On Apr 5, 11:33 am, "MRW" wrote:
On Apr 5, 1:44 pm, "K7ITM" wrote:



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

Thank you everyone! I have a better understanding now. I guess part of
my confusion is that on the same chapter thay have a table on the
electromagnetic spectrum. In it, they list Radio Waves as having
frquencies between 10kHz to 300Ghz and wavelengths of 30,000km to 1mm
(I guess the 30,000 km is a typo in the book). Are these wavelength
values based in a vacuum then?


Clearly, the definition for the frequency range is somewhat
arbitrary. The boundary between infra-red and radio waves will
probably continue to be blurred as electronics advances further.

Radio waves down to much lower frequencies than 10kHz have been
used...the longer wavelengths penetrate water further, and are useful
for communicating with submarines. So don't be surprised if you come
across references to radio signals at 50Hz or so. Because
communications with radio waves is almost always based on propagation
through the vacuum of space, or through air which is only very
slightly slower, yes, the values for wavelength are based on c being a
constant, the speed of light in a vacuum.

Once you figure out one wavelength-frequency relationship, decade
(power-of-ten) values are easy:

1MHz = 300 meters (actually 299.792458, but almost universally taken
to be 300...)
10MHz = 30 meters
100MHz = 3 meters
etc...

Cheers,
Tom