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?

On 5 Apr 2007 07:36:49 -0700, "MRW" wrote:

c = f*w (c = m/s, f = frequency, w = wavelength)

This frequency is relevant ONLY for vacuum (or with a very, very
slight alteration) air.

Now, it may seem that all air is air, but no. There are slight
variations here too that on the global scale small shifts make large
changes. Those small shifts are accounted for by pressure, water
content (vapor), and temperature.

73's
Richard Clark, KB7QHC

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?

Refraction occurs when an EM wave, having frequency f and wavelength w
enters a medium in which the speed of propagation (speed of light) is
different than vacuum. A medium with an index of refraction greater
than one produces a speed of light which is slower than in vacuum
(index of refraction is simply the ratio of vacuum speed to speed in
that medium). This changes the proportionality between frequency and
wavelength. Since w = c / f, the slower speed at a given frequency
will now have a correspondingly shorter wavelength. And, as f = c /
w, the slower speed at a given wavelength will now have a
correspondingly lower frequency.

I hope that makes sense.

73, Jim AC6XG

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?

'c' decreases because of the fractional velocity
factor in a transmission line. The decrease in 'c'
compresses the wavelength but doesn't change the
frequency. 'c' is less in a transmission line than
it is in free space. The speed of light in RG-213,
for instance, is 2/3 of the speed of light in free
space.
--
73, Cecil, w5dxp.com

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?

frequency stays the same, but since it's moving slower, c is smaller, so
lambda (wavelength) is shorter.

Same thing goes on in coaxial cable.. the wave propagates in a
dielectric with a propagation speed, say, 66% of the free space speed.
In such a case, a one wavelength long piece of coax for 30 MHz is 6.6
meters, not 10 meters (the free space wavelength)

The challenge, of course, would be in getting the opposite phenomenon to
occur (propagation faster than free space)...but that's a topic for a
different day.

jim

On Thu, 05 Apr 2007 09:23:13 -0700, Jim Lux wrote:

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?

frequency stays the same, but since it's moving slower, c is smaller, so
lambda (wavelength) is shorter.

Same thing goes on in coaxial cable.. the wave propagates in a
dielectric with a propagation speed, say, 66% of the free space speed.
In such a case, a one wavelength long piece of coax for 30 MHz is 6.6
meters, not 10 meters (the free space wavelength)

The challenge, of course, would be in getting the opposite phenomenon to
occur (propagation faster than free space)...but that's a topic for a
different day.

jim

Speedy Gozales did it, but that's also a topic for a different day.

Walt, W2DU

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

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?

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