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

K7ITM wrote:


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

Hi Tom -

This is becoming circuitous. What you're saying is exactly what led
the original correspondent to be confused in the first place. Since
the relavant equation doesn't read c = f*w/n, the only way to explain
the phenomenon is by using a value of c that varies with medium. That
was the entire point.

73. Jim AC6XG

K7ITM wrote:
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.

That's why I put it in quotes - to signify an unusual notation.
--
73, Cecil, w5dxp.com

MRW wrote:

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?

Yes. And it's very, very nearly the same for air.

The 30,000 km would be a typo -- the wavelength in a vacuum at 10 kHz
would be 30 km.


Roy Lewallen, W7EL

On Apr 5, 1:14 pm, Jim Kelley wrote:
K7ITM wrote:
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

Hi Tom -

This is becoming circuitous. What you're saying is exactly what led
the original correspondent to be confused in the first place. Since
the relavant equation doesn't read c = f*w/n, the only way to explain
the phenomenon is by using a value of c that varies with medium. That
was the entire point.

73. Jim AC6XG

Hi Jim,

OK, but I still say that, in that case, the equation (c=f*w) uses c in
a way that's inconsistent with common usage of c. I don't know if the
article quoted by the OP mentions that, or if somewhere it adds other
qualification, but if it's not out of context, then it would confuse
me, too, if I were trying to understand it for the first time. At the
very least, the article should say somewhere that c is the speed of
propagation in whatever medium we're dealing with, and if it did,
perhaps the OP wouldn't have been confused about it in the first
place. His posting makes it very clear to me that HE thought c was a
constant, as I would if the author didn't tell me otherwise.

Cheers,
Tom

On 5 Apr 2007 18:15:30 -0700, "K7ITM" wrote:

HE thought c was a
constant, as I would if the author didn't tell me otherwise.

Hi Tom,

The speed of light is always constant - within its frame of reference.
It is only for those that inhabit a different frame that it "appears"
to be different. By Lorentzian laws, there is no time at the speed of
light and everything is simultaneous - source and load are
inseparable.

To illustrate at a slightly slower speed (from Feynman):
"A very interesting example of the slowing of time with motion
is furnished mu-mesons (muons), which are particles that
disintegrate spontaneously after an average lifetime of 2.2 µS.
They come to earth in cosmic rays.... It is clear that in its
short lifetime a muon cannot travel, even at the speed of light,
much more than 600 meters. But although the muons are created at
the top of the atmosphere, some 10 kilometers up, yet they are
actually found in a laboratory down here, in cosmic rays. How can
that be? The answer is that .... While from OUR own point of view
they live considerably longer ... time is increased ... by
1/SQRT(1-(u²/v²))."

73's
Richard Clark, KB7QHC

Richard Clark wrote:
While from OUR own point of view
they live considerably longer ... time is increased ... by
1/SQRT(1-(u²/v²))."

I wonder what that implies about the alleged age
of the universe?
--
73, Cecil http://www.w5dxp.com

On Apr 6, 12:08 am, Richard Clark wrote:
On 5 Apr 2007 18:15:30 -0700, "K7ITM" wrote:

HE thought c was a
constant, as I would if the author didn't tell me otherwise.

Hi Tom,

The speed of light is always constant - within its frame of reference.
It is only for those that inhabit a different frame that it "appears"
to be different. By Lorentzian laws, there is no time at the speed of
light and everything is simultaneous - source and load are
inseparable.

To illustrate at a slightly slower speed (from Feynman):
"A very interesting example of the slowing of time with motion
is furnished mu-mesons (muons), which are particles that
disintegrate spontaneously after an average lifetime of 2.2 µS.
They come to earth in cosmic rays.... It is clear that in its
short lifetime a muon cannot travel, even at the speed of light,
much more than 600 meters. But although the muons are created at
the top of the atmosphere, some 10 kilometers up, yet they are
actually found in a laboratory down here, in cosmic rays. How can
that be? The answer is that .... While from OUR own point of view
they live considerably longer ... time is increased ... by
1/SQRT(1-(u²/v²))."

73's
Richard Clark, KB7QHC

Seems to me you're way off point here, Richard. I'm in my lab, my
inertial frame of reference. I send some EM waves through my vacuum
chamber and I measure their speed as 2.997...*10^8 meters/second. The
same waves continue on through the glass of the bell jar keeping air
out of my vacuum, and I happen to notice that their speed through that
glass is1.684*10^8 meters/second. I notice that light from my
hydrogen light source contains certain well-defined spectral lines,
but each of those passes through my vacuum at the same speed.
However, I notice that those lines, in a short pulse of light, come
out of the glass separated in time slightly, implying that they took
different times to get through the glass, and were therefore not even
travelling through the glass at the same velocity; I notice no such
separation for the light passing through the vacuum. Further, I
notice that light from a distant star has apparently the same set of
spectral lines, but they are shifted to slightly longer wavelengths.
However, they take the same time to pass through the vacuum as my
locally-generated hydrogen light. All my measurements are in the same
frame of reference, and IN VACUUM the speed of em radiation appears
from all my measurements to be the same, no matter its wavelength,
even for very long wavelengths, but in other media, still the same
inertial reference frame, it's different. I also happen to notice
that the light from the distant star was created in a different
inertial frame of reference...

OK, I'll shut up on this now.

Cheers,
Tom

K7ITM wrote:
I also happen to notice
that the light from the distant star was created in a different
inertial frame of reference...

Not to mention being created in a different medium.
--
73, Cecil http://www.w5dxp.com

On Apr 5, 4:40 pm, Roy Lewallen wrote:
Yes. And it's very, very nearly the same for air.

The 30,000 km would be a typo -- the wavelength in a vacuum at 10 kHz
would be 30 km.

Roy Lewallen, W7EL

Thanks again everyone! It makes sense to me to just treat c, in this
case, as a relative speed dependent on the medium.