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:
"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