Variation Of Phase Angle Research Articles

Weber's law, the "near miss," and binaural detection.

Weber functions (ΔI/I in dB) for gated 250-Hz tones were studied for monaural and several binaural stimulus configurations (homophasic, and antiphasic with varying phase angle for addition of signal to masker). The various cues for discrimination of signal plus masker from masker alone are functions of intensity increments at one or both ears, an intensity increment at one ear coupled with a decrement at the other, or the introduction of a phase difference between the ears. The decline of the Weber fraction with increasing masker level (the “near miss” to Weber’s law) was confirmed for monaural discrimination over the entire 40-dB range, and a similar rate of decline was found for various binaural stimuli over the lower half of that range. The data also confirm the individual differences found in other studies for sensitivity favoring either interaural amplitude or interaural phase shifts.

A highly variable opto-acoustic phase angle within the S o → S 1 band of glyoxal

The S 0 → S 1 transition in the opto-acoustic spectrum of glyoxal vapor exhibits a variable phase angle which follows the pattern of absorption intensity. This unusual phenomenon results from a quenching of T 1 by S o to form a long-lived intermediate, M, which then produces heat via an M + M reaction.

Unsteady flow of an inelastic power-law fluid in a circular tube

Flow of a power-law fluid with a suddenly applied arbitrary time-dependent pressure gradient in a horizontal circular tube is presented. The momentum equations are solved numerically using a implicit finite-difference technique for the time-dependent velocity profiles for both start up and oscillating pressure gradients. Dimensionless curves are presented showing velocity profile development and phase angle variation for a variety of power-law index values.

Biophysics of the ensiferan ear

1. Laser vibrometry is used for observing vibrations of tympanal membranes. With this technique, the velocity and phase lag of vibrations can be measured from areas of 5–100 μm in diameter. The resolution of the apparatus is 10 Angstroms (vibration amplitude) in ‘real time’ broad-band operation (up to 100 kHz), but with averaging or selective filtering it is possible to perform more sensitive measurements. 2. At ‘low’ frequencies (1–3 kHz) the sound acting upon the back of the bushcricket tympanum has almost the same numerical pressure as that acting on the front. The ear, therefore, is an ideal pressure gradient receiver. 3. At ‘high’ frequencies (above 10 kHz) the sound pressure acting on the back of the tympanum is somewhat larger than that acting on the front. The membrane vibrates in its basic mode (like a piston) in the entire frequency range investigated (1–40 kHz). 4. These properties are for ears with open ‘hearing trumpets’ (i.e., the horn-shaped trachea conducting sound to the back of the tympanal membranes). When the opening of the hearing trumpet is closed by blocking it with wax, the ear becomes a pressure receiver (at least at ‘low’ frequencies). It is now more sensitive to ‘low’ frequencies and less sensitive to ‘high’ frequencies. 5. The vibrations of a membrane backed by a horn-shaped structure are considered theoretically. The expected variation in amplitude and phase angle of the driving force is calculated for systems in which sound is conducted through the horn-shaped structure with different amounts of gain.

Circuit models of the passive electrical properties of frog skeletal muscle fibers.

The relation between the fine structure, electric field equations, and electric circuit models of skeletal muscle fibers is discussed. Experimental evidence illustrates the profound variation of potential with circumferential position, even at low frequencies (100 Hz). Since one-dimensional cable theory cannot account for such variation, three-dimensional cable theory must be used. Several circuit models of a sarcomere are presented and plots are made of the predicted phase angle between sinusoidal applied current and potential. The circuit models are described by equations involving normalized variables, since they affect the phase plot in a relatively simple way. A method is presented for estimating the values of the circuit elements and the standard deviation of the estimates. The reliability of the estimates is discussed. An objective measure of fit, Hamilton's R test, is used to test the significance of different fits to data. Finally, it is concluded that none of the proposed circuit models provides an adequate description of the observed variation of phase angle with circumferential location. It is not clear whether the source of disagreement is inadequate measurements or inadequate theory.

