scholarly journals On the problem of the electrified disc

1947 ◽  
Vol 8 (1) ◽  
pp. 14-19 ◽  
Author(s):  
E. T. Copson
Keyword(s):  
External Field ◽  
Gravitational Potential ◽  
Electrostatic Field ◽  
Surface Density ◽  
Wave Length ◽  
Circular Disc ◽  
Sound Waves ◽  
Total Potential ◽  
Induced Charge ◽  
Lord Kelvin

When a perfectly conducting uniform thin circular disc is kept at a potential V0 in an external electrostatic field of potential Φ, electric charge is induced on the surface of the disc; the problem is to find the surface-density σ of this induced charge and its potential V so that the total potential V + Φ has the constant value V0 on the surface of the disc. This problem was first discussed by Green in 1832, and the solution in the case when there is no external field was deduced by Lord Kelvin from the known formula for the gravitational potential of an elliptic homoeoid. The problem is still of interest since similar ideas occur in the theory of diffraction by a circular disc and in the theory of the generation of sound waves by a vibrating disc when the wave-length is large compared with the radius of the disc.

scholarly journals On the theory of the inertia and diffraction corrections for the Rayleigh disc

1935 ◽  
Vol 153 (878) ◽  
pp. 17-40 ◽  
Keyword(s):  
Wave Front ◽  
Acoustic Radiation ◽  
Stationary Wave ◽  
Negative Sign ◽  
Circular Disc ◽  
Sound Waves ◽  
Velocity Amplitude ◽  
Radiation Fields ◽  
Quartz Fibre

A thin circular disc suspended by a quartz fibre tends to set itself broadside on to the direction of the propagation of incident sound waves, and its use in combination with resonators is well known as a means of measuring relative intensities of acoustic radiation fields. In a progressive or stationary wave in which the velocity amplitude is │ξ│, the average couple on a circular disc of radius a is usually given by the well-known formula L͞ = - ⅔ρ 0 a 3 │ξ│ 2 sin 2α, (1) where ρ 0 is the density of the medium and α is the angle between the direction of propagation of the wave-front and the normal to the disc, while the negative sign indicates that the couple tends to diminish α.

Note on the Problem of the Electrified Disc

1956 ◽  
Vol 10 (3) ◽  
pp. 123-124
Author(s):  
A. A. Ashour
Keyword(s):  
External Field ◽  
Integral Equations ◽  
Circular Disc ◽  
Oblate Spheroidal ◽  
Constant Potential

1. Prof. E. T. Copson has discussed the well-known problem of a circular disc kept at a constant potential Vo in an external field of potential Φ by reducing it to the solution of two integral equations. Tho solution is however fairly simple if we use oblate spheroidal co-ordinates. This is due to the fact that in this system of coordinates the disc can be represented in terms of one co-ordinate only. This method is applied to the above problem and Copson's results are obtained. The solution when Vo is not constant, but any surface function of the disc, is also obtained.

scholarly journals On the Peculiarities of Realization of Electrostatic Instability of Charged Liquid Surface in Various Geometries

2021 ◽  
Vol 57 (4) ◽  
pp. 15-23
Author(s):  
A.I. Grigoriev ◽  
◽  
S.O. Shiryaeva ◽  
Keyword(s):  
Electric Charge ◽  
Electrostatic Field ◽  
Surface Density ◽  
Flat Surface ◽  
Liquid Surface ◽  
Critical Values ◽  
Charged Surface ◽  
Spatial Change ◽  
Non Equilibrium

The paper deals with some peculiarities of realization of electrostatic instability of a charged liquid surface on the vertices of the charged and uncharged drops in an external electrostatic field in a cylindrical jet and a flat surface. It was shown that the critical values of the surface density of the electric charge under the mentioned conditions on the threshold of the realization of instability are different in magnitude, despite the phenomenological similarity. Most probably, the reason is the differences (under all mentioned conditions) in the spatial change in the strength of the electrostatic field in the vicinity of the growing (when the charged surface of the liquid is unstable) emission protrusion. Both equilibrium and non-equilibrium forms of droplets, jets, planes and their symmetry were discussed.

