Volume 34, Issue 8, August 1962
Index of content:
34(1962); http://dx.doi.org/10.1121/1.1918241View Description Hide Description
Exact solutions for the interaction between two concentric cylindrical waves and between two concentric spherical waves are presented. The scattered‐pressure amplitude in the far field is shown to be constant in the cylindrical case and to be proportional to r −1 lnr in the spherical case, where r is the distance to the source of primary waves.
A near‐field solution is derived for the scatteredwaves generated when two sharply defined, plane‐wave beams of square cross section intersect at right angles. A comparison is made of the theory with recent experiments in which beams of circular cross section were used. It is concluded that if the scatteredwaves do exist, their amplitudes are at least 40 dB below those that are predicted by this theory.
When a hard object is placed in the region of intersection, scatteredwaves are observed. This effect can be explained by the fact that with the addition of the hard object (a cylinder) the primary waves have components of the same symmetry. These components are the wavesscattered from the primary beams by the object. Evidence is presented to show that these components, having the same symmetry, interact strongly in the volume surrounding the object.
34(1962); http://dx.doi.org/10.1121/1.1918242View Description Hide Description
The sound generated by the nonlinear interaction of two sound beams of high intensity, arranged to cross each other perpendicularly, is computed to the first order of interaction. Several of the assumptions and specializations in previous treatments of this problem, whose effects on the result it is hard to estimate, are avoided. The interaction is supposed to take place in the Fraunhofer zone of both beams.
Some results obtained are of general validity. For instance, the Doppler angles computed and measured by Ingard and Pridmore‐Brown are found, without any strict specializations of the primary beams and the interaction region.
Estimates of the amplitudes of the generatedpressure, governing rather wide ranges of frequencies of the primary beams, seem to agree with the previous apparently strongly differing results. This correspondence is brought forward by an amplitude factor, depending on the frequencies of the primary beams.
In the high‐frequency limit, the destructive interference among the quadrupoles which give rise to the generated sound dominates the results and gives an over‐all zero value of the generatedpressure, in accordance with Westervelt's treatment.
34(1962); http://dx.doi.org/10.1121/1.1918243View Description Hide Description
Experiments are reported on the measurement of the scattered pressure from two finite‐amplitude, collinear sound beams. The measurements were carried out at a carrier frequency of 13.5 Mc in water and of 350 kc in air. The slope of the half‐pressure angle vs difference frequency curve agrees well with that predicted by Westervelt, although the radiation pattern measured experimentally was in each case more directive than predicted by the theory.
Influence on the Behavior of a Linear Dynamical System of Some Imposed Rapid Motions of Small Amplitude34(1962); http://dx.doi.org/10.1121/1.1918244View Description Hide Description
Occasionally, linear dynamical system must operate under the influence of imposed motions of very small amplitude and high frequency which were not contemplated in its design. The influence of such motions on the behavior of the system is therefore of paramount interest. It is shown that, although the differential equations of motion are linear with oscillatory coefficients when the imposed motions are present, it is possible under certain conditions to determine the behavior in an average sense from the solution of a system of linear differential equations with constant coefficients. Criteria to determine the influence of the imposed motions on the stability and response to various inputs of the original system are easily found.
34(1962); http://dx.doi.org/10.1121/1.1918245View Description Hide Description
A method is presented for determining the differential equations of the output moments of a linear random system in which the coefficients are components of vector Markov processes. The method is based upon well‐known results in applied stochastics. It appears considerably simpler than methods recently suggested for studying the behavior of linear random systems.
A stability criterion previously published is obtained with little effort. Reasons are presented for disagreeing with published results that mean motion of linear random systems with Gaussian parameter variations is not influenced by these variations.
34(1962); http://dx.doi.org/10.1121/1.1918246View Description Hide Description
The paper presents a theoretical development of the equations of motion for the flexural vibrations of a shallow spherical shell of orthotropic material. For symmetrical vibrations, the motion is described by two ordinary sixth‐order differential equations with variable coefficients. Factorization of the sixth‐order operators into second‐order operators is discussed and the details of solution are worked out for the case in which the equations are reduced to those for the isotropic shell. It is shown that equations for the latter case agree exactly with those derived previously by Reissner. A table of calculated frequencies is given along with some experimental results for steel shells.
