Mike Monett wrote:
"Tom Donaly" wrote:

[...]

Most undergraduate physics texts have, or should have, discussions
of vibrating strings. There's a good treatment of the subject in
William C. Elmore's and Mark A. Heald's book _Physics of Waves_
published by Dover.

If you wanted to get in an argument you could say that the energy
on both sides of the node isn't traveling, but is merely
alternating between potential and kinetic.

Yes, I thought about that a bit before posting. It seems logical a
plucked string sends a wave in both directions, where it is
reflected and returns to create a standing wave.

When it forms a standing wave, it seems reasonable to say the energy
is alternating between potential and kinetic. But isn't that similar
to what happens on a transmission line that is exactly some multiple
of a quarter wavelength long?


Demo 4 of the TLVis1 program I posted reference to, shows that in a
transmission line with a pure standing wave (load reflection coefficient
magnitude of 1), the energy between nodes alternates between the
electric field (line capacitance) and magnetic field (line inductance).
This is true regardless of the line length or the source termination.

Roy Lewallen, W7EL

Roy Lewallen wrote:

Demo 4 of the TLVis1 program I posted reference to, shows that in
a transmission line with a pure standing wave (load reflection
coefficient magnitude of 1), the energy between nodes alternates
between the electric field (line capacitance) and magnetic field
(line inductance).

This is true regardless of the line length or the source
termination.

Roy Lewallen, W7EL

Yes, this is a very nice demo. Thank you for posting it.

I have a question. In demo 4, the bottom window shows the Ee field
in green, Eh in red, and ETot in black.

When the demo starts, you can only see a green and a black trace.

If you pause it just as the wave hits the end, you can now see the
red trace, Eh. (This is an actual statement and has nothing to do
with the fact I am Canadian.)

What happened to the Eh trace as the wave is initally moving to the
right? Is it overlaid by the Ee trace in green? Or is it just not
plotted?

Then, when the wave hits the end and starts reflecting, the red
trace remains attached to ground, and the green trace moves up and
connects with the black trace. (Sorry for the confusing description
- you have to try it yourself to see.)

Now, as you single step, the green trace and the red trace appear to
be 180 degrees out of phase.

My problem here is someone wrote a web page that claims the electric
and magnetic fields are orthogonal:

http://www.play-hookey.com/optics/tr...etic_wave.html

I tried sending him an email to show if the fields were orthogonal
as he claims, it would look like a pure reactance, and no energy
would be transmitted. But he is stuck on his idea and won't budge.

Now my problem is figuring out exactly what happens at the
reflection, and why the Eh field behaves the way shown in your demo.

Regards,

Mike Monett

Mike Monett wrote:

Yes, this is a very nice demo. Thank you for posting it.

I have a question. In demo 4, the bottom window shows the Ee field
in green, Eh in red, and ETot in black.

When the demo starts, you can only see a green and a black trace.

If you pause it just as the wave hits the end, you can now see the
red trace, Eh. (This is an actual statement and has nothing to do
with the fact I am Canadian.)

What happened to the Eh trace as the wave is initally moving to the
right? Is it overlaid by the Ee trace in green? Or is it just not
plotted?

The traces are drawn in the order Eh, Ee, and total. During the initial
forward wave, Eh and Ee are equal, so the Ee overwrites the Eh trace.

Then, when the wave hits the end and starts reflecting, the red
trace remains attached to ground, and the green trace moves up and
connects with the black trace. (Sorry for the confusing description
- you have to try it yourself to see.)

Hopefully it'll all make sense once you think about how one trace will
always win when more than one have the same value.

Now, as you single step, the green trace and the red trace appear to
be 180 degrees out of phase.

My problem here is someone wrote a web page that claims the electric
and magnetic fields are orthogonal:

http://www.play-hookey.com/optics/tr...etic_wave.html

You're making the same error that Cecil often does, confusing time phase
with directional vector orientation. The orthogonality of E and H fields
refers to the field orientations of traveling plane TEM waves in
lossless 3D space or a lossless transmission line, at the same point and
time. The E and H fields of these traveling waves are always in time
phase, not in quadrature. The graphs show the magnitudes of the waves at
various points along the line. These represent neither the time phase
nor the spatial orientation of the E and H fields.

I tried sending him an email to show if the fields were orthogonal
as he claims, it would look like a pure reactance, and no energy
would be transmitted. But he is stuck on his idea and won't budge.

Good for him -- he's absolutely correct. If the E and H fields were in
time quadrature, you'd have a power problem. But they're not. They're in
phase in any medium or transmission line having a purely real Z0 (since
Z0 is the ratio of E to H of a traveling wave in that medium). This
includes all lossless media. But they're always physically oriented at
right angles to each other -- i.e., orthogonally, according to the right
hand rule.

