Stationary Wave Pattern Research Articles

“Supersonic” flow in the animal world

The analogy between the formation of large amplitude waves (hydraulic jumps) on the surface of shallow flowing water, and shock waves in supersonic air flow is well-known. In addition to the correspondence between the wave patterns the variation in water depth can be related to the pressure distribution.This “hydraulic analogy” is usually demonstrated in the laboratory in a tank which produces a shallow flow of water over a horizontal surface, on which the appropriately shaped body is mounted. The resulting stationary wave patterns may then be examined. Fig. 1 shows a typical bow-wave on a double-wedge.

Shear-Wave Interference observed by Optical Birefringence Induced in a Viscoelastic Liquid

A theoretical and experimental study of the shear-wave field and the associated optical birefringence produced by interfering primary and reflected wavetrains propagating in a viscoelastic medium is presented. The shear-wave field is generated by two parallel planes, one oscillating sinusoidally in its own plane, the other held motionless at a fixed distance from the driving plane. The shear-wave propagation is characterized by a complex propagation constant, while the optical birefringence is related to the shear strain rate in the field by a complex mechano-optic constant. The shear-wave-induced birefringence is analyzed by a determination of the modification of the state of polarization of incident circularly polarized light upon passage through the medium. The limiting cases of small and large separation between generating surface and reflecting surface with respect to the shear wavelengths in the medium are useful for determination of the propagation constant and the mechano-optic constant, while intermediate values of separation of surfaces are useful for demonstrations of the character of the stationary wave patterns. Theoretical determinations of the velocity gradient distribution in the medium for various ratios of surface separation to shear wavelength are presented, together with experimental determinations for an aqueous suspension of milling yellow.

XXXVI. An Anomalous Periodic Flicker Effect†

ABSTRACT An investigation of the anode currents of diodes with directly heated cathodes and cylindrical anodes has shown that irregularities occur hi the current v voltage characteristic curves when high cathode heating currents are used. Low frequency oscillations are observed in the region of the irregularities, and numerous experiments have shown the phenomena to be independent of the external circuit, electrode vibrations, and electrode material. A theoretical investigation of a simplified model of an oscillating space charge has given expressions for the changes in current to be expected from mode jumping between different stationary transverse wave patterns in the space charge. The limitations of this model, and certain outstanding difficulties are discussed briefly.

A Study of Emulsification with Ultrasonic Waves I

An attempt has been made to study and evaluate some of the factors involved in emulsification with ultrasonic energy. The stability of the emulsifying agent to ultrasonic waves is a factor in its choice in emulsification. Two exposure chambers were found to be superior; one a cellulose acetate chamber and the other a Pyrex test tube fitted with a brass diaphragm. These two types produced the best emulsions and showed no appreciable stationary wave pattern found to be unfavorable to emulsification. Orientation of the exposure chamber was shown to be important in emulsification with ultrasonic waves. A distance of an exact number of half wavelengths between the bottom of the exposure chamber and the crystal was shown to deliver maximum acoustical energy to the contents of the chamber and at these points emulsification was best.

A STUDY OF THE EFFECTS OF LARGE BLOCKING HIGHS ON THE GENERAL CIRCULATION IN THE NORTHERN-HEMISPHERE WESTERLIES

The basic problems involved in the investigation of the effects of “blocking action” upon the circulation pattern of the northern-hemisphere westerlies are defined and the mode of attack outlined. By application of turbulence principles seasonal variations in lateral mixing and northward heat transport across the westerlies are related to variations in the extent of blocking action. Evidence is presented indicating that blocking action, lateral mixing, and northward heat transport are all greater in the winters of years when strong north–south thermal gradients exist and vice versa. The year-to-year variations in these quantities exhibit a long-period and relatively large amplitude climatic swing with a period of roughly 12–14 years. Considerable year-to-year variation in the radiative properties of the earth's surface and atmosphere, or in incoming radiation, is thus implied. An analysis of heat convergence through the lateral turbulence process shows in general the heart of the westerlies losing heat, particularly from the east coasts of the continents to the Aleutian and Icelandic Lows. This mechanism is apparently the means by which the large amount of heat picked up by the air from the oceans off the east coasts is dispersed. A distinction is made between the turbulent eddy sizes identified with unstable, migratory systems and those of blocking action, the latter representing dynamically quasistable systems capable of producing effects upon the general circulation of the westerlies at great distances both upstream and downstream and over a period of many days. Effects resulting from the intrusion of stable, persistent high-pressure cells into the normal westerly flow of the general circulation of the atmosphere in the characteristic manner of blocking action are investigated by means of empirical, semi-statistical procedures. These processes are found to cause the development of long stable wave patterns in the atmosphere downstream from the point of inception. These stationary patterns may occasionally exist for periods of as long as a month. The wave lengths are found to be longer than those generally considered representative of stationary wave patterns. Presumably this difference is due to the distorting effect of the larger amplitude of the long waves associated with the blocking action process. A theory of the formation of these blocking high cells is suggested based on the accumulation of heat in low latitudes and the necessity for the readjustment of the general circulation to redistribute this heat. One means of dissipation of the blocking cells is shown to be the formation of a wave pattern in the atmosphere which is out of phase with the stable wave pattern formed by the blocking high.

