On Apr 5, 11:56 am, "Jim Kelley" wrote:
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


Hi Jim,

Some people may use only c-sub-zero for the speed of light in a
vacuum, but most commonly I see it simply as c, a fundamental physical
constant. To avoid confusion, I would HIGHLY recommend that either
you be very explicit that you're using co as the constant, and c as
the speed of light in whatever medium you're dealing with -- OR that
you're using c as the constant and whatever other notation for the
speed elsewhere.

NIST lists the constant both ways: c, c-sub-zero. SEVERAL other
places I just looked (reference books from my bookshelf; a web survey
including US, UK and European sites--mostly physics sites; several
university sites) only used c as the constant, except the NIST site
and one other, which both listed it as c or c-sub-zero with equal
weight.

It's clearly a matter only of notation, but I'll elect to stay with
the most commonly used notation, and from what I've seen just now,
most think c is a constant.

Cheers,
Tom