Volume 36, Issue 8, August 1964

Acoustic Properties of Fluid‐Filled Chambers at Infrasonic Frequencies in the Absence of Convection
View Description Hide DescriptionThe general equation of heat conduction inside a fluid‐filled chamber takes two forms, which correspond to zero and infinite acoustic impedance of the driving source, respectively. By means of a simple transformation, it is possible to convert this equation to the standard diffusionequation with simple initial and boundary conditions. Special solutions to this equation are used to derive transfer functions E, which relate the impressed temperature to the resultant average temperature. The equation of state of the fluid is then used to determine the relationships between pressure and volume changes in terms of E. These relationships take the form of two different acoustic impedances Z_{p} and Z_{v} which correspond to zero and infinite source impedance, respectively. In general, the chamber impedance is a function of Z_{p} , Z_{v} , and the external impedances. The above results can be used to extend the validity of acoustic circuit diagrams to zero frequency. The infrasonicacoustic impedance is an R C network, and numerical values of the components can be calculated in a simple manner.

Calculation of Dynamic‐Pressure Changes in the Presence of Free Convection
View Description Hide DescriptionIf a piston compresses and heats gas in a chamber that is larger than a few cubic inches, then the heat exchange between the gas and the wall is governed by convection. The simultaneous, nonlinear partial‐differential equations of free convection are given. Application of dimensional analysis to these equations indicates that the convection process can be described in terms of three dimensionless variables: the Grash of number, the Prandtl number, and the thermal‐diffusion number. A simplified model of the process of free convection is derived and it is shown that the geometrical constants of the model can be expressed in terms of the Grashof and Prandtl numbers. The chamber length l and the boundary‐layer thickness l_{b} play a key role. Mathematical solutions for the chamber pressure that follows a step piston displacement are derived and they agree within 1% with the measured pressure.

Compression Wave Surrounding an Expanding Sphere
View Description Hide DescriptionThe method of describing the propagation of finite‐amplitude waves based on the introduction of coordinates “accompanying” the wave system is used for the consideration of the radiation of a compression wave by a sphere that is expanding at a constant rate in a perfect medium. To estimate the degree of accuracy of this method, the results are compared with the exact solution of G. I. Taylor. [Proc. Roy. Soc. (London) A186, 273–292 (1946)].

Signal Detection by Arrays in Noise Fields with Local Variations
View Description Hide DescriptionThe signal‐detection capabilities of an array that is essentially DIMUS in nature are analyzed for the situation in which the background‐noise power from hydrophone to hydrophone is not the same. The signal to be detected is assumed to be a plane‐wave random time function. The signal power at different hydrophones is assumed to be constant. The performance of the DIMUS system, with infinite clippers, is compared to that for a similar array with purely linear signal processing. Results indicate that the performance of the system with infinite clippers is generally superior on a signal‐to‐noise basis and on the basis of normalized signal output.

International Audiometric Zero
View Description Hide DescriptionInternational reference‐zero levels for pure‐tone audiometers have been recommended by the International Organization of Standardization (ISO) and are under consideration for inclusion in a new American Standard for Audiometers. The new ISO levels are desirable because (1) the shape of the threshold contour is more accurate, (2) the threshold levels are reproducible from laboratory to laboratory and from country to country, and (3) they represent the only apparent escape from permanent ambiguity and confusion in the international exchange of audiometric information. The new ISO levels differ significantly from the American Standard values of 1951, but readings on one of these bases can readily be transferred to readings on the other base by a simple arithmetical adjustment. For instance, for the determination of percentage impairment of the ability to hear speech by calculation from the average of the decibel readings at 500, 1000, 2000 cps, an adjustment of 11 dB in the average of these readings provides the transfer from one base to the other.

Effect of Noise Crosscorrelation on Binaural Signal Detection
View Description Hide DescriptionThe effects of varying the crosscorrelation of a noise masker upon the detection of a 500‐cps tonal signal were investigated. The correlation was varied by introducing a time delay into the channel to one ear. Ten delays yielding various positive and negative correlations and nine delays yielding zero correlations were employed with in‐phase and reversed‐in‐phase signals. A two‐interval forced‐choice procedure was used to obtain MLD's relative to the diotic condition. The function relating MLD's to delay is periodic, the largest values occurring for the antiphasic conditions and the smallest for the homophasic. The function for zero correlations is not periodic, but decreases regularly to a value near that found for uncorrelated noise. No difference is apparent between the two conditions of signal phase for zero correlations. The temporal interval over which the binaural system is able to effect a correlation between events occurring at the two ears is estimated to be at least 9 msec.