Frequency control using binary rate multipliers for automatic testing on c.w. radar systems

R.F. signals with certain defined characteristics have to be generated for ground testing on f.m. c.w. radar airborne-guidance systems. Normally in flight, two r.f. signals would be received; one direct from the ground transmitter and the other originating at the same transmitter, but reflected from a target. A lowfrequency wide-deviation frequency modulator is applied to the carrier at the ground transmitter. Owing to a difference in the path lengths of the two signals, a difference in phase angle of the modulating signal results, and, owing to the Doppler effect, the carrier frequencies are slightly separated. For testing therefore two r.f. signals with a precise and variable difference frequency have to be generated. Also both signals must be frequency modulated at the same frequency to the same deviation, but with a variable phase angle between the two modulating signals. For this purpose, a study has been made of the behaviour of binary rate multipliers used partly to shift the frequency, and partly to frequency modulate the r.f. carriers. A common crystal oscillator would feed into two b.r.m.s each shifting the carrier by a different amount, and each frequency modulating the shifted carriers with the same deviation. The b.r.m. operates by removing pulses from an uninterrupted pulse train according to the digital address. Thus the mean output frequency is lower than the input, but is contaminated with phase jitter. Jitter magnitude varies considerably with the address pattern, and it increases with the number of address lines. A graph of maximum jitter is given for increasing numbers of address lines up to 13. It isshown how phase jitter may be reduced to an acceptable limit, and how a system to meet the requirements may be designed.

Unsteady Aerodynamic Response of a Two-Dimensional Airfoil at High Reduced Frequency

An experimental technique is described which corroborates the predictions of several new analyses of the unsteady response of an airfoil to high frequency flow fluctuations. The periodically fluctuating flowfield was produced by the natural shedding of vortices from a transverse cylinder to yield a reduced frequency of 3.9 based on airfoil semichord. Unsteady pressure measurements were made on an instrumented airfoil mounted downstream and above the turbulent wake of the cylinder. These unsteady pressures were found to be in good agreement with current compressible theories and show a chordwise variation of pressure phase angle which is not predicted by the incompressible analysis of Sears. Large reductions of the unsteady lift and phase angle were also observed for large airfoil incidence angles.

On the Nature of Iapetus

For solar system bodies with little or no atmosphere, a linear relation exists between the depth of the negative polarization branch and the reciprocal of the geometric albedo. Considered in this fashion, the polarization data for Iapetus imply an albedo difference by about a factor of 6 between its leading and trailing hemispheres, and are consistent with the amplitude of the light curve for Iapetus. The brightness of the satellite at any particular maximum or minimum is unpredictable by a certain factor because of inadequately understood variations in solar phase angle and rotation. Although other measurements of the Iapetus albedos give results different from those in the presented paper, it is still clear that the two hemispheres have very different albedos.

Wave Energy Reflection And Transmission In Open Channel Gradual Transitions

This paper deals with the analytical development of the transformation of oscillatory surface gravity wave characteristics in the reflection and transmission processes, through channel transitions of varying cross-section connecting two segments of a prismatic channel of constant geometry. The theoretical approach is based on small amplitude linear shallow wave theory of a homogeneous, incompressible and non-viscous liquid in an adiabatic motion. Reflection and transmission coefficients and phase angle variations are determined for shallow progressive waves for three gradual channel transitions of linear and parabolic variation of depth and width. Comparison of theoretical and experimental results for the transition of gradually varying depth and width shows fair agreement.

A steady-state transfer function analysis of portions of the circulatory system using indicator dilution techniques

A digital computer program has been developed whereby the distribution of dye-particle transit times across circulatory pathways can be found from recordings of upstream and downstream indicator-dilution curves. This distribution or transfer function is computed from Fourier-series representations of the upstream and downstream indicator curves and makes possible, for the first time, the calculation of transit-time distributions independent of the effects of recirculating dye. Since a discontinuity is introduced into the tails of the upstream and downstream curves at the end of sampling, the method requires an iterative approach in the termination of the upstream and downstream curves. The accuracy of the calculated distribution pattern is determined by comparison of the recorded downstream curve with the results of the convolution of the recorded upstream curve and computed transfer function. Effects of noise, bandwidth and sampling rate have been investigated through the use of analog computer models of the circulatory pathways. These studies show that the transfer-function description is limited by the bandwidth of the upstream (input) curve. Noise, or variations in magnitude and phase angle of input- and output-curve frequencies, tends to introduce oscillations into the time-domain representation of the transfer function as does the use of too few frequencies. This means that in biological systems the upstream sampling site must be relatively close to the dye injection site if the input and output sampling sites are close together. Circulatory transfer functions have been obtained from dogs across their lower extremity, renal and systemic circulations before, during and following moderate exercise (walking on treadmill at two miles per hour for four minutes).

The Behaviour of the Impact Damper

In this investigation a theory is developed relating to the behaviour of the impact damper. The analysis is based on the assumptions that (1) two un-equispaced impacts per cycle occur in the steady state, and (2) the impact force-time curve is of rectangular shape and of infinitesimal duration. Fourier series are used to represent the impact cycle and the differential equation of motion is derived. This is solved using the dynamic equations of impact to determine the boundary conditions. Three equations are developed to determine the variation of impulse, phase angle and vibrational amplitude with the change of the damper parameters. Resonance curves are obtained and the theory is examined experimentally. The regions of validity of the above assumptions are studied both theoretically and experimentally. Non-linearity in the behaviour of this damper is very clear, especially in the range of its optimum behaviour. Two design curves are developed which can be used to determine the damper parameters necessary for a certain amplitude reduction.

