Mike Monett wrote:
Roy Lewallen wrote:
[... very nice explanation]

Sine waves are another problem -- there, we can easily have
overlapping waves traveling in the same direction, so we'll run into
trouble if we're not careful. I haven't worked the problem yet, but
when I do, the energy will all be accounted for. Either the energy
ends up spread out beyond the overlap region, or the energy lost
during reflections will account for the apparent energy difference
between the sum of the energies and the energy of the sum. You can
count on it!

As always, I appreciate any corrections to either the methodology or
the calculations.

Roy Lewallen, W7EL

How about analyzing a vibrating string? If you play guitar, there's a very
nice note you can make by plucking a high string, then putting your finger
at exactly the correct spot and removing it quickly. The note will jump to
a much higher frequency and give a much purer sound. Clearly, the
mechanical energy has split into two waves that cancel at the node.

In principle, you could show the node is stationary, thus contains no
energy. But there is energy travelling on both sides of the null point -
you can hear it.

You can also create other notes by touching different spots on the
vibrating string. These create standing waves with energy travelling in
both directions, but cancelling at the null points. Very similar to
transmission lines.

Regards,

Mike Monett


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. Such strings have loss
(or you wouldn't be able to hear them). Loss is a taboo subject on this
newsgroup because it makes wave behavior too hard to understand for the
savants posting here.
73,
Tom Donaly, KA6RUH

"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?

Such strings have loss (or you wouldn't be able to hear them).

Loss is a taboo subject on this newsgroup because it makes wave
behavior too hard to understand for the savants posting here.

73,
Tom Donaly, KA6RUH

Regards,

Mike Monett

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

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

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?

Such strings have loss (or you wouldn't be able to hear them).

Loss is a taboo subject on this newsgroup because it makes wave
behavior too hard to understand for the savants posting here.

73,
Tom Donaly, KA6RUH

Regards,

Mike Monett

When you pluck a string, you are exciting the whole string at once.
If a sound wave of the right frequency impinges on a string
perpendicular to the string's axis, the string will vibrate
sympathetically. In that case, it's hard to justify saying that two
waves are traveling in opposite directions up and down the string.
Nevertheless, the solution of the partial differential equation
describing the motion of the string, as proposed and solved by
the French mathematician D'Alembert, in 1747, is consistent with the
idea of two waves of arbitrary function traveling in opposite directions
on the string. If I were you, I'd find a copy of the differential
equation of a wave on a string and compare it to the same equation
describing an electromagnetic wave on a transmission line. How similar
are the two?
73,
Tom Donaly, KA6RUH

"Tom Donaly" wrote:

When you pluck a string, you are exciting the whole string at
once.

If a sound wave of the right frequency impinges on a string
perpendicular to the string's axis, the string will vibrate
sympathetically. In that case, it's hard to justify saying that
two waves are traveling in opposite directions up and down the
string.

OK, lets change the string. Now it's the top guy wire for a 1/4 wave
vertical at 560KHz. When you pluck it, you can hear it pinging as
the waves are reflected. Maybe it would be difficult to take that to
a symphony performance, but hey, true art is art no matter where you
find it

Nevertheless, the solution of the partial differential equation
describing the motion of the string, as proposed and solved by the
French mathematician D'Alembert, in 1747, is consistent with the
idea of two waves of arbitrary function traveling in opposite
directions on the string. If I were you, I'd find a copy of the
differential equation of a wave on a string and compare it to the
same equation describing an electromagnetic wave on a transmission
line. How similar are the two?

We may have lost the validity of the comparison to EM waves.

73,
Tom Donaly, KA6RUH

Regards,

Mike Monett