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Not understanding some parts of wave refraction
K7ITM wrote: On Apr 5, 7:36 am, "MRW" wrote: I am skimming thru the Propagation chapter of the ARRL handbook, and I am having a difficult time understanding the shortening of wavelength and the retainment of frequency. They have an equation showing that wave velocity is: c = f*w (c = m/s, f = frequency, w = wavelength). It also states that during refraction "the wavelength is simultaneously shortened, but the wave frequency (number of crests that pass a certain point in a given unit of time) remains constant." I don't understand. If the wavelength is shortened, then shouldn't the frequency increase instead of remaining constant? Others have posted, correctly, that the propagation velocity is slower in some mediums than in others. I think it's a mistake, though, to say that c changes! c is supposed to be a constant, the speed of electromagnetic wave propagation in a vacuum--in fact, I suppose, in a vacuum with no gravitational fields in it. A description of fields in an electromagnetic wave often used the permittivity, epsilon, and permeability, mu, of the medium through which the wave is travelling. If it's through a vacuum, the values of epsilon and mu have values that are used often and have special notation--epsilon-sub-zero and mu- sub-zero. For convenience here, call them eo and uo. Then note that eo*uo = 1/c^2. As you might suspect, the propagation in a medium with larger values of e and u than eo and uo is slower than c. In fact, it should be velocity = sqrt(1/(e*u)). Note that e has the units of capacitance/length -- commonly farads/ meter -- and u has the units of inductance/length -- commonly henries/ meter. But a farad is an ampere*second/volt, and a henry is a volt*second/amp, so the units of sqrt(1/(e*u)) are sqrt(1/((A*sec/ V*meter)*(V*sec/A*meter))) = sqrt(meter^2/sec^2) = meters/sec. A unit analysis is often useful to insure you haven't made a mistake in your manipulation of equations. So...in summary, c = f*w is actually not quite correct. It should be wave_velocity = f*w. c should be reserved to mean only the speed of light in a vacuum. If you're in a non-vacuum medium, and measure very accurately, you'll measure the same frequency, but a shorter wavelength: the wave doesn't travel as far to push a cycle past you, as compared with in vacuum. It's going slower. If the propagation medium is, for example, solid polyethylene (the dielectric of most inexpensive coax cable), you'll find that w is about 0.66 times as much as it is in a vacuum, and the propagation velocity is similarly 0.66*c. Cheers, Tom Hi Tom - That's certainly one way to look at it. (Though it is a little like saying there is only one speed of sound.) Another way is to say that c = 1/root(mu*epsilon) for any media. Light does after all, always travel at the speed of light. ;-) Besides, it's more difficult to explain Cherenkov radiation without the expression 'faster than the speed of light in that medium'. I thoroughly enjoyed the discussion you and Owen were (are) having regarding amplifiers. Thank you for that. 73, Jim AC6XG |
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