Now my problem is figuring out exactly what happens at the
reflection, and why the Eh field behaves the way shown in your demo.

Go for it!

Roy Lewallen, W7EL

Roy Lewallen wrote:

[...]

The traces are drawn in the order Eh, Ee, and total. During the
initial forward wave, Eh and Ee are equal, so the Ee overwrites
the Eh trace.

Good - thanks.

[...]

My problem here is someone wrote a web page that claims the
electric and magnetic fields are orthogonal:

http://www.play-hookey.com/optics/tr...etic_wave.html

You're making the same error that Cecil often does, confusing time
phase with directional vector orientation. The orthogonality of E
and H fields refers to the field orientations of traveling plane
TEM waves in lossless 3D space or a lossless transmission line, at
the same point and time.

Now you are confusing me with Cecil. I have no difficulty with the E
and H field orientation.

The E and H fields of these traveling waves are always in time
phase, not in quadrature.

Yes, that's what I tried to explain to him also.

The graphs show the magnitudes of the waves at various points
along the line. These represent neither the time phase nor the
spatial orientation of the E and H fields.

I tried sending him an email to show if the fields were
orthogonal as he claims, it would look like a pure reactance, and
no energy would be transmitted. But he is stuck on his idea and
won't budge.

Good for him - he's absolutely correct.

There is a bad mixup here. He claims:

"Note especially that the electric and magnetic fields are not in
phase with each other, but are rather 90 degrees out of phase. Most
books portray these two components of the total wave as being in
phase with each other, but I find myself disagreeing with that
interpretation, based on three fundamental laws of physics"

He claims the E and H fields are in quadrature. I claim he is wrong.

If the E and H fields were in time quadrature, you'd have a power
problem.

I believe that is what I tried to tell him. He bases his argument on
the following:

1. "The total energy in the waveform must remain constant at all
times."

Not true. It obviously goes to zero twice each cycle.

2. "A moving electric field creates a magnetic field. As an electric
field moves through space, it gives up its energy to a companion
magnetic field. The electric field loses energy as the magnetic
field gains energy."

Only if the environment is purely reactive. Not true with a pure
resistance.

3. "A moving magnetic field creates an electric field. This is
Faraday's Law, and is exactly similar to the Ampere-Maxwell law
listed above. A changing magnetic field will create and transfer its
energy gradually to a companion electric field."

Again, not true in a resistive environment.

But they're not. They're in phase in any medium or transmission
line having a purely real Z0 (since Z0 is the ratio of E to H of a
traveling wave in that medium). This includes all lossless media.

But they're always physically oriented at right angles to each
other - i.e., orthogonally, according to the right hand rule.

Yes, there is no confusion about this whatsoever.

[...]

Roy Lewallen, W7EL

Regards,

Mike Monett

Mike Monett wrote:
Roy Lewallen wrote:

[...]

The traces are drawn in the order Eh, Ee, and total. During the
initial forward wave, Eh and Ee are equal, so the Ee overwrites
the Eh trace.

Good - thanks.

[...]

My problem here is someone wrote a web page that claims the
electric and magnetic fields are orthogonal:

http://www.play-hookey.com/optics/tr...etic_wave.html

You're making the same error that Cecil often does, confusing time
phase with directional vector orientation. The orthogonality of E
and H fields refers to the field orientations of traveling plane
TEM waves in lossless 3D space or a lossless transmission line, at
the same point and time.

Now you are confusing me with Cecil. I have no difficulty with the E
and H field orientation.

The E and H fields of these traveling waves are always in time
phase, not in quadrature.

Yes, that's what I tried to explain to him also.

The graphs show the magnitudes of the waves at various points
along the line. These represent neither the time phase nor the
spatial orientation of the E and H fields.

I tried sending him an email to show if the fields were
orthogonal as he claims, it would look like a pure reactance, and
no energy would be transmitted. But he is stuck on his idea and
won't budge.

Good for him - he's absolutely correct.

There is a bad mixup here. He claims:

"Note especially that the electric and magnetic fields are not in
phase with each other, but are rather 90 degrees out of phase. Most
books portray these two components of the total wave as being in
phase with each other, but I find myself disagreeing with that
interpretation, based on three fundamental laws of physics"

He claims the E and H fields are in quadrature. I claim he is wrong.

And you're right. I apologize. "Orthogonal" usually refers to spatial
orientation, so when you said that he said they're orthogonal, my
reaction was that it's correct. But I didn't look at the web page. I see
by looking at it that he also says the two are in time quadrature, which
of course is incorrect as you say. His "fundamental laws of physics" are
certainly different from everyone else's. Thanks for providing a good
example of the pitfalls of relying on the web for information.