Some possibilities of heating by centimetric power

A study of the basic principles, range of applications, and methods of utilization of dielectric loss heating by electro-magnetic energy at radio-frequencies above 500 Mc/s.New problems arise because linear dimensions of the system and load are now large compared with the operating wavelength. In particular, the mode of formation of stationary wave patterns in the load, methods of preventing consequent non-uniform heating, and methods of avoiding or automatically correcting mismatch due to reflected waves reaching the generator are dealt with in detail.Methods of localizing the dissipation of high frequency power in the load are analysed and three basic systems—resonator, beam and transmission line—are distinguished, and are illustrated by application to the performance of suitable heating operations.

The vibration spectra of crystals

The paper presents the author’s theory of the vibration spectra of crystals from a fresh point of view. It is shown that the nature of the spectra is necessarily different in the two regions of frequency in whioh they represent respectively the characteristic eigenvibrations of the crystal structure and the stationary wave-patterns of elastic vibration. The eigenvibrations repeat themselves in volume elements within the crystal having twice the linear dimensions and eight times the volume of the lattice cells. The number of modes of eigenvibration is (24p-3),p being the number of atoms in each lattice cell. The spectral frequencies which are (24p-3) in number (or less by reason of crystal symmetry) ate accordingly monochromatic. In relation to the entire crystal, they are highly degenerate. The three missing degrees of freedom are exactly accounted for when the possible elastic vibrations which give a quasi-continuous spectrum of frequencies are enumerated. The limiting elastie wave-lengths come out as four times the lattice spacings of the crystal. The effects of anharmonicity are also considered. It is shown that they result in lowering and spreading out the spectral frequencies of the crystal when its temperature is elevated.

XXXIV. The shape of a liquid jet

Abstract A jet of liquid falling at low speed on to a smooth surface assumes a corrugated or beaded shape, hitherto regarded as a stationary wave pattern, caused by progressive disturbances travelling over the surface with the same speed as the falling liquid. An alternative explanation, based on a graphical solution to Bernoulli's equation, is put forward, and is in agreement with observation.

An electrostatic audio generator

Design and operating features of a multi-harmonic electrostatic audio frequency generator are described in this paper. The harmonics are generated singly by the rotation of a shielded segmented disk adjacent to a stationary wave pattern plate; the resulting changes in capacitance between disk and plate produce a sinusoidal charging and discharging current through an input resistance of a vacuum tube amplifier. Each harmonic is controlled independently in amplitude and in phase, and provisions are made for combining any 2 or more harmonics to obtain complex wave forms. Although designed specifically for psychological tests, the device should prove useful in any work requiring a flexible audio frequency supply of small capacity.

An Electrostatic Audio Generator

Design and operating features of a multiharmonic electrostatic audio frequency generator are described in this paper. The harmonics are generated singly by the rotation of a shielded segmented disk adjacent to a stationary wave pattern plate; the resulting changes in capacitance between disk and plate produce a sinusoidal charging and discharging current through an input resistance of a vacuum tube amplifire. Each harmonic is controlled independently in amplitude and in phase, and provisions are made for combining any 2 or more harmonics to obtain complex wave forms. Although designed specifically for psychological tests, the device should prove useful in any work requiring a flexible audio frequency supply of small capacity.

Surface tension measurements by the ripple method

A modification of the ripple method of measuring surface tension is described, in which a stationary wave pattern is formed between two vibrating styles. The pattern is projected by reflection on to a ground glass screen. Measurements of the decrease in the surface tension of tap water caused by contact with a bituminous paint are cited in illustration of the method.

LXXVII.An acoustical interpretation of the Schrödinger wave equation

Abstract Investigation is made of the one-dimensional compressional vibrations of an ideal fluid o? variable density (in equilibrium under the action of an external force) confined in an infinite tube of bounded but variable cross-section. The non-homogeneity, is so chosen that the wave velocity is everywhere the same. It is assumed that the ordinary acoustic equations are applicable except as modified by the non-homogeneity and that the cross-section is small enough so that transverse motions may be neglected. It is then found that the problem of determining the stationary wave-pattern in such a tube satisfying the boundary condition that the condensation s=δρ/ρ 0 (where ρ 0 is the equilibrium density at any point and δρ the excess density) shall remain analytic, everywhere ≪ 1 and vanish at infinity, is formally equivalent to the problem of solving a one-dimensional Schrödinger wave equation subject to the usual boundary condition. The appropriate density variation and the shape of the tube are related to the potential energy of the particle whose motion is described by the Schrödinger equation. As illustrations the free particle, the simple harmonic oscillator, and the one-dimensional hydrogen atom are investigated. The motion of the first corresponds to the oscillations of a homogeneous fluid in an infinite tube of uniform cross-section. For the simple harmonic oscillator the corresponding tube is a surface of revolution obtained by revolving the curve representing the error function about the x axis. A method of generalizing the results to the case of three degrees of freedom is indicated.