Effect of Variations in Lift Coefficient, Phase Angle and Waveform on Fluttering Lift in the Desert Locust

Effect of Variations in Lift Coefficient, Phase Angle and Waveform on Fluttering Lift in the Desert Locust

A Continuous Wave Sonic Anemometer-Thermometer

A sonic anemometer-thermometer, based on transmission of continuous sound waves and determination of phase angle variations, has been developed. The instrument is designed to measure the fluctuations in the vertical wind component and temperature simultaneously. Measurement of these two quantities enables one to determine the eddy heat flux in the turbulent boundary layer. Field tests indicate that the instrument performs satisfactorily.

Quantum statistics of irreversible processes

Synopsis The concept of time-proportional transition probabilities is essential for statistical mechanics of non-equilibrium states. In quantummechanical treatments it is usually justified by an appeal to Dirac's perturbation theory. This justification is here criticized, and a new approach is developed. The main problem is to understand, why it should be allowed to discard the cross-products of two different probability amplitudes, which appear on calculating probabilities (“interference of probabilities”). For this purpose phase cells are introduced, consisting of a large number of different quantum states which are indistinguishable for a macroscopic observer. In the expression for the expectation value of a macroscopic variable the cross-products between all probability amplitudes-belonging to a cell occur. It is argued that, owing to their large number and their randomly varying complex phase angles, these terms tend to cancel each other, so that only the squared terms survive. Hence, the macroscopic aspect of the state is determined if only the total probability in each cell is known. Moreover, the values of these probabilities at any time t> 0 can be expressed in those at t = 0. Thus the macroscopic behaviour in time can be described by a first-order differential equation of the customary type (1). (Irreversibility here enters through the assumption of randomly varying phase angles.) The coefficients in the equation may be interpreted as transition probabilities; they satisfy a symmetry relation, which is sometimes called microscopic reversibility. After a transformation to observable quantities the differential equation takes the form of the usual “phenomenological equations”, and the symmetry gives rise to the Onsager relations.

2-Phase A-C Servo Motor Operation for Varying Phase Angle of the Control Winding Applied Voltage

The results of the empirical and analytical methods are identical. Since the motor design data are not always easy to obtain, the motor time constant can be computed directly from the torque speed curve. It is interesting to note that the motor velocity constant is twice the carrier or excitation frequency. This fact is readily proved experimentally providing another check on the validity of the motor equation derivation. The system is thus basically nonlinear as shown by the sine function in the torque equation. To use this motor with phase control in a servo system requires that the error (difference between input and output of closed loop system) be transferred into a directly proportional amplified phase shift. The signal then applied to the motor must be of the form sin K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> (θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">input</sub> -θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">output</sub> ) giving: T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> /dt <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> +dθ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> /dt=K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> sin K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> (θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">input</sub> -θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">output</sub> ) where T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> is the over-all system time constant and K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> is system velocity constant. In a practical system employing phase shift control some means will have to be employed to cause the motor to exert maximum torque (90-degree phase shift) even when the quantity K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> (θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> -θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) is greater than 90 degrees. This is necessary in order to prevent false zeroes since the motor torque decrease when the phase shift across its terminals is greater than 90 degrees. This is probably one of the principal disadvantages of a system employing phase shift control.

The input impedances of thermionic valves at low frequencies

It is shown that accurate measurements of input admittance (or of input impedance) under various conditions can be made by means of the Schering Capacity Bridge. The input circuit is regarded as being equivalent to a condenser with a definite phase , or loss angle, δ=90° - , and the results are expressed by stating the effective capacity and value of tan δ for each set of experimental conditions. A series of measurements made on an R valve is recorded, and it is shown that the results are in good agreement with the theoretical investigations of Miller and Nichols. The theoretical investigation has been extended to allow for the effect of dielectric losses in the valve, since these were found by experiment to be rather large, and to have an appreciable effect on the capacity and phase angle of the input circuit. It is shown that the effective capacity may vary from about 10μμF. to 100μμF. for an R valve, and the phase angle may vary from about 80° leading to 126° leading, depending mainly on the load in the anode circuit. Values of phase angle greater than 90° correspond to a negative resistance, or negative power factor, and occur when the load in the anode circuit is inductive. The variations of input capacity and phase angle with filament voltage, anode voltage, input voltage, and frequency are also investigated.