Volume 37, Issue 6, June 1965

Aerodynamic Sound from Centrifugal‐Fan Rotors
View Description Hide DescriptionThe sound powers of small uncased centrifugal‐fan rotors were measured at low‐tip Mach numbers. Correlation of the data by use of a similarity relationship derived from theory has shown that the broad‐band rotor sound is a result of randomly oriented dipole sources caused by fluctuations in fluid momentum. Deviations of the dependence of sound power on speed from that theoretically predicted were found. Speed dependences less than that predicted can be explained as a nearfield effect; the lack of agreement between theory and the fan law for sound can be explained on the same basis. Observed speed dependences greater than that predicted appear to result from having fixed frequency limits on the measurement system. A sharp wedge placed near the rotor periphery was found to generate discrete‐frequency dipole sound. Quadrupole sound appeared to be negligible.

Focusing Ultrasonic System Applicable to Two‐Dimensional Optical Beam Scanning and Laser Output Modulation
View Description Hide DescriptionRecent interest in (1) the directional control of highly collimated light beams and (2) internal modulation of laser action has stimulated a variety of experiments. This paper reports on experiments utilizing a bariumtitanateceramictransducer formed into an arc of a short section of right circular cylinder and radiating into a tetrachloroethylene‐filled cell at 400 kc/sec. A helium‐neon laser beam was used to examine the index of refraction gradients produced in the liquid and to illustrate the possible deflection patterns. When the beam traversed the cell near the focal line, circular scanning was observed, with maximum deflection angles of approximately ±1.0°. Linear scanning reached ±1.3°. Data describing the experimentally observed beam motion showed good agreement with a theoretical analysis of the complex acoustic field in this region. Deflections produced by pulse excitation of the transducer exceeded ±1.5°. Ruby laser spiking was modulated to follow the 400‐kc/sec field, and in pulsed operation giant spikes were obtained, using the cell to control the Q of the optical resonatorcavity. High‐speed photographs of both the partial standing acoustic wave, the traveling shock waves, and the circular beam‐deflection pattern were taken.

Effect of Water Vapor on the Napier Frequency of Oxygen and Air
View Description Hide DescriptionThe Napier frequency (frequency of maximum absorption per wavelength) in oxygen and in air is shifted to higher values by water vapor according to a quadratic law that has different coefficients in the two cases. It is shown that proper treatment of the relevant equations leads to the correct experimental relationship between them. From this relationship, all the various velocity constants in the equilibrium equations may be determined numerically. It turns out that nitrogen has a somewhat stronger effect than oxygen on the relaxation of water vapor, and that the rate of resonant interchange of energy between oxygen and water vapor is, in fact, smaller than the rate of relaxation of water vapor by itself. It is also shown that the postulate of dimer formation in water vapor as an explanation of the quadratic relationship leads to a contradiction with experiment.

Reflection and Refraction of Sound by a Nonequilibrium Relaxing Medium
View Description Hide DescriptionThe reflection and refraction of a plane sound wave by a nonequilibrium relaxing medium are examined. Since the medium is dissipative, Snell's law of refraction is modified depending not only on the properties of the media, but also on the angle of incidence. The amplitudes of the reflected and refracted waves are complex. Variations of both the angle and amplitude are analyzed and supplemented with calculations for different reaction rates and relative Mach numbers.

Thermal Circuit Approach to Vibrations in Coupled Systems and the Noise Reduction of a Rectangular Box
View Description Hide DescriptionStationary, wide‐band vibrations of complex dynamic systems are treated in terms of energy quantities, neglecting details of structure and excitation. Approximate relations between the average energies in loosely and conservatively coupled systems are obtained in terms of modal densities, internal losses, and coupling losses. It is shown that the products of modal density and coupling‐loss factor are equal within each pair of subsystems. The general theory is applied to study the noise reduction of a rectangular box, and experimental results are compared with theoretical predictions with generally good agreement. The transmission behavior of a box at a given frequency is shown to depend on the relation of this frequency to the lowest mechanical‐ and acoustic‐resonance frequencies and the critical frequency of the walls. Theory and experiment show that near the lowest mechanical resonances the pressure in the box may considerably exceed that in the incident sound field.

