Index of content:
Volume 32, Issue 6, June 1960
32(1960); http://dx.doi.org/10.1121/1.1908167View Description Hide Description
Tables for the speed of sound in sea water are presented. These tables have been prepared from an empirical formula which was derived to fit measured sound‐speed data obtained over the temperature range −3°C to 30°C, the pressure range 1.033 kg/cm2 to 1000 kg/cm2, and the salinity range 33‰ to 37‰. The discrepancy of −3.0 m/sec found by Del Grosso at 1 atm., as compared to the tables of Kuwahara, is substantiated. In addition, the pressure coefficient of sound speed observed in the present work differs from that predicted by Kuwahara.
32(1960); http://dx.doi.org/10.1121/1.1908169View Description Hide Description
The acoustic field of a 10‐cps cw source, towed at slow speeds at a depth of 24 m was measured by a stationary hydrophone out to ranges of about 70 km. The depth of the hydrophone was approximately 450 m. The records obtained are compared with theoretical calculations of the wave field, using a method developed by one of the authors. The degree of agreement is fair enough for one to feel that further work along these lines should lead to a quantitative understanding of long range sound propagation in the oceans.
32(1960); http://dx.doi.org/10.1121/1.1908171View Description Hide Description
A moiré fringe analog of the normal modes of sound propagation in shallow water is described, in which interesting patterns are obtained both by direct visual observation and by photographic recording. These are analogs for the profiles of sound pressure as a function of range and depth in the underwater field due to a single‐frequency source. Since phase is correctly represented, the interaction patterns due to the presence of considerable numbers of interfering modes may be investigated experimentally. This is important since mathematical analysis becomes difficult when there are more than two modes. There is a discussion of the characteristics of these patterns (including the formation of “loops”) and also of those obtained by A. B. Wood in his sound propagationmodelexperiments.
A Numerical Solution for the Problem of Long‐Range Sound Propagation in Continuously Stratified Media, with Applications to the Deep Ocean32(1960); http://dx.doi.org/10.1121/1.1908173View Description Hide Description
Since the formal solution for guided waves excited by a point source in an arbitrarily stratified medium is well known, in the sense that it can be written down in terms of (unexplicited) eigenfunctions and their derivatives, it follows that evaluation of the long‐range sound field becomes a purely computational problem once these eigenfunctions can be calculated. One of a number of possible methods is presented here. It consists of two steps. First, the continuous sound velocity, α(z), is approximated by a succession of layers such that α has the form in each: the exact wave functions for a layer are then known (combinations of Bessel functions of order ). The second step, which puts this scheme within easy reach of moderately fast computers such as the IBM 650, consists in representing these wave functions by polynomials (argument of Bessel function ⩽ 2.5π) or by the first few terms of their asymptotic expansions (with better than six‐figure accuracy in both cases). Accurate solutions are obtained in this manner without difficulty, for both strong or weak velocity gradients. Some typical results for a deep ocean are displayed. It is also shown that near field problems can be solved in the case of a source and receiver in, or near, a local velocity minimum or duct.
32(1960); http://dx.doi.org/10.1121/1.1908175View Description Hide Description
From detailed acoustical studies made in over 40 large concert halls and opera houses in 15 countries, absorption coefficients are derived for audience, chorus, and orchestra areas, unoccupied seating areas, plaster walls and wood walls. It is postulated that the absorbing power of a seated audience, chorus or orchestra in a large hall is proportional to the floor area it occupies. This postulate is validated for audience densities of between 4.5 and 8.5 sq ft per person, including aisles, and for halls with volumes between 200 000 and 1 500 000 cu ft. The “area” concept as opposed to the “per person” concept of audience absorption explains the serious differences reported repeatedly in the literature between reverberation times calculated during design and those measured after completion of the halls. This paper also presents graphical relations between empty and fully occupied hall reverberation times; shows the effect of seat design on empty hall reverberation times; and gives typical reverberation time vs frequency characteristics for fully occupied halls. The results of this study may not be applicable to rooms whose volume, shape, and materials are substantially different from the large concert halls and opera houses included this study.
