Juneau Amateur Radio Club, Inc.
Propagation of Waves
The process of communication involves the transmission of information from one location to another. As we have seen, modulation is used to encode the information onto carrier waves, and may involve analog or digital methods. It is only the characteristics of the carrier wave which determine how the signal will propagate over any significant distance. This chapter describes the different ways that electromagnetic waves propagate.
An electromagnetic wave is created by a local disturbance in the electric and magnetic
fields. From its origin, the wave will propagate outwards in all directions. If the medium in
which it is propagating (air for example) is the same everywhere, the wave will spread out
uniformily in all directions.
Far from its origin, it will have spread out enough that it will appear have the same
amplitude everywhere on the plane perpendicular to its direction of travel
(in the near vicinity of the observer). This type of wave is called a plane wave.
A plane wave is an idealization that allows one to think of the entire wave traveling
in a single direction, instead of spreading out in all directions.
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Electromagnetic waves propagate at the speed of light in a vacuum. In other mediums, like air or glass, the speed of propagation is slower. If the speed of light in a vacuum is given the symbol c0, and the speed in some a medium is c, we can define the index of refraction, n as: n=c0/c
When a plane wave encounters a change in medium, some or all of it may propagate
into the new medium or be reflected from it. The part that enters the new medium is
called the transmitted portion and the other the reflected portion. The part which
is reflected has a very simple rule governing its behavior. Make the following
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Angle of Incidence = the angle between the direction of propagation and a line perpendicular to the boundary, on the same side of the surface. Angle of Reflection = the angle between the direction of propagation of the reflected wave and a line perpendicular to the boundary, also on the same side of the surface. Then the rule for reflection is simply stated as: The angle of reflection = The angle of incidence
If the incident medium has a lower index of refraction then the reflected wave has a 1800 phase shift upon reflection. Conversely, if the incident medium has a larger index of refraction the reflected wave has no phase shift.
When you look into a pool, the light from the bottom is refracted away from the perpendicular, because the index of refraction in air is less than in water. To the observer at the side of the pool, the light appears to come from a shallower depth.
For the same reason, when you look at objects underwater through a mask, they will appear to be larger than they really are. The light from the object is spread outwards at the water-air interface of your mask. To you it will appear the object is closer
All electromagnetic waves can be superimposed upon each other without limit. The electric and magnetic fields simply add at each point. If two waves with the same frequency are combined there will a be a constant interference pattern caused by their superposition. Interference can either be constructive, meaning the strength increases as result, or destructive where the strength is reduced. The amount of interference depends of the phase difference at a particular point. It can be shown that constructive interference occurs for phase differences of 0-1200, and 240-3600. Thus destructive interference occurs from 120-2400. For two identical waves, no phase shift results in total constructive interference, where the strength is maximum and 1800 phase shift will create total destructive interference (no signal at all).
The phase shift that causes the interference can occur either due to a difference in path length, Dx, or a difference in the arrival time, Dt. The amount of phase shift, Df, can be computed for these two cases by: Example: Omega is a radio navigation system that used the phase difference in the same signal from two fixed transmitters to determine a line-of-position. The same phase difference corresponded to multiple lines of position separated by a distance equivalent to 3600 of phase shift. Since the frequency was 10.2 kHz, the wavelength corresponding to 3600 phase shift was 16 miles, which was the lane width on an Omega overprinted chart. Loran-C also has a phase-difference mode with a lane width of only 3000 m since it operates at 100 kHz.
Recall that the idealized plane wave is actually infinite in extent. If this wave passes through an opening, called an aperture, it will diffract, or spread out,
from the opening. The degree to which the cropped wave will spread out depends on the size of the aperture relative to the wavelength. In the extreme case where the aperture is very large compared to the wavelength, the wave will see no effect and will not diffract at all. At the other extreme, if the opening is very small, the wave will behave as if it were at its origin and spread out uniformly in all directions from the aperture. In between, there will be some degree of diffraction.
When the wave enters the new medium, the speed of propagation will change. In order to match the incident and transmitted wave at the boundary, the transmitted wave will change its direction of propagation. For example, if the new medium has
a higher index of refraction, which means the speed of propagation is lower, the wavelength will become shorter (frequency must stay the same because of the boundary conditions). For the transmitted wave to match the incident wave at the boundary,
the direction of propagation of the transmitted wave must be closer to perpendicular. The relationship between the angles and indices of refraction is given by Snell's Law:
When the direction of propagation changes, the wave is said to refract. It is most useful to know in which direction the wave will refract, not necessarily by how much.
The transmitted wave will bend more towards the perpendicular when entering a medium with higher index of refraction (slower speed of propagation). Example: Why a pool is deeper than it looks.
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What is a Magnetosphere?
As shown in the picture below, a planetary magnetosphere is the region where the planetary magnetic field dominates over the solar wind. This region is defined at the boundary of where the solar wind pressure is balanced with the planetary magnetic field and internal plasma pressure.