scholarly journals Non-Wovens as Sound Reducers

2018 ◽  
Vol 55 (2) ◽  
pp. 64-76
Author(s):  
D. Belakova ◽  
A. Seile ◽  
S. Kukle ◽  
T. Plamus
Keyword(s):  
Absorption Coefficient ◽  
Surface Density ◽  
Sound Absorption ◽  
Transmission Loss ◽  
Sound Transmission ◽  
Sound Insulation ◽  
Material Structure ◽  
Sound Transmission Loss ◽  
Sound Waves ◽  
Frequency Range

Abstract Within the present study, the effect of hemp (40 wt%) and polyactide (60 wt%), non-woven surface density, thickness and number of fibre web layers on the sound absorption coefficient and the sound transmission loss in the frequency range from 50 to 5000 Hz is analysed. The sound insulation properties of the experimental samples have been determined, compared to the ones in practical use, and the possible use of material has been defined. Non-woven materials are ideally suited for use in acoustic insulation products because the arrangement of fibres produces a porous material structure, which leads to a greater interaction between sound waves and fibre structure. Of all the tested samples (A, B and D), the non-woven variant B exceeded the surface density of sample A by 1.22 times and 1.15 times that of sample D. By placing non-wovens one above the other in 2 layers, it is possible to increase the absorption coefficient of the material, which depending on the frequency corresponds to C, D, and E sound absorption classes. Sample A demonstrates the best sound absorption of all the three samples in the frequency range from 250 to 2000 Hz. In the test frequency range from 50 to 5000 Hz, the sound transmission loss varies from 0.76 (Sample D at 63 Hz) to 3.90 (Sample B at 5000 Hz).

A MEASUREMENT OF ULTRASONIC ATTENUATION COEFFICIENT BY FREQUENCY RESPONSE IN STEELS WITH DIFFERENT GRAIN SIZES

2003 ◽  
Vol 26 (4) ◽  
pp. 389-402
Author(s):  
Kyung-Cho Kim
Keyword(s):  
Frequency Response ◽  
Attenuation Coefficient ◽  
Evaluation Method ◽  
Ultrasonic Attenuation ◽  
Wave Length ◽  
Structural Behavior ◽  
Response Property ◽  
Sound Waves ◽  
Grain Sizes ◽  
Plate Specimen

A new evaluation method of ultrasonic attenuation in materials is proposed based on the frequency response property of the material evaluated by employing the sound impulse of a wide frequency band. Borrowing from ordinary system theory, the material to be tested is considered to have a characteristic impulse response, representing its micro-structural non-uniformities and thus resulting in the sound attenuation of the material. The concept is resumed as an attenuation system that simulates the material’s micro-structural behavior. Experimental results on a series of specimens, having different grain sizes but all made of a single austenitic stainless steel, showed that the attenuation could properly be evaluated from a single bottom echo in a plate specimen. The attenuation coefficient α, was corrlated in this case to the grain size, D, by the equation, αD=H(πD/λ)n, where λ is wave length and H and n are constants. It was also shown that the micro structural change of materials could be evaluated by the energy loss of sound waves passing through the attenuation systems.

scholarly journals Semicompressible Ocean Dynamics

2015 ◽  
Vol 45 (1) ◽  
pp. 149-156 ◽  
Author(s):  
W. K. Dewar ◽  
J. Schoonover ◽  
T. J. McDougall ◽  
W. R. Young
Keyword(s):  
Gravitational Potential ◽  
General Circulation ◽  
Equations Of Motion ◽  
Boussinesq Approximation ◽  
Ocean Dynamics ◽  
Navier Stokes ◽  
Sound Waves ◽  
Circulation Modeling ◽  
Potential Fluid

AbstractThe equations of motion are reexamined with the objective of improving upon the Boussinesq approximation. The authors derive new equations that conserve energy, filter out sound waves, are more accurate than the Boussinesq set, and are computationally competitive with them. The new equations are partly enabled by exploiting a reversible exchange between internal and gravitational potential fluid energy. To improve upon these equations appears to require the inclusion of acoustics, at which point one should use full Navier–Stokes. This study recommends the new sets for testing in general circulation modeling.

scholarly journals On the acoustic radiation pressure on spheres

1934 ◽  
Vol 147 (861) ◽  
pp. 212-240 ◽  
Keyword(s):  
Radiation Pressure ◽  
Acoustic Radiation ◽  
Wave Length ◽  
Theoretical Development ◽  
Order Effects ◽  
Pressure Amplitude ◽  
Sound Waves ◽  
Radiation Fields ◽  
Acoustic Radiation Pressure ◽  
Relative Measurements