Forced Motion of a Thin Bonded Plate
View Description Hide DescriptionIn many cases of interest to experimentalists and geophysicists, the situation exists where a light, thin layer of material, such as glue or adhesive, is bonded to a heavier structure. If the layer is thin enough and if its acoustic impedance is small as compared to the underlying structure, then the layer can be thought of as having little effect upon the motion of the substructure. Thus, the effect of the substructure is to force motion of the thin layer. This paper considers the dynamic problem of a thin layer forced by displacements on the lower face and tractions upon the upper face. The exact solution is derived for the two‐dimensional case, while the three‐dimensional case is first considered using Bernoulli‐Euler‐Kirchhoff plate theory and, after this, including the effects of shear deformation and rotatory inertia. It is found that, if shear deformation and rotatory inertia are included, the theory is fairly accurate for problems in which the quarter‐wavelength of the disturbance is greater than or equal to the plate thickness.

Wave Propagation in Transversely Isotropic Circular Cylinders Part I: Theory
View Description Hide DescriptionA two‐part study concerning the wave propagation of free harmonic waves in hollow and solid circular cylinders of transversely isotropic material is discussed on the basis of the linear theory of elasticity. The three‐dimensional equations of elastodynamics are solved in terms of three displacement potentials, and the resulting frequency equation is discussed for several special cases.

Wave Propagation in Transversely Isotropic Circular Cylinders Part II: Numerical Results
View Description Hide DescriptionNumerical results to the exact frequency equations obtained in Part I [J. Acoust. Soc. Am. 37, 1016–1021 (1965)] are presented here for hollow circular cylinders, and comparisons are made with an approximate shell theory developed previously.

Occurrence of Wave Effects in Rubber Antivibration Mountings
View Description Hide DescriptionAn approximate theory of rod vibration given Love has been extended to describe the occurrence of wave effects, or wave resonances, in rubber antivibration mountings. Thus, the longitudinal vibration of a mass‐loaded rubber mount of significant lateral dimensions and uniform cross section has been determined with the assumption that the elastic modulus and damping factor of the rubber are frequency‐ dependent quantities. Knowledge of the manner in which the elastic modulus and damping factor of natural rubber, natural rubber filled with carbon black, and a high‐damping synthetic rubber depend upon frequency has enabled realistic computations of transmissibility to be made. These computations have been contrasted with results obtained, for the same rubbers, from the simple one‐degree‐of‐freedom theory in which the occurrence of wave effects is disregarded. The effectiveness of the natural‐rubber mountings, which have relatively small clamping, is overestimated by the simple theory at high frequencies, although transmissibility will normally remain a small quantity. In the case of the high‐damping rubber considered, the results of the simple and Love theories are in relatively close agreement.

Interference Pattern Observed in Reflections from the Ocean Bottom
View Description Hide DescriptionA strong interference pattern has been observed in the reflection of monochromatic, acoustic pings from the ocean bottom. In our experiment, performed in the Gulf of Mexico at 24°16′N, 85°15′W, the pings had a frequency of 120.5 cps, a length of 0.12 sec, and were repeated every 5 sec. The transmitter was at a depth of 75 ft and the receiver at 3000 ft. The energy in successive bottom reflections varied by as much as 6 to 1, with a mean fluctuation of 30%. This rapid change in level was largely owing to the fact that the source was shallow and the air‐water interface was rough. Averaging the bottom reflections in groups of ten produces a moderately smooth relation between signal level and range. This relation exhibits a pronounced interference structure. The pattern observed can be interpreted in terms of a 130‐ft bottom layer having a velocity of 6650 ft/sec.