Note on the Radial Deformation of a Piezoelectric, Polarized Spherical Shell with a Symmetrical Temperature Distribution34(1962); http://dx.doi.org/10.1121/1.1918247View Description Hide Description
The solution of the problem of static radial deformation of a piezoelectric spherical shell, polarized in the radial direction corresponding to uniform pressures on the inner and outer surfaces of the shell, and a given voltage difference between these surfaces, coupled with a radial distribution of temperature from the inner to the outer surface, forms the chief interest of the present note. The constitutive relations, deduced by Mindlin are taken in a form which closely resemble those of Toupin.
34(1962); http://dx.doi.org/10.1121/1.1918248View Description Hide Description
Combined random and swept sinusoidal vibration is used in the qualification of missileelectronic equipment. The subject of this report is how structural fatigue produced by a combined excitation is related to structural fatigue produced by another combined excitation or to that produced by individually applied random or sinusoidal excitation. In particular, a method is given by which different random or combined random and sinusoidal vibration excitations can be compared. This method finds practical application in comparing vibration specifications and tests, and for the purpose of modifying vibration requirements from one type to another.
In this derivation, substitute sinusoidal vibration excitations and sweep rates are based on the response characteristics of a single resonator system, while amplitude and time relationships are based on the S‐N diagram of the material under consideration. Equations and curves are given and their use illustrated by means of a numerical example.
34(1962); http://dx.doi.org/10.1121/1.1918249View Description Hide Description
General expressions are derived for the loss factors of axially uniform linear composite structures in terms of properties of the constituents. Specializations applicable to practical composites incorporating free and constrained viscoelastic components are introduced. The results are shown to be generalizations of earlier studies of coated and sandwich plates [Ross, Ungar, Kerwin, Sec. 3 of Structural Damping, ASME (1959)], and it is demonstrated that much of the abundant information available for such plates may be carried over to more complicated structures by redefinition of the structural and shear parameters.
34(1962); http://dx.doi.org/10.1121/1.1918250View Description Hide Description
A hydrophone assembly with terminals the Lerner Marine Laboratory, Bimini, Bahamas, has been installed on the east bank of the Straits of Florida in order to study the sounds produced by marine animals in the natural environment. Sounds from two bottom‐mounted hydrophones, one in 100 ft of water and the other in 1200 it, were recorded on dual track, magnetic tape on a 24‐h basis. The tapes were played back at eight times recording speed and monitored for sounds possibly of marine animal origin. More than 25 categories of sounds were observed during the initial period from November 1960 to July 1961. A number of the categories showed repetitive, diurnal patterns and possible seasonal patterns of soniferous activity. In general, sound categories the shallow and deep sites were different. Usually, only a single category was heard from a hydrophone at one time. Some tentative identifications have been made.
34(1962); http://dx.doi.org/10.1121/1.1918251View Description Hide Description
34(1962); http://dx.doi.org/10.1121/1.1918252View Description Hide Description
The authors describe the methods used and results obtained in a series of experiments designed to examine the effects of unilateral auditory masking upon the apparent position of a sound in space. Listeners were asked to locate various pure‐tone and complex‐sound signals delivered by a concealed loudspeaker while pure tone or complex masking stimuli were delivered to one ear by means of a single headphone. The results of these experiments indicate that masking can have a strong and consistent effect in pulling the apparent source of the free‐field signal toward the masked ear. The authors interpret this as evidence that binaural interaction is taking place and stress that most other methods of examining the phenomenon would fail to detect interaction between the types of stimuli used. The experimental data also indicate that intensity and frequency relations between signal and mask play a major role in determining the extent to which a masking stimulus will pull the apparent source of sound toward the masked ear; the effect is striking when the frequency spectrum of the mask covers that of the free‐field signal; the effect may still be evident, however, when signal and mask have no frequency components in common. The wide range of frequency relations between interacting signals and masks is consistent with the findings of neurophysiological and neuroanatomical studies of the auditory nervous system.
34(1962); http://dx.doi.org/10.1121/1.1918253View Description Hide Description
“Backward masking” is the term used to denote the situation in which one auditory stimulus is masked by another auditory stimulus which follows it in time while in “forward masking” the temporal positions of masking and masked signals are reversed. In this study, backward and forward masking were investigated for both monotic and dichotic conditions using white noise as the masking signal and a 1000‐cps probe signal. Results indicate that monotic backward masking occurs over intervals up to 50 msec while, for the dichotic condition, backward masking occurs for intervals as long as 15 msec. Less monotic forward masking is obtained for brief masking intervals and very little dichotic forward masking is observed. These findings are considered in relationship to other experimental results.
