Volume 33, Issue 11, November 1961
Index of content:
33(1961); http://dx.doi.org/10.1121/1.1908468View Description Hide Description
Exact general solutions of the three‐dimensional elasticityequations of motion in polar cylindrical coordinates are written for axisymmetric and antisymmetric axial shear vibrations. The frequency equation follows immediately from the boundary conditions for the problem of the infinitely long, composite cylinder with two concentric circular‐cylindrical layers which are perfectly bonded at their interface. The branches of the frequency equation are plotted and analyzed. The conditions are pointed out under which it is possible to obtain reasonably accurate estimates of the natural frequencies by assuming that the motions of the casing and core are uncoupled.
33(1961); http://dx.doi.org/10.1121/1.1908470View Description Hide Description
An analysis is presented of the effect of weak damping on the natural frequencies of linear dynamic systems. It is shown that the highest natural frequency is always decreased by damping, but the lower natural frequencies may either increase or decrease, depending on the form of the damping matrix.
33(1961); http://dx.doi.org/10.1121/1.1908472View Description Hide Description
Axial resonances of long rods and tubes were used to generate motion for accurate calibration of vibration pickups over the frequency range from below 1 to above 20 kc at acceleration levels up to 12 000g. The resonators were driven by an electromagnetic shaker at low frequencies and by a piezoelectricceramic stack shaker at high frequencies. Vibration amplitude was measured optically by means of a microscope using stroboscopic light and by means of the interference fringe disappearance technique. Adequate overlap between the two methods was achieved by going up to the 60th disappearance of the fringes. A simple, direct measurement of the phase angle between the pickup signal and the motion is described. Construction details of a small, light pickup which is unaffected by the high acceleration levels are given.
33(1961); http://dx.doi.org/10.1121/1.1908474View Description Hide Description
Expressions have been derived from which the isolation provided by a simple mounting system when supported by any nonrigid foundation may be determined, if the mechanical impedance of the foundation is known. As an example, the mechanical impedance of a damped beam at its midpoint has been employed to simulate the behavior of such a foundation. Knowledge of the dynamic mechanical properties of natural rubber and a high‐damping synthetic rubber has enabled the behavior of antivibration mountings to be described realistically.
If the ratio of the mass of the mounted item to the mass of the foundation is large, the isolation afforded by a mounting is found to be much less than that predicted by its transmissibility curve, which relates to an ideally rigid foundation. It is shown, however, that the isolation provided by a mounting can be increased significantly at high frequencies if an additional mass is employed to load the foundation, the greatest isolation then being provided by a low‐damping rubber such as natural rubber. Damping of the foundation is found to have little influence upon the over all level of the isolation afforded by the mounting system.
33(1961); http://dx.doi.org/10.1121/1.1908476View Description Hide Description
Measurements are reported of some characteristics of the response of a simple panel to a steady periodic sound pressure intense enough to cause nonlinearity in the response. The panel is a 2‐in. wide, thin aluminum strip, clamped at its ends with the clamp faces 12 in. apart, and left free on its edges. Attention is focused principally on the fundamental resonance point, which occurred at frequencies as large as twice the low‐level resonance frequency.
Measurements of the frequency and strain at resonance, under various levels of excitation, are compared with predictions from a simple one‐mode nonlinear dynamic equation. For good agreement it is found necessary to include not only a nonlinear stiffness but also a nonlinear damping term. Theoretical predictions of the nonlinear stiffness from the physical characteristics of the panel are in error by a factor of 4.7 when based on an assumed mode shape for transverse deflection which is identical with the linear characteristic function of a clamped‐clamped beam.
33(1961); http://dx.doi.org/10.1121/1.1908478View Description Hide Description
The dynamic tensile strength of a piezoelectric lead titanate zirconate ceramic used for power transducers was tested by driving small bars of ceramic electrically at their longitudinal resonance until they fractured. The measured dynamic tensile strength of small specimens of ceramic of good quality was found to be about 13 000 psi. This value was very drastically reduced for ceramic which was not of optimum quality.
33(1961); http://dx.doi.org/10.1121/1.1908480View Description Hide Description
A simplified theory is presented for obtaining the frequencies, deflections, and stresses in cross stiffened and sandwich plates under dynamic loading. Formulas are derived giving the effect of the water on the natural frequency and the approximate Q of the plate. The application of resonant plates as underwater sound radiators is discussed, and procedures for designing such radiators are given.
33(1961); http://dx.doi.org/10.1121/1.1908482View Description Hide Description
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.