32(1960); http://dx.doi.org/10.1121/1.1908177View Description Hide Description
Auditory thresholds may become lower (improve) following stimulation by sound of low intensity. This shift in threshold was determined by comparing the reference threshold of a test pulse, presented alone, to the threshold for the test pulse preceded by a stimulating pulse. Duration, intensity, and frequency of the stimulating pulse were controlled, as were duration and frequency of the test pulse and duration of the interval between pulses. For pulses of 1000 cps, facilitation, or a lowering of the threshold, consistently follows stimulation by sound of 25 db SL or less; the lower the stimulating intensity, the more widespread the facilitation, over the various poststimulatory intervals tested. Facilitation reaches a maximum of 5 to 7 db 160 msec after the termination of the stimulating pulse, although some negative shift in threshold occurs after the longest interval (2 sec). Stimulation by white noise may depress the threshold for a pure tone, although a pure tone seems to have no effect upon the threshold for a white noise. When the stimulating pulse is a 1000‐cps tone, facilitation occurs for test tones between 500 and 2000 cps. The maximal shift is at 160 msec for all test tones except 2000 cps. The nature of the facilitatory process, auditory or attentional, and its locus, whether peripheral or central, are discussed.
32(1960); http://dx.doi.org/10.1121/1.1908179View Description Hide Description
Ear defenders were worn for protection against the distracting effects of bursts of loud, but not unacceptable, noise during a mental task. Two types of noise were used: one characterized by high and the other by low frequencies. Performance was better with defenders than without them. The improvement was particularly marked with the high‐frequency burst.
32(1960); http://dx.doi.org/10.1121/1.1908181View Description Hide Description
The time‐vs‐intensity trade (ΔT/ΔI) in binaural lateralization was measured for pure tones and impulsive stimuli by the null method for high‐pass and low‐pass clicks at a repetition rate of 20 pps and pure tones of 200, 500, and 700 cps. Mean sensation levels (SL) of 20, 30, and 40 db and interaural intensity differences of 0, 4, and 6 db were used. The data on four subjects indicate a difference between high‐pass and low‐pass clicks: for instance, ΔT/ΔI≈0.025 msec/db for low‐pass clicks below 1000 cps and I = 30 db SL, whereas at the same intensity ΔT/ΔI≈0.060 msec/db for high‐pass clicks above 4000 cps.
It is concluded that the time vs‐intensity trade is important for the localization of high‐frequency impulsive stimuli. The interaural intensity difference also affects the ability to liberalize since the error of lateralization is least when both the interaural intensity difference and interaural time difference are zero. From the foregoing and from experiments with two liberalized images, it is concluded that the timing information used in binaural lateralization travels along frequency‐dependent neural pathways. Any physiological timing signal must be able to explain this phenomenon.
32(1960); http://dx.doi.org/10.1121/1.1908183View Description Hide Description
This study deals with the influence of preceding and following consonants on the duration of stressed vowels and diphthongs in American English. A set of 1263 CNC words, pronounced in an identical frame by the same speaker, was analyzed spectrographically, and the influences of various classes of consonants on the duration of the nucleus were determined. The residual durational differences are analyzed as intrinsic durational characteristics, associated with each syllable nucleus. The theory is tested with a set of 30 minimal pairs of CNC words, uttered by five different speakers.
32(1960); http://dx.doi.org/10.1121/1.1908185View Description Hide Description
The variation of ultrasonic velocity with concentration of phenyl salicylate, o‐chloronitrobenzene, stearic acid, naphthalene, o‐nitrophenol, m‐nitrophenol, and palmitic acid in suitable solvents has been studied using an ultrasonicinterferometer. The linear plots of velocity vs percentage weight of the solute are extrapolated to evaluate the velocities corresponding to 100% of the solute in each case. The agreement between the values obtained from solutions using different solvents is good. Sound velocities in the melts of the above substances have also been determined. It is found that the characteristic velocity obtained from data on solutions corresponds to the velocity at melting point in all cases except in that of naphthalene.
32(1960); http://dx.doi.org/10.1121/1.1908187View Description Hide Description
Light intensities in the orders of diffraction patterns produced by two distorted ultrasonic waves 180° out of phase are investigated. In the case where the two waves have the same intensity, the first diffraction orders vanish. The simultaneous increase in light intensity in the second orders is a measure of the second harmonic present in the waves, given for varying distances from the transducers. The change in light intensities in the zero and second orders is given for varying pressure ratios of the two waves.
32(1960); http://dx.doi.org/10.1121/1.1908189View Description Hide Description
The diffraction of light by two parallel ultrasonic waves of the same frequency is investigated. Measurements which were made with waves 180° out of phase with each other agreed with the predicted results. When the two waves were made nearly identical, the diffraction vanished almost completely. It is suggested that this might be applied as a method for the comparison of ultrasonicpressures, the measurement of absorption, and the investigation of finite amplitude distortion.
