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, 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.

MRW wrote:
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.

As others have pointed out, it's risky to treat c as a variable or
medium-dependent speed. That letter is nearly always used to designate
the speed of light (or any EM plane wave) in a vacuum. Using that
nearly-universal definition, the speed of an EM wave in any other medium
is VF * c where VF is the "velocity factor". It's important to realize
that while there's a single value for the speed of all EM waves in a
vacuum (c), this isn't true in many other media. In many media, the
speed of the wave depends on its frequency, a phenomenon called
"dispersion". So in many media there's no universal EM velocity
equivalent to c, but rather a frequency-dependent velocity factor.

In environments where the field is confined such as a waveguide, the
velocity can also depend on the mode, that is the orientation of the
fields. So there's not even a single value for each frequency. And this
can be true even if the waveguide is filled with a vacuum.

Roy Lewallen, W7EL

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

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

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

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

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