33(1961); http://dx.doi.org/10.1121/1.1908484View Description Hide Description
Computation of propagation losses are presented for 200‐ to 2000‐cps sound in 25‐fathom water to ranges of 250 miles over different bottoms for a zero gradient (isospeed), and out to 50 miles for a both weak negative gradient and a strong negative gradient. The ray method is used, together with the assumption of random phase after the first bottom reflection, to formulate the theory. The resulting computed transmission loss anomalies exhibit a marked dependence on: (1) the ratio of source depth to wavelength, (2) the sound‐speed gradients, and (3) bottom reflection losses at small grazing angles. The bottom reflection losses are strongly dependent on the attenuation in the bottom. Some long‐range experimental data are presented which show a quantitative agreement with the computed curves out to ranges of 40 miles.
33(1961); http://dx.doi.org/10.1121/1.1908486View Description Hide Description
While extensive information is available on flat pistons and on spherical radiators, no data have been given in the literature for the intermediate case of convex circular pistons of elliptical profile. In order to fill this gap, this paper presents information on the radiation loading and on the near and far field of such pistons. For the case of a free piston it is found that at small ka (where 2a is the diameter or major axis) the reactance decreases with increasing thickness (minor axis), while the resistance increases at small ka and decreases at large ka with increasing thickness. In the intermediate ka‐region, that is, when the wavelength in the fluid is of the order of magnitude of the dimensions of the piston, the dependence of the impedance on the thickness is more complicated. For the case of a piston in an infinite baffle the behavior of the reactance is similar to that for the free pistons. The resistance however is independent of the thickness in the limit of small ka and decreases with increasing thickness at larger ka. The effect of flexure on the impedance is briefly considered for the case of the free piston.
33(1961); http://dx.doi.org/10.1121/1.1908488View Description Hide Description
A laboratory facility is described as evolved for the measurement of sound transmission through suspended acoustical ceilings under field conditions of erection over part high partitions. The results of exploratory measurements are reviewed for a wide range of the dimensional and acoustical parameters of the ceiling‐plenum system. Consideration is extended to the ceiling‐partition system and to the importance of an accurate simulation of field conditions of erection for the testing of all elements, individually and interacting, in the ceiling‐plenum‐partition system. The compatibility of this approach with conventional test methods is suggested.
Problems of Field Measurement of Transmission Loss as Illustrated by Data on Lightweight Partitions Used in Music Buildings33(1961); http://dx.doi.org/10.1121/1.1908490View Description Hide Description
Field measurements of airborne sound‐transmission loss involve several practical difficulties and limitations as compared to the laboratory standard test procedures for such measurements. Data from field measurements are valuable to architects and acoustical consultants, in spite of these limitations. A workable procedure for field measurements is described, along with a discussion of the difficulties. Measured transmission loss data are presented for double plaster walls on cork isolation, double plaster walls on concrete slabs, double concrete block walls, double brick walls, single concrete block walls, and a floor slab with resiliently suspended plaster ceiling.
33(1961); http://dx.doi.org/10.1121/1.1908492View Description Hide Description
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.
33(1961); http://dx.doi.org/10.1121/1.1908494View Description Hide Description
Thresholds of audibility are determined by the Békésy technique for four periodic trains of rectangular pulses. The pulses of a given train are uniform in amplitude and duration, and the trains differ in their periodic patterns of pulse polarity. The parameters considered are pulse rate, pulse duration, and polarity pattern. The stimuli are presented binaurally in quiet over headphones. Data for four subjects are reported. The results show the threshold amplitudes to be little dependent upon polarity pattern. For pulse rates less than about 100 pps the thresholds are also little dependent upon pulse rate. They approach constant values determined by pulse duration. Above 100 pps the thresholds diminish with increasing pulse rate. The experimental technique also provides an estimate of the intensity limen at threshold. An analytical specification of the stimulus is derived which provides an objective correlate of the threshold percept. An electrical circuit model of the threshold is developed which takes account of middle‐ear and basilar membrane transmission. The threshold model reflects a constancy of percept over a pulse‐rate range of 10 octaves and a pulse‐duration range of ten to one. Its application to the metering of subjective loudness is suggested.