Although frequent reference is made to acoustic radiation pressure in treatises and memoirs on sound, there appears to be no systematic theoretical development of the subject enabling actual pressures on obstacles of simple geometrical form to be calculated. In the audible range of acoustic frequencies, it is possible to devise, in a number of ways, means of measuring pressure amplitudes in sound waves as first order effects. At supersonic frequencies, however, these methods are no longer serviceable. When the dimensions of resonators of diaphragms become comparable with the wave-length, the physical effects which enable the pressure amplitude to be measured involve intractable diffraction problems, while the extremely high frequencies and small amplitudes involved make the employment of stroboscopic methods of observation extremely difficult. It has been shown, however, that at supersonic frequencies the acoustic radiation pressures on spheres and discs become sufficiently large to be measured easily, at any rate, in liquids. The mean pressure is generally assumed to be proportional to the energy density in the neighbourhood of the obstacle, and on this basis relative measurements can be made, for instance, in the radiation field of a supersonic oscillator. Such formulæ may be obtained without restriction as to wave-length, for spheres in plane progressive and stationary radiation fields, and the magnitude of the pressure is found to be of entirely different orders of magnitude in the two cases.

scholarly journals On electrical effects due to sound waves in colloidal suspensions

1951 ◽  
Vol 207 (1090) ◽  
pp. 329-342 ◽  
Keyword(s):  
Double Layer ◽  
Colloidal Particles ◽  
Wave Train ◽  
Wave Length ◽  
Colloidal Suspensions ◽  
Exact Expression ◽  
Particle Radius ◽  
Potential Difference ◽  
Sound Waves ◽  
Leading Term

In this paper, the electrical effects accompanying the propagation of sound waves through a suspension of spherical colloidal particles in an electrolyte are examined. It is shown that, for charged colloidal particles, differences of potential arise between different points in the wave train. A general method is given for obtaining the amplitude of the potential difference in the case when the thickness of the double-layer surrounding the particles is small compared with the particle radius, as a power series in the zeta-potential and the leading term in this series is evaluated, so that the results will be adequate for zeta-potentials which are not too large. An exact expression is obtained for the case when the thickness of the double-layer is very much greater than the particle radius but still much less than the mean separation. An attempt is also made to estimate the effect for intermediate values of the double-layer thickness. The amplitude of the potential difference decreases with increasing concentration of electrolyte and, when measured between points a half-wave-length apart, is substantially independent of the frequency of the sound waves, except at very high frequencies. The results are compared with the experimental data.

Spherical tensor approach to multipole expansions. I. Electrostatic interactions

1976 ◽  
Vol 54 (5) ◽  
pp. 505-512 ◽  
Author(s):  
C. G. Gray
Keyword(s):  
External Field ◽  
Interaction Energy ◽  
Charge Distribution ◽  
Electrostatic Interaction ◽  
Electrostatic Field ◽  
Spherical Harmonic ◽  
Electrostatic Interactions ◽  
Tensor Method ◽  
Multipole Expansions ◽  
A Charge

Using spherical harmonic expansions, the electrostatic field due to a given charge distribution, the interaction energy of a charge distribution with a given external field, and the electrostatic interaction energy of two charge distributions are decomposed into multipolar components. Extensive use is made of symmetry arguments. Comparisons with the Cartesian tensor method are also given.

Note on an electrified circular disk situated inside an earthed coaxial infinite hollow cylinder

1961 ◽  
Vol 57 (3) ◽  
pp. 623-627 ◽  
Author(s):  
W. D. Collins
Keyword(s):  
Integral Equation ◽  
Charge Density ◽  
Closed Form ◽  
Hollow Cylinder ◽  
Electrostatic Field ◽  
Fredholm Integral Equation ◽  
Surface Density ◽  
Surface Charge Density ◽  
Circular Disk ◽  
Constant Potential

Copson(1) has shown that the problem of determining the surface density of electric charge induced on a thin circular disk maintained at a constant potential in an external electrostatic field can be solved by two applications of the known solution of Abel's integral equation. This note shows that Copson's method can be extended to determine the surface charge density induced on the disk when situated inside an earthed coaxial infinitely long hollow cylinder. Whilst this problem is not solved in closed form, it is shown to be governed by a Fredholm integral equation of the second kind, which can be solved approximately by iteration when the radius of the cylinder is large compared with that of the disk.

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