34(1962); http://dx.doi.org/10.1121/1.1918254View Description Hide Description
34(1962); http://dx.doi.org/10.1121/1.1918256View Description Hide Description
Data on loudness estimates at 60, 200, 500, 1000, 5000, and 10 000 cps were continued at the University of Arkansas from 1933 to 1959. A recalculation of all data to 1950 indicated that fractional judgments required a smaller decibel change of intensity than the corresponding multiple loudness estimates. This new result, hereafter referred to as the directional dependency, accompanied by a provisional explanation, was recorded in the Journal of the Arkansas Academy of Sciences in 1950, and reported together with certain additional experiments at the Second ICA Congress in June of 1956.
Since reluctance to accept unanticipated results is considerable, a new approach to a series of experiments designed to explore this directional dependency was preceded by review of a possible dynamical explanation. The follow‐up experiments included the proposed dynamical explanation as a part of the experimental objective and included new methods in our laboratory for the recording of judgments.
The results of the earlier series have been confirmed, but a satisfying explanation has not been established.
34(1962); http://dx.doi.org/10.1121/1.1918257View Description Hide Description
Subjects were asked to center a noise presented via earphones, by adjusting a delay line controlling interaural time differences. Various noise correlations were employed ranging from 1.00 to 0.10. Even in the latter case, which represents a signal to noise difference of −9.5 dB the subjects were able to perform well above a chance level.
34(1962); http://dx.doi.org/10.1121/1.1918258View Description Hide Description
Masking level differences obtained for 167 cps are presented. Some involved shifting the phase of the signal through various angles, and others, shifting the noise in interaural time. Where the experimental conditions are comparable to Hirsh's at 200 cps, the data agree very closely with his. The data obtained with various interaural time differences in the noise are shown to differ sharply from comparable data taken at 500 cps.
34(1962); http://dx.doi.org/10.1121/1.1918259View Description Hide Description
Animalexperiments have suggested the possibility that the compressional mode of bone conduction might produce a displacement of the cochlear partition, even when the cochlear windows and all other potential pressure outlets are closed. This assumption was found correct for the case of a cochlear model. It executed so‐called “distortional” vibrations, i.e., while its walls in one place moved inward, those in the other moved outward and vice versa. This mode of motion tends to keep constant the total volume of the enclosed incompressible fluids.
The two perilymphatic spaces are known to differ in volume. Distortional motion causes the volume difference to alternate, thus producing compensatory displacements of the partition. This is in contrast to the effect upon the partition of the translatory and antiphasic movements of the cochlear windows in response to air‐conducted sound. When both windows are open, or only one is occluded, the displacement of the partition, due to bone‐conducted sound, represents the combined result of distortional and translatory motion.
The generation of traveling waves, when input and output are distributed over the entire cochlear shell, as in bone conduction, is discussed in terms of general cochlear mechanics.
Studies on the Aural Reflex. III. Reflex Latency as Inferred from Reduction of Temporary Threshold Shift from Impulses34(1962); http://dx.doi.org/10.1121/1.1918260View Description Hide Description
The effective protection provided by arousal of the acoustic reflex against temporary threshold shift (TTS) at 4 kc from exposure to impulse noise was studied by comparing the rate of growth of TTS produced by 2‐min exposures to clicks of successively higher peak levels under two conditions: first, when the clicks were heard alone, and second, when each click was preceded at various intervals from 25 to 150 msec by a 1000‐cps 100‐dB pure tone presented to the contralateral ear. The results imply that the effective attenuation amounts to 1 dB at 25 msec, 5 dB at 62 msec, and 13 dB at 100 msec. Individual differences were large; some of the most slowly responding ears did not show significant protection until the delay reached 150 msec. The practical conclusion reached is that a reflex‐arousal stimulus to be used to protect gun crews should precede firing by 150 msec or more. In regard to theory, the results support the hypothesis that the value of the acoustic impedance of an ear at any instant is an accurate indicator of the protection provided by the middle earmuscles. However, there is also evidence that part of the protection may stem from a change, with reflex arousal, in the peak‐limiting characteristics of the middle ear.
- LETTERS TO THE EDITOR
Determination of the Energy Reflection, Absorption, and Transmission Coefficients of Acoustical Materials34(1962); http://dx.doi.org/10.1121/1.1918262View Description Hide Description
The measuredabsorption coefficients of acoustical materials are often misleading when the material is mounted in a manner which differs from the test procedure. It is suggested that the use of the energy reflection, absorption, and transmission coefficients of the material would obviate this difficulty.