Perception and Retention of Verbal Information Presented during Auditory Shadowing
View Description Hide DescriptionNine subjects listened through one earphone of a binaural headset to 50‐word lists of common English words read to them at a rate of two words per second. They repeated the words that they heard while listening for an occasional word that might or might not be presented on the other earphone. This word, should it appear, was to be remembered until the conclusion of the 50‐word list, at which time it was to be recalled. No more than three target words were presented with any one 50‐word list for shadowing. The results indicate that shadowing performance is almost totally disrupted at the point of insertion of the target word, whether the target word is finally correctly remembered or not. Memory for the target word deteriorates as some function of the time between presentation and recall. Since time between presentation and recall and amount of intervening material between presentation and recall are directly correlated, it is impossible to say with certainty that the recall data support a decaying‐trace theory of immediate memory or an interference‐type theory. The results of a similar study using visual target words are cited to lend support to the position that an interference‐type theory is to be preferred in this case. Finally, these data further confirm the validity of the concept that man's perceptual system is basically a single‐channel one with a limited information‐handling capacity.

Experimental Study of “Tone Deafness”
View Description Hide DescriptionIn a series of experiments designed to compare the efficiency of human observers in amplitude‐discrimination tasks to their efficiency in frequency‐discrimination tasks, the behavior of one of the four observers suggested that he was completely insensitive to frequency differences. The procedure of the experiments was then diverted to conduct an experimental case study comparing the “tone deaf” observer to three observers with normal frequency discrimination under a variety of experimental conditions. In amplitude‐discrimination experiments in which he is detecting pulses of sine waves, he compares favorably. He far surpasses the other three observers when the signal is a sample of “white Gaussian” noise. An interesting aspect in the experiments reported is that the “tone deafness” of the participating observers suggests the possibility that these particular experiments may reflect culture‐bound conditions. A further program is planned that may yield data on the question of the environmental influences on sensory capabilities.

Two Experiments concerning Rise Time and Loudness
View Description Hide DescriptionSome experiments are performed to test the influence of rise time on loudness of a 750‐cps sinusoid and a broad‐band noise. Rise times, defined for a 50‐dB exponential variation in sound pressure level, were applied in the interval 0.025–1.6 sec. Maximum sound pressure level was 70–100 dB with duration 0.6 and 1.3 sec. A “paired comparison” method was used, and a decrease in loudness corresponding to approximately 3 dB in sound‐pressure level was found for the broad‐band noise. A smaller change was found for the 750‐cps sinusoid.

Direct Mechanical Determination of the Dynamic Response of Diaphragms
View Description Hide DescriptionThe freefield resonant frequency and the deflection under given static pressure of a thin, circular, clamped‐edge diaphragm may be calculated theoretically by well‐known equations. Also, experimental means exist for a determination of these quantities. No satisfactory theoretical or experimental method has appeared, however, by which it is possible to obtain, for a complicated physical system, the diaphragm deflection as a function of the frequency of an applied sinusoidal pressure, over a frequency range that includes the natural diaphragm resonance. An experimental method is described by which a piezoelectric driver is employed to generate a sinusoidal pressure of variable frequency in a confined gas, to which one side of a test diaphragm may be exposed. Equations are derived describing the gas‐coupling medium and the piezoelectric driver. By use of these equations, it is possible to predict the characteristics of the apparatus. A study is made of the dynamic response of a series of thin, circular, clamped‐edge diaphragms. Since the diaphragm geometry is simple, the resonant frequency may be calculated theoretically. A shock‐excitation technique is also employed to determine the resonant frequency. Comparison is then made between the latter two methods and the result given by the apparatus. The static‐pressure dependence of the resonant amplitude and resonant frequency of the diaphragms is studied and discussed. The magnitude of the dynamic‐pressure amplitude is determined, employing a calibrated commercial pressure gauge below its own resonance. Modifications of the apparatus are reported that extend the dynamic‐pressure amplitude and the useful frequency range, and the possibility of utilizing the apparatus for dynamic calibration of pressure gauges is noted.

Distribution of Losses in Longitudinally Excited Vibrators
View Description Hide DescriptionA study of the loss distribution in longitudinally excited vibrators has been made for application to transducer design. The relative importance of losses related to longitudinal and shearing strains, the surface, and impedance transformations has been made. The experimental methods are described and analytical methods for the prediction of losses in various geometries are given. The losses at changes in cross section of a vibrator are found to behave in a predictable manner.

Determination of the Propagation Constants for Ultrasonic Waves in Melting and Molten Polyethylene
View Description Hide DescriptionAn extension of McSkimin's technique to polymer melts and soft amorphous polymers is reported. For 12‐Mc/sec longitudinal waves, the modulus and internal friction are presented for the melting, super‐cooling, and annealing or recrystallization of polyethylene. Maxima of internal friction are observed in the solid at −52°, 60°, and 100°–130°C. The last is associated with the presence of crystals, decreases sharply near the melting temperature, and is not present in the supercooled melt. At 129.5°C, the modulus increases linearly with the logarithm of recrystallization time and the internal friction decreases. Correlation of the modulus and lamellar thickness during recrystallization indicates that the effects above 100°C are related to recrystallization. For the melt between 140° and 290°C, the internal friction exhibits a low, nearly constant value. In this temperature range, the ratio of the thermal coefficient of velocity change to the thermal coefficient of volume expansion is −2.6. A decrease of modulus and increase of internal friction above 300°C is believed to be associated with thermal degradation of the polymer.