Reflection of Low‐Frequency Sonar Signals from a Smooth Ocean Bottom
View Description Hide DescriptionMeasurements of the bottom‐reflection losses for a low‐frequency sonar signal (0.7–3.0 kc/sec) are reported for two areas off the California coast and for a third area in the Bering Sea. At all three areas, the bottom losses were large at small grazing angles. Comparisons are made between the measured values of bottom loss and those calculated for a plane sound wave reflecting from a layered model of the ocean sediments. The sediment model consists of a number of absorbing solid layers. Reasonable agreement is shown between the experimental and calculated values of bottom loss.

Deformation of an Exponential Pulse with a Finite Rise Time in the Region of Total Reflection
View Description Hide DescriptionThe peak of an exponential pulse with a finite rise time is investigated in the region of total reflection. It is shown numerically that the peak is amplified in this region. The amplification seems to increase with a decreasing decay factor and or rise time of the initial pulse.

Scattering Theory, with Applications to One‐Dimensional Problems
View Description Hide DescriptionA recently developed analytical method employing an integral‐equation technique is used to compute the reflection coefficient, as a function of frequency, of an acoustic wave encountering a one‐dimensional scattering layer. The reflection coefficients are calculated for inhomogeneous layers in which the propagation function varies in a complicated manner and also for homogeneous layers in which the propagation function remains constant. The validity of the integral‐equation technique is demonstrated, and it is shown that due to rapid convergence only a few iterations are needed to calculate the reflection coefficients with reasonable accuracy.

Theory of Signal Detectability: Deferred‐Decision Theory
View Description Hide DescriptionThe theory of signal detectability is extended to include observation‐decision procedures in which the available observation time is bounded. The special case of a simple signal hypothesis with stationary normal observation statistics is worked in detail. (“Signal known exactly in added white Gaussian noise” is an example of such a case.) The optimization is of the minimum average risk type, with constant cost of observation to facilitate comparison with work based on Wald's sequential analysis and comparison with fixed observation procedures. An unexpected result is that for large available observation lengths, approaching Wald's unbounded case, the optimization dictates that the primary improvement is in error performance rather than observation time.

Approximation to the Array Signal‐Gain Fluctuation Spectrum
View Description Hide DescriptionIt is known that the signal gain of an array of hydrophonesfluctuates randomly in time. Several authors have investigated these fluctuations from different viewpoints; most of them determine mean‐square array responses assuming correlated phase fluctuations. Since the signal gain varies with time, it should be regarded as a stochastic process. All attempts to find the multidimensional distribution functions of this process assuming Gaussian inputs have failed. It is not difficult, however, to develop an approximation for the power spectrum of the gain fluctuations of the array output in terms of the spectra at the individual hydrophones and the cross spectra between the array elements. Data were taken on the individual elements of an array of five hydrophones and the spectrum of the array gain variations was computed in accordance with the procedure given. This spectrum is compared with the spectrum obtained directly from the fluctuations of the array output. It is hoped that measuring array fluctuations in terms of spectra at individual hydrophones and cross spectra between hydrophones will give some insight into the mechanism causing the fluctuations.

Pseudorandom Signal‐Correlation Methods of Underwater Acoustic Research I: Principles
View Description Hide DescriptionNew methods of underwater acoustic‐propagation research have been developed in which noiselike or pseudorandom signals, generated by shift‐register encoders, are detected by correlation techniques. The principles and problems of three classes of experiments are discussed: (1) the signal received is crosscorrelated with a time‐delayed and time‐compressed replica of the transmitted signal; (2) two received signals are crosscorrelated and studied as a function of hydrophone separation; (3) the received signal is correlated with that received from a later repetition of the transmitted signal. It is shown theoretically that the results of the first class of experiments are different from and unpredictable from those obtained by employing the usual filtering and detection of impulsive or single‐frequency signals. The severe problem arising from multipath interference in the second class of experiments, which is different for the multipath problem in the first class of experiments, is discussed and some solutions proposed. The essential identity of the second and third classes of experiments is discussed. A companion paper discusses the instrumentation for and execution of the experiments and presents some preliminary observations.