Again my apology. You do indeed have it right. Incidentally, it's not
possible for a medium to have a purely reactive (imaginary) Z0 at any
non-zero frequency.

Roy Lewallen, W7EL

Roy Lewallen wrote:

[..]

And you're right. I apologize. "Orthogonal" usually refers to
spatial orientation, so when you said that he said they're
orthogonal, my reaction was that it's correct. But I didn't look
at the web page. I see by looking at it that he also says the two
are in time quadrature, which of course is incorrect as you say.

His "fundamental laws of physics" are certainly different from
everyone else's. Thanks for providing a good example of the
pitfalls of relying on the web for information.

Again my apology. You do indeed have it right. Incidentally, it's
not possible for a medium to have a purely reactive (imaginary) Z0
at any non-zero frequency.

Roy Lewallen, W7EL

Thanks very much, Roy. It was probably my mistake, using the word
"Orthogonal" when quadrature would probably have worked better.

Can you explain your last sentence? Why does this happen?

I have been following these threads with some interest, and I very
much appreciate your analysis, as it adds greatly to my
understanding. Thank you very much for taking the time to write so
clearly.

There is one point I still have trouble with. The concept of power
flowing in standing waves where the superposition goes to zero, and
yet the energy flow is unaffected and continues in opposite
directions on either side of the null point.

Anyway, I have googled until my fingers get sore, and I haven't
found a good explanation of why this happens. Everyone says it is
well understood from basic undergraduate theory, but the only
references I can find are from graduate studies in Quantum
Electrodynamics. This is not much help.

So I have to form some image in my mind of why these waves do not
interact. Here is a partial pictu

1. Electromagnetic waves travel at the speed of light in whatever
medium they are in. For them to interact, there must be some advance
information they are about to collide. But that would require
transferring information faster than the speed of light, which is
forbidden.

2. The fields in electromagnetic waves are at right angles to the
direction of propagation. There is no longitudinal component, and
therefore the waves have no advance warning they are about to
collide. There is no vector component that is common to both that
would allow any interaction, so there is no way this can happen.

3. Photons carry no charge. They are not deflected by electrostatic
or electromagnetic fields, and do not interact with other photons.
Electromagnetic waves are made up of photons. Since photons do not
interact, EM waves also do not interact with each other.

The above concepts seem to make sense, and allow me to get some
sleep at night. Can you tell me if they are valid, and if there are
other ways of explaining this phenomenon?

Regards,

Mike Monett

Mike Monett wrote:
Since photons do not
interact, EM waves also do not interact with each other.

The following quote sounds like an interaction of photons to me.

http://micro.magnet.fsu.edu/primer/j...ons/index.html

"... when two waves of equal amplitude and wavelength that are
180-degrees ... out of phase with each other meet, they are not
actually annihilated, ... All of the photon energy present in
these waves must somehow be recovered or redistributed in a new
direction, according to the law of energy conservation ... Instead,
upon meeting, the photons are redistributed to regions that permit
constructive interference, so the effect should be considered as
a redistribution of light waves and photon energy rather than
the spontaneous construction or destruction of light."

I suspect that coherent photons can interact at an impedance
discontinuity which causes reflections.
--
73, Cecil http://www.w5dxp.com

Mike Monett wrote:
Roy Lewallen wrote:
. . .
Again my apology. You do indeed have it right. Incidentally, it's
not possible for a medium to have a purely reactive (imaginary) Z0
at any non-zero frequency.

Roy Lewallen, W7EL

Thanks very much, Roy. It was probably my mistake, using the word
"Orthogonal" when quadrature would probably have worked better.

Can you explain your last sentence? Why does this happen?

The "non-zero" was unnecessary, and a result of a too-quick evaluation
of an equation, although the meaning of Z0 at DC isn't clear anyway.

There are at least two related ways to show that a medium can't have a
purely imaginary Z0 (more correctly, intrinsic impedance). One is to use
the telegrapher's equation for a transmission line immersed in the medium:

Z0 = sqrt((R + jwL)/(G + jwC)) (w = omega, the rotational frequency)

For Z0 to be purely imaginary, the quantity under the radical has to be
purely real and negative. A little algebraic manipulation shows that
this requires that RG + w^2LC 0. All the quantities are positive, so
it can't happen.

You can also use

Zc = sqrt(mu/ceps) where ceps = the complex permittivity, mu = the
permeability of the medium, and Zc the intrinsic impedance.

