scholarly journals On the propagation of waves through a stratified medium, with special reference to the question of reflection

1912 ◽  
Vol 86 (586) ◽  
pp. 207-226 ◽  
Keyword(s):  
Special Reference ◽  
Finite Thickness ◽  
Plane Waves ◽  
Stratified Medium ◽  
Negative Wave ◽  
Positive Direction ◽  
Negative Direction ◽  
Principal Problem ◽  
Propagation Of Waves ◽  
The Waves

The medium is supposed to be such that its properties are everywhere a function of but one co-ordinate x , being of one uniform quality where x is less than a certain value x 1 , and of another uniform quality (in general, different from the first) where x exceeds a greater value x m -1; and the principal problem is the investigation of the reflection which in general ensues when plane waves in the first medium are incident upon the strati-fications. For the present we suppose the quality to be uniform through strata of finite thickness, the first transition occurring when x = x 1 , the second at x = x 2 , and the last at x = x m -1. The expressions for the waves in the various media in order may be taken to be ϕ 1 = A 1 e i [ ct + by - a 1 ( x - x 1 )] + B 1 e i [ ct + by + a 1 ( x - x 1 )] , ϕ 2 = A 2 e i [ ct + by - a 2 ( x - x 1 )] + B 2 e i [ ct + by + a 2 ( x - x 1 )] , ϕ 3 = A 3 e i [ ct + by - a 3 ( x - x 2 )] + B 3 e i [ ct + by + a 3 ( x - x 2 )] , and so on, the A's and B's denoting arbitrary constants. The first terms represent the waves travelling in the positive direction, the second those travelling in the negative direction; and our principal aim is the determina­tion of the ratio B 1 /A 1 imposed by the conditions of the problem, including the requirement that in the final medium there shall be no negative wave.

Kompressionswellen in einer isothermen Atmosphäre mit vertikalem Magnetfeld

1966 ◽  
Vol 21 (7) ◽  
pp. 1098-1106 ◽  
Author(s):  
R. Lust ◽  
M. Scholer
Keyword(s):  
Magnetic Field ◽  
Strong Influence ◽  
Vertical Direction ◽  
Time Dependent ◽  
Solar Chromosphere ◽  
Magnetohydrodynamic Equation ◽  
One Dimensional ◽  
Spatial Dimensions ◽  
Propagation Of Waves ◽  
The Waves

The propagation of waves in the solar atmosphere is investigated with respect to the problem of the chromospheric spiculae and of the heating of the solar chromosphere and corona. In particular the influence of external magnetic fields is considered. Waves of finite amplitudes are numerically calculated by solving the time-dependent magnetohydrodynamic equation for two spatial dimensions by assuming axial symmetry. For the case without a magnetic field the comparison between one dimensional and two dimensional treatment shows the strong influence of the radial propagation on the steepening of waves in the vertical direction. In the presence of a magnetic field it is shown that the propagation is strongly guided along the lines of force. The steepening of the waves along the field is much larger as compared to the case where no field is present.

scholarly journals The effect of junctions on the propagation of electric waves along conductors

1913 ◽  
Vol 88 (601) ◽  
pp. 103-110
Keyword(s):  
Cylindrical Shell ◽  
Wave Length ◽  
General Character ◽  
Original Form ◽  
Annular Space ◽  
Approximate Methods ◽  
Positive Direction ◽  
Positive Side ◽  
The Waves ◽  
Electric Waves

Some interesting problems in electric wave propagation are suggested by an experiment of Hertz. In its original form waves of the simplest kind travel in the positive direction (fig. 1), outside an infinitely thin conducting cylindrical shell, AA, which comes to an end, say, at the plane z = 0. Co-axial with the cylinder a rod or wire BB (of less diameter) extends to infinity in both directions. The conductors being supposed perfect, it is required to determine the waves propagated onwards beyond the cylinder on the positive side of z , as well as those reflected back outside the cylinder and in the annular space between the cylinder and the rod. So stated, the problem, even if mathematically definite, is probably intractable; but if we modify it by introducing an external co-axial con­ducting sheath CC (fig. 2), extending to infinity in both directions, and if we further suppose that the diameter of this sheath is small in comparison with the wave-length (λ) of the vibrations, we shall bring it within the scope of approximate methods. It is under this limitation that I propose here to consider the present and a few analogous problems. Some considerations of a more general character are prefixed.

scholarly journals Propagation of Surface Waves in Asphalt Pavements Generated by Different Load Impulse of Falling Weight Deflectometer

2019 ◽  
Vol 15 (1) ◽  
pp. 29-35
Author(s):  
Jozef Komačka ◽  
IIja Březina
Keyword(s):  
Surface Waves ◽  
Travel Time ◽  
Time History ◽  
Asphalt Pavements ◽  
Load Force ◽  
Falling Weight Deflectometer ◽  
Waves Propagation ◽  
Propagation Of Waves ◽  
Falling Weight ◽  
The Waves