Linear Modeling of Long Underwater Acoustic Paths
View Description Hide DescriptionThe effective treatment of signal‐transmission problems requires an analytical representation or “model” of the signal path. Long underwater acoustic‐signal paths fall in the class of randomly time‐varying dispersive channels, which show approximate linearity and short‐term statistical stationarity. A mathematical model for such paths is proposed that is based on the statistical behavior of the time‐varying impulse response h (η,τ). This model has sufficient generality to account for the fluctuating dispersive characteristics of underwater paths and their property of increasing attenuation with frequency. Certain constraints may be included, however, so as to provide the model with a high level of mathematical manageability. The effects, of the channel model on the transmission of white noise, stationary random signals, and CW signals are treated. In addition, the use of the complete model in the optimization of a simple binary communication system is illustrated. The detailed treatment is confined to the point‐to‐point transmission situation although some discussion presented on the more complicated problem of multiple‐input/multiple‐output channels, including interior reflective and refractive bodies.

Can a Sensory System be Specified by Its Internal Noise?
View Description Hide DescriptionThe detection model is used to describe the detection of scarcely discernible noiseless signals by human observers. Detection is hampered by an internal noise generated by the sensory system itself. In the present study, it appears that increments of loudness of a tone and increments of intensity of a light can be detected independently and simultaneously. Here, the internal noise is specific for the system responsible for this detection. On the other hand, detection of an increment in duration of visual and auditory signals is completely correlated. This correlation and the similarity of the detectability of the two kinds of signals indicate that a “duration center” exists, serving to estimate the duration of both visual and auditory signals. The methods developed are useful for identification of separate or common parts of sensory systems.

Detectability Threshold for Combination Tones
View Description Hide DescriptionExperiments were performed on the detectability threshold for combination tones, defined as the sensation level of primary tones for which combination tones become audible. Investigated were (1) detectability threshold for h−l with (h−l)<<(h+l), where h and l are the frequencies of the higher and lower primary tone, respectively; (2) detectability threshold for 200, 400, and 600 cps with 800+1000 and 800+1400 cps as primary tones; (3) audibility of combination tones for l = 1000 cps and h variable between 1000 and 3000 cps; (4) detectability threshold for the “missing fundamental” of , with f varying from 125 to 1000 cps. From the experimental data, we may conclude that (1) there are large individual differences in the minimum sensation level of primary tones for which combination tones appear; (2) for usual listening levels of speech and music, the ear's distortion is sufficiently low to avoid audible combination tones; (3) the same holds for the “missing fundamental,” so the fact that the pitch of a complex tone without fundamental is equal to the pitch of this tone cannot be explained by the assumption that the fundamental tone is reintroduced in the listener's ear; (4) the fact that the detectability thresholds for combination tones are significantly lower for small than for large tone intervals indicates that, for both cases, the ear's distortion cannot be represented by the same nonlinear characteristic and supports the evidence that the tones are produced in the inner ear.

Theory for Psychophysical Learning
View Description Hide DescriptionA model for psychophysical learning is constructed by imposing some conditioning principles on concepts derived from the theory of signal detectability. The effects of a priori probability, feedback, and practice are derived in part by Monte Carlo simulation and in part by analysis. The theory makes some novel predictions for the effects of these variables, all of which find support in the literature. Some theoretical results are: (a) performance improves with practice; (b) feedback can be detrimental to performance in a psycho‐physical task; (c) when the a priori probabilities of the stimuli are unequal and feedback is provided, the response criterion moves in the direction of optimality, but does not move far enough to reach optimality; however, when no feedback is provided, the criterion moves in the opposite direction.