The complex permittivity ceps = eps - j*sigma/w

where eps = the real (DC) permittivity
sigma = the conductivity of the material

You end up with the same situation, where for Zc to be purely imaginary,
the quantity under the radical has to be purely real and negative, which
requires that mu * eps 0. Remember that mu and eps here are the actual
permeability and permittivity, not the relative values we often use.

A little further research reveals that there are some fairly recently
created man-made materials which have a negative permeability. Those
could presumably have a purely imaginary intrinsic impedance, provided
that they have a positive permittivity. So there might be an exception
to my statement, although it isn't something you're likely to encounter
for some time to come.

I have been following these threads with some interest, and I very
much appreciate your analysis, as it adds greatly to my
understanding. Thank you very much for taking the time to write so
clearly.

There is one point I still have trouble with. The concept of power
flowing in standing waves where the superposition goes to zero, and
yet the energy flow is unaffected and continues in opposite
directions on either side of the null point.

Anyway, I have googled until my fingers get sore, and I haven't
found a good explanation of why this happens. Everyone says it is
well understood from basic undergraduate theory, but the only
references I can find are from graduate studies in Quantum
Electrodynamics. This is not much help.

Please exclude me from the "everyone" in "everyone says". I don't say
that power flows, period. We've seen the serious traps people have
fallen into by making this assumption and trying to build from it.
That's why you won't find it in texts.

So I have to form some image in my mind of why these waves do not
interact. Here is a partial pictu

1. Electromagnetic waves travel at the speed of light in whatever
medium they are in. For them to interact, there must be some advance
information they are about to collide. But that would require
transferring information faster than the speed of light, which is
forbidden.

You don't need a reason for them to not interact, you need a reason for
them to do so. In a linear medium, there is none.

2. The fields in electromagnetic waves are at right angles to the
direction of propagation. There is no longitudinal component, and
therefore the waves have no advance warning they are about to
collide. There is no vector component that is common to both that
would allow any interaction, so there is no way this can happen.

3. Photons carry no charge. They are not deflected by electrostatic
or electromagnetic fields, and do not interact with other photons.
Electromagnetic waves are made up of photons. Since photons do not
interact, EM waves also do not interact with each other.

The above concepts seem to make sense, and allow me to get some
sleep at night. Can you tell me if they are valid, and if there are
other ways of explaining this phenomenon?

I'm glad they work for you. I'll have to leave it to others to comment
on their validity, since I don't buy into the notion of flowing power in
the first place.

Roy Lewallen, W7EL

Mike Monett wrote:


There is a bad mixup here. He claims:

"Note especially that the electric and magnetic fields are not in
phase with each other, but are rather 90 degrees out of phase. Most
books portray these two components of the total wave as being in
phase with each other, but I find myself disagreeing with that
interpretation, based on three fundamental laws of physics"

He claims the E and H fields are in quadrature. I claim he is wrong.

If the E and H fields were in time quadrature, you'd have a power
problem.

I believe that is what I tried to tell him. He bases his argument on
the following:

1. "The total energy in the waveform must remain constant at all
times."

Not true. It obviously goes to zero twice each cycle.

2. "A moving electric field creates a magnetic field. As an electric
field moves through space, it gives up its energy to a companion
magnetic field. The electric field loses energy as the magnetic
field gains energy."

Only if the environment is purely reactive. Not true with a pure
resistance.

3. "A moving magnetic field creates an electric field. This is
Faraday's Law, and is exactly similar to the Ampere-Maxwell law
listed above. A changing magnetic field will create and transfer its
energy gradually to a companion electric field."


Regards,

Mike Monett

Mike,

This concept is not unique to the web site you referenced. I have seen
several other debates about the same thing.

One thing that is missed in this simple analysis is a consideration of
the uncertainty principle. Heisenberg proposed in 1927 that it is not
possible to simultaneously know the value of position and momentum to
arbitrarily high accuracy or to know the value of energy and time to
arbitrarily high accuracy.

The uncertainly for energy and time is given as delta E x delta t must
be greater than or equal to h-bar, which is Planck's constant divided by
2 pi.

The energy of a photon is h-bar x omega, where omega is the angular
frequency of the photon.

In order to declare a violation of energy conservation in the wave
example above, one would need to examine the energy at time intervals at
least as short as half the wave period. Guess what, the uncertainty
principle says that if we attempt to do so we cannot determine the
energy to the accuracy required in order to claim a violation of energy
conservation. Note carefully that "determine" does not mean we must
actually measure the energy. The energy cannot even be defined more
accurately than the limit imposed by the uncertainty principle.

One way to look at this is that during the interval over which one might
try to claim a violation of energy conservation the energy is in a
virtual state. As you may know, this sort of consideration is everywhere
when one delves into atomic scale and quantum mechanics.

73,
Gene
W4SZ