Abstract The propagation of waves generated by load impulse of two FWD types was assessed using test outputs in the form of time history data. The calculated travel time of wave between the receiver in the centre of load and others receivers showed the contradiction with the theory as for the receivers up to 600 (900) mm from the centre of load. Therefore, data collected by the sensors positioned at the distance of 1200 and 1500 mm were used. The influence of load magnitude on the waves propagation was investigated via the different load force with approximately the same load time and vice versa. Expectations relating to the travel time of waves, depending on the differences of load impulse, were not met. The shorter travel time of waves was detected in the case of the lower frequencies. The use of load impulse magnitude as a possible explanation was not successful because opposite tendencies in travel time were noticed.

scholarly journals The relativity theory of plane waves

1926 ◽  
Vol 111 (757) ◽  
pp. 95-104 ◽  
Keyword(s):  
Gravitational Field ◽  
Electromagnetic Waves ◽  
Small Amplitude ◽  
Plane Waves ◽  
Cumulative Effect ◽  
Relativity Theory ◽  
Transverse Waves ◽  
Propagation Of Light ◽  
Cumulative Change ◽  
The Waves

Weyl has shown that any gravitational wave of small amplitude may be regarded as the result of the superposition of waves of three types, viz.: (i) longitudinal-longitudinal; (ii) longitudinal-transverse; (iii) transverse-transverse. Eddington carried the matter much further by showing that waves of the first two types are spurious; they are “merely sinuosities in the co­ordinate system,” and they disappear on the adoption of an appropriate co-ordinate system. The only physically significant waves are transverse-transverse waves, and these are propagated with the velocity of light. He further considers electromagnetic waves and identifies light with a particular type of transverse-transverse wave. There is, however, a difficulty about the solution as left by Eddington. In its gravitational aspect light is not periodic. The gravitational potentials contain, in addition to periodic terms, an aperiodic term which increases without limit and which seems to indicate that light cannot be propagated indefinitely either in space or time. This is, of course, explained by noting that the propagation of light implies a transfer of energy, and that the consequent change in the distribution of energy will be reflected in a cumulative change in the gravitational field. But, if light cannot be propagated indefinitely, the fact itself is important, whatever be its explana­tion, for the propagation of light over very great distances is one of the primary facts which the relativity theory or any like theory must meet. In endeavouring to throw further light on this question, it seemed desirable to avoid the assumption that the amplitudes of the waves are small; terms neglected on this ground might well have a cumulative effect. All the solu­tions discussed in this paper are exact.

scholarly journals On the acoustic disturbances produced by small bodies in plane waves transmitted through water, with special reference to the single-plate direction finder

1921 ◽  
Vol 100 (704) ◽  
pp. 261-288
Keyword(s):  
Special Reference ◽  
Plane Waves ◽  
Maximum Amplitude ◽  
Sound Waves ◽  
Small Bodies ◽  
Acoustic Disturbances ◽  
Sense Of Direction ◽  
Single Plate ◽  
Direction Finder ◽  
Metal Diaphragm

The experiments to be described were carried out for the Board of Invention and Research, under the direction of Sir William Bragg, between October 1916 and February 1917, on the Cullaloe Reservoir, near Aberdour, Fifeshire, and are now published with the permission of the Admiralty. A form of directional hydrophone has already been described by Sir William Bragg. It consists of a metal diaphragm, A, about four inches in diameter, mounted in a heavy ring, B, and open to the water on both sides ( vide Chart 9). In the centre of the diaphragm is a small metal box, C, carrying a carbon granule microphone of the button type. The microphone is connected into an ordinary telephone circuit. If the instrument is rotated about a vertical diameter in water through which sound waves are passing the sound heard in the receivers passes through a number of maxima and minima. When the diaphragm is turned “edge-on” to the source of sound it is obvious that the pressure pulses will reach the two faces of the diaphragm symmetrically and the diaphragm will fail to vibrate. As, however, either face is turned toward the source this symmetry ceases to exist and the diaphragm is thrown into vibration, which reaches a maximum amplitude when the instrument is “broad-side” on to the source. The instrument, therefore, indicates the line of propagation of the sound, but owing to the existence of two positions of maximum or minimum its indications are ambiguous as regards the sense of direction.

