Where's the energy? (long)
 

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

Where's the energy? (long)
 

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

Where's the energy? (long)
 

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

Where's the energy? (long)
 

Cecil Moore wrote:

If the intensity of the bright rings is 4P there is
indeed greater than average energy which requires a
zero P dark ring somewhere else in order to
average out to 2P.

I guess you didn't notice the thing about the square of the sum of two
numbers being four times as great as the square of one of the numbers.
It simply means, for example, that a doubling in voltage is a
quadrupling in power. It doesn't mean there's "extra" energy anywhere.

The "extra" energy in the bright
rings comes from the dark rings.

There really is no extra energy.

The conservation of
energy principle allows nothing else.

Conservation of energy doesn't allow for there to *be* extra energy in
the first place! That's the most fundamental principle. Putting the
word 'extra' in quotes doesn't change that.

It is not a
sophomoric notion.

The notion was apparently contrived so that sophomores wouldn't feel
the need to ask as many questions.

It is the laws of physics in action.

As far as you know.

ac6xg

Where's the energy? (long)
 

Jim Kelley wrote:
I guess you didn't notice the thing about the square of the sum of two
numbers being four times as great as the square of one of the numbers.
It simply means, for example, that a doubling in voltage is a
quadrupling in power. It doesn't mean there's "extra" energy anywhere.

On the contrary, constructive interference cannot happen
without that "extra" energy sucked up from destructive
interference (or from a local source). That's what you
are completely missing. Constructive interference between
two waves requires more energy than exists in those two
component waves. In the absence of a local source, another
two waves *must* be engaging in destructive interference
at the same time in order to supply the constructive
interference.

Conservation of energy doesn't allow for there to *be* extra energy in
the first place!

Therefore, those bright rings are just an illusion and
don't contain more than the average energy in the two
superposed waves. I guess that's your story and you
are sticking to it.
--
73, Cecil http://www.w5dxp.com

Where's the energy? (long)
 

The idiot savant Cecil Moore wrote:

Therefore, those bright rings are just an illusion and
don't contain more than the average energy in the two
superposed waves.

You couldn't be more wrong in your interpretation.

Perhaps you will understand it this way: the bright rings have an
intensity which is equal in energy to the sum of the energy in the two
superposed waves. Energy doesn't have to come from anywhere else to
balance the equation.

The error you're making is the assumption that since the intensities
don't add up, something has to come from somewhere else. But that's a
wrong assumption to make. One shouldn't expect intensity to add like
that. Obviously it doesn't add like that. The fields are what add and
subtract, not intensity (or power). Power is the time derivative of
energy - that's the reason a squared term comes in. But power and
intensity don't propagate, therefore they don't superpose, and
shouldn't be added algebraically. Fields, voltage, current, energy -
it makes sense to sum those things algebraically.

When you double something and then square the sum, you get a factor of
four. But you're still only doubling the 'thing' of interest.
Depositing two paychecks and squaring the sum doesn't make your bank
balance go up by a factor of four. But it is certainly true that you
would have to borrow money from someone to make that happens. The
point is that it's not a realistic expectation.

I assume you know that the meter face on your Bird wattmeter is
calibrated exponentially. So, when your Bird power meter reading goes
up by a factor of four, what do you think the voltage across its meter
movement has actually increased by? The thing is, the Bird company
understands that when power reading quadruples, the circuit voltage
has only doubled. You'll note they don't claim that since the reading
quadrupled instead of doubling, the "extra" power had to come from
somewhere else.

If you can't understand this, that's fine. But it's not an excuse to
get so bloody belligerent with people about it.

ac6xg

Where's the energy? (long)
 

Jim Kelley wrote:
The idiot savant Cecil Moore wrote:

Therefore, those bright rings are just an illusion and
don't contain more than the average energy in the two
superposed waves.

You couldn't be more wrong in your interpretation.

Perhaps you will understand it this way: the bright rings have an
intensity which is equal in energy to the sum of the energy in the two
superposed waves. Energy doesn't have to come from anywhere else to
balance the equation.

The error you're making is the assumption that since the intensities
don't add up, something has to come from somewhere else. But that's a
wrong assumption to make. One shouldn't expect intensity to add like
that. Obviously it doesn't add like that. The fields are what add and
subtract, not intensity (or power). Power is the time derivative of
energy - that's the reason a squared term comes in. But power and
intensity don't propagate, therefore they don't superpose, and shouldn't
be added algebraically. Fields, voltage, current, energy - it makes
sense to sum those things algebraically.

When you double something and then square the sum, you get a factor of
four. But you're still only doubling the 'thing' of interest.
Depositing two paychecks and squaring the sum doesn't make your bank
balance go up by a factor of four. But it is certainly true that you
would have to borrow money from someone to make that happens. The point
is that it's not a realistic expectation.

I assume you know that the meter face on your Bird wattmeter is
calibrated exponentially. So, when your Bird power meter reading goes
up by a factor of four, what do you think the voltage across its meter
movement has actually increased by? The thing is, the Bird company
understands that when power reading quadruples, the circuit voltage has
only doubled. You'll note they don't claim that since the reading
quadrupled instead of doubling, the "extra" power had to come from
somewhere else.

If you can't understand this, that's fine. But it's not an excuse to
get so bloody belligerent with people about it.

ac6xg


What! You mean you don't believe in the law of the conservation of
power? Cecil does. Don't tell anyone, but I think he may believe in
the law of the conservation of speed, too.
73,
Tom Donaly, KA6RUH

Where's the energy? (long)
 

Jim Kelley wrote:
Perhaps you will understand it this way: the bright rings have an
intensity which is equal in energy to the sum of the energy in the two
superposed waves. Energy doesn't have to come from anywhere else to
balance the equation.

That just shows that you still don't understand the
interference process. The bright rings have an intensity
which is equal in energy to *double* the sum of the energy
in the two superposed waves. If P1 = P2, the total energy
in the bright rings is P1+P2+2*SQRT(P1*P2) = 2*(P1+P2).

That "extra" constructive interference energy has to come
from somewhere and it comes from the dark areas where
destructive interference occurs. In the dark areas,
P1+P2-2*SQRT(P1*P2) = 0. Taking the average of those two
equations yields (P1+P2) which is the sum of the energy
in the two superposed waves. That's only half as bright
as the bright rings.

The constructive interference energy has to exactly equal
the destructive interference energy or else the conservation
of energy principle is violated and, sure enough, they do
equal each other.
--
73, Cecil http://www.w5dxp.com

Where's the energy? (long)
 

Tom Donaly wrote:
What! You mean you don't believe in the law of the conservation of
power? Cecil does.

You know that is a lie, Tom. I believe in the conservation of
energy and momentum. I do not believe in any conservation of
power and speed.
--
73, Cecil http://www.w5dxp.com

Where's the energy? (long)
 

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