaged to adjust and play these drums with several tension adjustments. A tape‐recorded analysis was made of their sounds, including single impact beats and steady rolls. The sound spectra of the quasi‐steady‐state drum rolls were determined by half‐octave bands, by a method similar to that of Sivian, Dunn, and White. Spectra of the peak sound‐pressure levels were obtained with a General Radio impact sound analyzer. The buildup and decay of the drum sounds were analyzed in chosen frequency bands by use of a high speed level recorder. The chief physical differences found are: (1) the calfskin head is capable of a much larger range of tension adjustment, and (2) under certain conditions has more damping. When the bassdrum is tuned to concert tightness, there is a significant difference between the spectra of the plastic and calfskin drumheads and in the time variation of sound output. For the field drum there is little spectral difference, but the calfskin gives a more staccato beat with less “metallic” ringing.
33(1961); http://dx.doi.org/10.1121/1.1908451View Description Hide Description
Previous calculations of the statistical behavior of a hard spring oscillator excited by purely random and Gaussian noise are extended. The moments of the displacement and its extrema are found in an analytic form and their interrelations are exploited. Recurrence relations, asymptotic expressions, and computations of the moments are presented. Envelope autocorrelations for three narrow‐band linear filters are found, and the mean size of clumps of cycles exceeding predetermined levels is obtained. For the hard‐spring oscillator we find that the relative envelope fluctuation is less than that of a linear oscillator and that the mean clump size is also smaller in general.
33(1961); http://dx.doi.org/10.1121/1.1908454View Description Hide Description
The response of an oscillator with a nonlinear stiffness of the hard‐spring type to narrow band Gaussian random noise is analyzedtheoretically by using the method of quasi linearization. The particular point of interest is the possibility of an occurrence of multiple valued response or “jumps” such as one observes when the exciting force is sinusoidal. It is argued that while it does not seem possible to have multivalued response with wide‐band (white noise) excitation, the response to narrow band excitation might exhibit such behavior owing to the temporal correlation of the source with the response. Numerical computations of the response curves do suggest multivalued response. In experiments with a nonlinear oscillator, multivalued response was observed, but agreement between theory and experiment may only be claimed to be qualitative.
33(1961); http://dx.doi.org/10.1121/1.1908456View Description Hide Description
Ultrasonic attenuationmeasurements were made in liquid carbon disulfide‐alcohol mixtures over a frequency range from 5 to 155 Mc at a temperature of −63°C. From these measurements the vibrational relaxation frequency for the liquid was calculated. Methyl, propyl, and butyl alcohol were added in various concentrations up to 0.6 mole percent. In every case the relaxation frequency increased with the addition of the impurity. This increase was found to be a linear function of the impurity concentration which is consistent with the assumption that the vibrational‐translational energy transfer is a binary collision process. The shifts in relaxation frequency per mol % of impurity were found to be a linear function of the molecular weight of the impurity molecules for both the gas and liquid data.
A comparison was made of the ratio of collision efficiency of like to unlike molecules in both the gas and liquid state. It was found that within experimental error this ratio is the same in both states. This was interpreted as meaning that the vibrational relaxation process for unlike collisions was the same in both liquids and gases. Further, it appears that the efficiency of an AB‐type collision is more strongly temperature dependent than for the AA‐type collisions.