Propagation of Alfvén-gravitational waves in a stratified perfectly conducting flow with transverse magnetic field

1972 ◽  
Vol 54 (2) ◽  
pp. 209-215 ◽  
Author(s):  
N. Rudraiah ◽  
M. Venkatachalappa
Keyword(s):  
Magnetic Field ◽  
Gravitational Waves ◽  
Transverse Magnetic Field ◽  
Transverse Magnetic ◽  
Constant Coefficients ◽  
Downward Propagation ◽  
The Mean ◽  
Propagation Of Waves ◽  
The Waves ◽  
Vertical Height

Alfvén-gravitational waves are found to propagate in a Boussinesq, inviscid, adiabatic, perfectly conducting fluid in the presence of a uniform transverse magnetic field in which the mean horizontal velocity U is independent of vertical height z. The governing wave equation is a fourth-order ordinary differential equation with constant coefficients and is not singular when the Doppler-shifted frequency Ωd = 0, but is singular when the Alfvén frequency ΩA = 0.If Ω2d < Ω2A the waves are attenuated by a factor exp − [2ΩA(N2−Ω2d)½−Ω2d + Ω2A]z, which tends to zero as z → ∞. This attenuation is similar to the viscous attenuation of waves discussed by Hughes & Young (1966). The interpretation of upward and downward propagation of waves is given.

Cyclic Voltammetric Studies of the Behavior of Pb-0.3%Ag-0.06%Ca Rolled Alloy Anode during and after Zinc Electrowinning

2013 ◽  
Vol 750-752 ◽  
pp. 2232-2235 ◽  
Author(s):  
Hai Tao Yang ◽  
Huan Rong Liu ◽  
Yong Chun Zhang ◽  
Bu Ming Chen ◽  
Zhong Cheng Guo ◽  
...  
Keyword(s):  
Electrochemical Behaviour ◽  
Anodic Oxide ◽  
Anodic Peak ◽  
Zinc Electrowinning ◽  
Positive Direction ◽  
Major Phase ◽  
Oxide Layers ◽  
Negative Direction ◽  
Alloy Anode ◽  
Sulphate Electrolyte

In this paper, electrochemical behaviour of Pb0.3%Ag0.06%Ca rolled alloy anode during the 6 days galvanostatic electrolysis in acid zinc sulphate electrolyte solution was investigated with Cyclic Voltammetry (CV) techniques. The phase composition of the anodic oxide layers during the electrolysis was observed using X-Ray Diffraction (XRD). The results revealed that with the increasing electrolysis time, the anodic peak (PbPbSO4) is mainly present a rise trend in the first day electrolysis, thereafter, almostly keep a constant value. And the anodic peak (PbPbSO4) gradually moved in the positive direction while the anodic peak (PbSO4β-PbO2, PbOα-PbO2) strongly moved in the negative direction. The cathodic peak (β-PbO2 and α-PbO2PbSO4) and (PbO and PbSO4Pb) mainly present a rise trend and gradually moved in the negative direction. Besides, the corrosion phase of the anodic oxide layers mainly consist of PbSO4, Pb, α-PbO2 and PbS2O3. After electrolysis for 3 days, the major phase of the anodic oxide layers is PbSO4 with a few Pb phase. When the electrolysis reaches the 6th day, the major phase of the anodic oxide layers is also PbSO4 with a few α-PbO2 phase. The preferred growth orientation of PbSO4 is (021) ,(121) and (212) planes.

Scattering ofs-polarized plane waves by finite-thickness periodic structures made of ultralow-permittivity metamaterials

2006 ◽  
Vol 73 (11) ◽  
Author(s):  
A. E. Serebryannikov ◽  
T. Magath ◽  
K. Schuenemann ◽  
O. Y. Vasylchenko
Keyword(s):  
Periodic Structures ◽  
Finite Thickness ◽  
Plane Waves

scholarly journals Electromagnetically induced transparency in plasma

2001 ◽  
Vol 19 (2) ◽  
pp. 175-179 ◽  
Author(s):  
B. ERSFELD ◽  
D.A. JAROSZYNSKI
Keyword(s):  
Electromagnetic Waves ◽  
Plasma Frequency ◽  
Electromagnetically Induced Transparency ◽  
Plane Waves ◽  
Electron Mass ◽  
Number Density ◽  
Relativistic Fluid ◽  
Longitudinal Plasma ◽  
Induced Transparency ◽  
The Waves

The coupled propagation of two electromagnetic waves in plasma is studied to establish the conditions for induced transparency. Induced transparency refers to the situation where both waves propagate unattenuated, although the frequency of one (or both) of them is below the plasma frequency so that it could not propagate in the absence of the other. The effect is due to the interaction of the waves through their beat, which modulates both the electron mass and, by exciting longitudinal plasma oscillations, their number density, and thus the plasma frequency. Starting from a relativistic fluid description, a dispersion relation for plane waves of weakly relativistic intensities is derived, which takes into account the polarization of the waves and the nonlinearities with respect to both their amplitudes. This serves as a basis for the exploration of the conditions for induced transparency and the modes of propagation.

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