Acoustic Power Radiated by an Infinite Plate Excited by a Concentrated Moment
View Description Hide DescriptionAn expression is derived for the acoustic power radiated by an infinite uniform isotropic plate excited by a time‐harmonic moment acting at a point on the plate. The effect of radiation loading is included. Results are obtained that are valid below the coincidence frequency.

Turning‐Point Peculiarities in the Near‐Resonant Response of Slightly Tapered Membrane Strips
View Description Hide DescriptionUnusual and surprising features of the response of a slightly tapered, nearly rectangular membrane, or analogous medium, excited at either the wider end or the narrower end and fixed on the other three sides are examined analytically. Radical differences between the two appear for the same “near‐resonant” frequency. For excitation at the wider end, there can be a large‐amplitude response in the wider half, while the narrower half remains almost undisturbed. For excitation at the narrower end, there is only small‐amplitude response throughout. These peculiarities are associated with the presence of a “turning point,” in the sense of the WKB method used in the analysis.

Vibrations of Coaxially Segmented, Longitudinally Polarized Ferroelectric Tubes
View Description Hide DescriptionFerroelectricceramicmaterials are often used in underwater soundtransducers by stacking a number of identical pieces together. In this paper, the theoretical behavior is derived for a ferroelectric, cylindrical tube consisting of any number of longitudinally polarized coaxial segments. The effects due to lateral dimensions, which may not be negligible, are included. Electromechanical equivalent circuits are developed that greatly simplify and improve the analysis of composite resonators in transducer design. The theoretical parameters are related simply to experimentally measured quantities so that the parameters can be evaluated even though the lateral dimensions are large relative to the length of each individual segment. The dielectric, piezoelectric, and elastic losses are included in the general theory but losses are not considered explicitly.

Theoretical and Experimental Results on Active Vibration Dampers
View Description Hide DescriptionThe use of active feedback elements to produce damping of multiresonant structures is examined analytically, and the analysis is compared with experimental results obtained for a 48 in.‐long uniform beam damped at its midpoint. The analysis method involves an adaption of the conventional Nichols‐chart technique and appears to be quite reliable. By using commercially available components, a simultaneous reduction in resonant mobilities of resonances below 10 kc/sec is predicted and demonstrated. Reductions were proportional to the mobility values prior to active‐damping applications and also to the gain in the feedback path. The limitations on the amount of damping possible are imposed by stability conditions for the feedback loop, which in turn depend primarily upon the transfer function of the forcing and pickup components of this loop. The stability analysis for particular components used in the beam experiment is presented.

Coupling of Sound and Panel Vibration below the Critical Frequency
View Description Hide DescriptionPrior analysis has shown that the sound power radiated from reverberant vibration of a simply supported panel is proportional to the length of the panel's perimeter when the frequency is below the critical frequency. A simple physical interpretation was made in terms of the mode shape of resonant modes. Other analyses for power radiation from a single straight boundary on an infinite panel indicated that twice as much power radiates from a clamped edge as from the simply supported edge, the spatial mean‐square velocity being held constant. It is shown here that the increased radiation from clamped edges is also predictable from simple considerations of the mode shape. Moreover, among all boundaries having a purely reactive rotatory impedance and restricting transverse displacement to zero, the clamped edge is found to be the most efficient radiator. For some impedances, power radiation is found to approach zero.

Mutual Radiation Impedance of Square and Rectangular Pistons in a Rigid Infinite Baffle
View Description Hide DescriptionAn integral solution has been obtained for the mutual radiation impedance of two identical rectangular or square pistons vibrating in an infinite rigid plane. These expressions are relatively easy to evaluate by machine computations. Numerical values of the radiation impedance are given for square pistons of dimension ka = , 1, and 2, separated by . For larger pistons, the orientation of the pistons with respect to each other becomes important. This is demonstrated for the case ka = 5.

Arctic Deep‐Water Propagation Measurements
View Description Hide DescriptionExperimental results of acoustic‐propagation measurements made in the Beaufort Deep of the Arctic Ocean in April 1963 are given. Explosive source stations were made by light aircraft at distances of 3, 6, 9.5, 13.5, 26.5, 46, and 115 nm (nautical miles) from a manned camp where the signals from hydrophones in the water and seismometers mounted in the ice were recorded. From these measurements, and from ray calculations based on measurements of water temperature made during the experiment, the following were derived and are presented: transmission loss as a function of frequency, range, the relative energy content of signals from surface‐ and bottom‐reflected rays; the relative effectiveness of hydrophones and ice‐mounted vertical seismometers in detecting underwater sound energy; transmission loss in excess of predicted divergence loss.

On the Autocorrelation of Random Inhomogeneities
View Description Hide DescriptionThe question of singularities at the origin in the autocorrelation function of temperature fluctuations is discussed. A series of singular autocorrelation functions of an exponential character is derived from a non‐singular model.