32(1960); http://dx.doi.org/10.1121/1.1908191View Description Hide Description
A simple model was used to describe the propagation of sound in water. This model assumed that sound waves travel at infinite velocity within the molecules and at gas kinetic velocities through the spaces between the molecules. Resulting calculations showed that the latter velocity increases with pressure. From the change of soundvelocity and acoustical properties for normal water and from those for nonassociated water, which were obtained from acoustical data for mixtures of alcohol and water, the change of the water structure with pressure was calculated and compared with the results of Gierer and Wirtz.
32(1960); http://dx.doi.org/10.1121/1.1908193View Description Hide Description
The system considered is a harmonic oscillator with a hard spring excited by random noise of the “infinitesimal impulse” type. An expression for the joint density of displacement and velocity is obtained and from this; the distributions of displacements and extrema and the average number of zero crossings are found. In addition, by solving a fundamental integral equation, we are able to find the shape of the distorted sine wave “carrier” for finite amplitude vibrations.
32(1960); http://dx.doi.org/10.1121/1.1908195View Description Hide Description
Values of the parameter of nonlinearity for acoustics , are given for all liquids for which experimental data are available. The experimental data indicate that B/A generally increases slowly with temperature. A method of computing B/A directly from finite‐amplitude acoustic measurements is also presented.
32(1960); http://dx.doi.org/10.1121/1.1908197View Description Hide Description
An infinitely long, circular cylindrical elastic shell is surrounded by an acoustic fluid. A plane pressure pulse, whose front is parallel to the axis of the shell, moves through the fluid, strikes the shell, and subsequently engulfs the shell.
The circular shell is replaced by a fictitious Riemann surface which effectively allows the range of θ (the angular coordinate) to be extended from − ∞ to + ∞. Exact expressions are then found for the subsequent shell and fluid motion in the form of double integrals by the use of integral transform techniques. These integrals are evaluated asymptotically by the method of steepest descent to determine the early time motion of the shell and fluid. In particular, it is found that during this early motion the radial shell velocity and bending moment have a maximum, and the fluid pressure at the interface experiences a minimum.
32(1960); http://dx.doi.org/10.1121/1.1908199View Description Hide Description
A series solution has been obtained for the mutual acoustic impedance between two identical circular disks vibrating in an infinite plane. Under simplifying conditions, the resistive and reactive components of the mutual impedance each can be expressed in terms of a simple trigonometric function. The problem was formulated in terms of Bouwkamp's method of integrating over real and complex angles the square of the directional characteristic (relative sound pressure at a large fixed distance) to yield the total radiation impedance. Integrals involved here are similar to a type previously evaluated by Stenzel and may be expressed in terms of a double series containing Bessel functions of integral and half‐integral order. Numerical values of the mutual acoustic impedance obtained by this method for two rigid disks are in good agreement with values obtained by Klapman by direct integration of the pressure at the surfaces of the disks. The acoustic self impedance and mutual impedance may also be calculated by the same methods for a more general type of circular disk having a prescribed radially symmetric velocity distribution.
To illustrate the applicability of these results, the total acoustic loading upon an array of circular disks is calculated by taking into account the mutual acoustic impedance between the disks comprising the array. Numerical results are given for a circular array of seven identical disks having a radius small relative to a wavelength and vibrating uniformly in a common, rigid plane.
32(1960); http://dx.doi.org/10.1121/1.1908201View Description Hide Description
A numerical method is presented for determining the axisymmetric modes of vibration and natural frequencies of thin conical shells such as loudspeaker cones. Assuming the applicability of the classical theory of thin shells, the pertinent differential equations are presented in a form which is well‐suited to numerical integration on an electronic digital computer. The method may be used also to determine the impedance of the cone at other than the natural frequencies, and to calculate the mechanical impedance of the assembly comprising the cone and the voice coil. Results are shown, by a numerical example, to compare favorably with a previously available method based upon the use of power series.
32(1960); http://dx.doi.org/10.1121/1.1908203View Description Hide Description
There is, at present, a great interest in random vibration as a special aspect of shock and vibration, especially in relation to effects on equipment. An attempt will be made to explain what is meant by random vibration as opposed to other excitations that might be confused with it, what is involved in random vibrationtesting, what the corresponding objectives are, why there is controversy about these general subjects, and how some of the controversies may be resolved.
32(1960); http://dx.doi.org/10.1121/1.1908205View Description Hide Description
The asymptotic vibration laws that describe the high‐frequency behavior of complex systems—on the basis of mode masses and the frequency difference between successive resonances and their damping—also give a significant description of the low‐frequency behavior of vibrators from their first resonance onwards. Thus, where problems of noise and vibration insulation are concerned, there seems to be no need for more accurate calculation. This paper derives the necessary theoretical background and substantiates the theory by means of a study of vibrating rods.