33(1961); http://dx.doi.org/10.1121/1.1908496View Description Hide Description
If a narrow bandpass filter is driven by a periodic train of narrow rectangular pulses, the resultant wave train elicits a strong pitch perception which varies monotonically with the pulse repetition rate. This periodic wave train can be used as a pitch reference to match against various stimuli. Consideration of double wave train stimuli with various delays establishes sharp dichotomy between the perception of pitch and timbre. Further evidence is adduced in support of the development of a partial model of psychoacoustic perception which is plausible in terms of the known physiologic mechanisms. In brief, the total acoustic stimulus undergoes a differential filtering action along the cochlear partition due to the resonantcharacteristic of the cochlear structure. The response characteristic of any particular segment of the partition exhibits a single broad peak and consequently has a relatively fast time response. The envelope of the response is assumed to be detected by a relaxation detector having a relatively wide dynamic range, and periodicity of the envelope is detected by a delay‐line detector. The second‐order time envelope of the cochlear‐partition response defines a function over the length of the partition. The shape of the envelope (along the partition) of the absolute value of this function elicits the perception of the timbre structure of the total stimulus. The total area under this envelope elicits the perception of the loudness of the total stimulus. This combination of broad‐band spectral filtering, envelope detection, and delay‐line periodicity detection provides both a mechanism for relatively sensitive pitch discrimination and for spectral discrimination with relatively fast time response.
Contralateral Threshold Shift and Reduction in Temporary Threshold Shift as Indices of Acoustic Reflex Action33(1961); http://dx.doi.org/10.1121/1.1908498View Description Hide Description
The purpose of the experiment was twofold: to compare the effectiveness of narrow band noise and a train of clicks in eliciting the middle‐ear acoustic reflex, and to correlate two methods of estimating amount of reflex activation. One method involved measurement of increase in threshold in the contralateral ear, the other, measurement of reduction of TTS produced by a series of gun shots. Sixteen subjects were employed. Shifts produced by the clicks and noise were of the same order of magnitude (after correction for the direct masking effect by the clicks), but there was considerable reflex adaptation to the noise and none for the clicks. Correlations between contralateral threshold shift and reduction of TTS were small and not significant.
33(1961); http://dx.doi.org/10.1121/1.1908501View Description Hide Description
In continuation of a previous paper, the relation between threshold, repetition time, and duration for periodically repeated tone pulses is treated. Experimental data at test frequencies of 250, 1000, and 4000 cps appeared to agree very well with a derived relation based on the following assumptions: Switching on a sinusoidal signal of intensity I results in an effect s somewhere in the hearing pathway, that approaches its final value asymptotically according to an exponential function; switching off this signal gives a decay of s also according to an exponential function; perception occurs when s exceeds a critical value s 0. For the time constants of the growth and decay of s the same value could be chosen, being in agreement with the corresponding value for single tone pulses (0.2–0.3 sec). For very short repetition times, the data deviate from the predicted curves, which is explained by the assumption that energy integration is restricted to a fixed bandwidth. These critical bandwidths determined for the periodic tone pulses are also in harmony with the results for single pulses.
33(1961); http://dx.doi.org/10.1121/1.1908503View Description Hide Description
If a 2200‐cps tone is pulsed 150 times/sec under appropriate conditions, a low pitch (periodicity pitch) will be heard corresponding to that of a 150‐cps pure tone. This experiment investigates the effectiveness of different bands of filtered noise in the masking of such pulses and in the masking of two pure tone stimuli, 150 and 2200 cps. Although the pulses and 2200‐cps pure tone yield quite different pitches, the present results indicate that the masking of each requires nearly identical frequency components and levels of noise. The 150‐cps tone, although yielding a pitch approximating that of the pulses, requires greatly different characteristics of noise to mask. Considering differences in apparatus and technique, reasonable agreement with other studies of pure tone masking by bands of noise is found. If masking is viewed as a neural phenomenon, these data provide additional evidence of the neural nature of periodicity pitch.
33(1961); http://dx.doi.org/10.1121/1.1908505View Description Hide Description
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 loudnessSt is given by , 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.
33(1961); http://dx.doi.org/10.1121/1.1908507View Description Hide Description
We raise again, in the framework of a very simple recognition task, the question of the relative efficacy of specifying the stimulus alternatives before and after the stimulus is presented. Our experiments show information given before the observation to facilitate recognition and information given after the observation to have little, if any, effect. We conclude that the facilitative effect of restricting alternatives, in the task studied, depends on a perceptual mechanism rather than on a response mechanism. These experiments are discussed in connection with two current psychological theories: the theory of signal detectability, which is essentially a perceptual theory, and the theory of individual choice behavior, which is essentially a response theory. The results of another experiment, the only other experiment discovered to date for which these two theories make different predictions, are also reported. In this experiment, too, the results are in agreement with the detection theory.