Group velocity or perhaps more aptly "information velocity" is always less
than or equal to the speed of light in a vacuum, but the "phase velocity" or
the speed at which a constant phase point on an electromagnetic wavefront
progates along the wall of a waveguide can actually exceed the speed of
light in a vacuum. This is analogous to a wave hitting the beach at a
oblique angle (as opposed to head on). The group velocity refers to the
speed with which the group of waves travels along the beach (imagine a
group of 3 or 4 waves traveling in a bunch on an otherwise calm sea).
Phase velocity refers to the speed with which a particular phase of one
of the waves (the crest for instance) races along the the shoreline as that
portion of the wave propagates forward. If the wave is moving parallel
to the shore, the group velocity and the phase velocity are equal. As the
wave direction is shifted towards being more perpendicular to the shoreline,
the phase velocity increases progressively until it becomes infinite when
the wave is perfectly perpendicular to the shore. Likewise, when the
waves are hitting the shore perfectly perpendicular, the group of 3 or 4
waves has zero motion along the line parallel to the shore, thus the
group velocity goes to zero.
In a piece of coax, the dominate propagation mode is TEM (tranverse
electromagnetic). In this case the shield is analogous to the shoreline and
the wave is traveling parallel to the shore - phase velocity = group
In a rectangular waveguide, supporting the TE10 mode, the wavefronts are
no longer traveling parallel to the waveguide walls. In this case they are
analogous to the waves hitting the beach at an oblique angle. Now phase
velocity is greater than group velocity. In the extreme case at the cutoff
frequency of the waveguide, the wavefronts are moving perpendicular to
the wall of the waveguide. Phase velocity becomes infinite and group
velocity goes to zero. Unfortunately, even though the wavefront phase
velocity can be greater than the speed of light, information only moves
at the group velocity which is always less than or equal to the speed of
light. Mr. Einstein can rest in peace (at least for now).
I don't know about this superluminal stuff. It sounds fishy to me.
73 de Mike, W4EF..........................
----- Original Message -----
From: "Jon Ogden" <firstname.lastname@example.org>
To: "Larry L Lindblom" <email@example.com>; <firstname.lastname@example.org>
Sent: Wednesday, September 25, 2002 8:47 PM
Subject: Re: [Towertalk] SWR & Speed of Light?
> Oh gosh, it goes back a bit to wave theory, but there's a couple of
> different "velocities" when speaking about interfering waveforms. The
> "group velocity" CAN indeed be faster than the speed of light if I
> correctly (All my EM books are in my office so I can't look this up.).
> However, the propagation velocity is always the speed of light in that
> Remember as well, that the speed of light varies depending upon the
> dielectric constant of the medium through which it is propagated. So I
> send a signal via a coax with one Dk and the same signal through a coax
> a different Dk and the two signals would arrive at the destination at
> different times.
> The bottom line is that as of now, no one has still been able to prove
> Einstein's Theory of Relatively incorrect. Being able to travel faster
> the speed of light would do that.
> on 9/25/02 7:41 PM, Larry L Lindblom at email@example.com wrote:
> > This is clipped from New Scientist. Though not mentioned directly in
> > article my wild guess is this effect is somehow due to SWR or something
> > akin to it. What do the feed line experts on the reflector have to say?
> > Speed of light broken with basic lab kit
> > Scientists have sent light signals at faster-than-light speeds over the
> > distances of a few meters for the last two decades - but only with the
> > aid of complicated, expensive equipment. Now physicists at Middle
> > Tennessee State University have broken that speed limit over distances
> > nearly 120 meters, using off-the-shelf equipment costing just $500.
> > Jeremy Munday and Bill Robertson made a 120-metre-long cable by
> > alternating six- to eight-metre-long lengths of two different kinds of
> > coaxial cable, each with a different electrical impedance. They hooked
> > this hybrid cable up to two signal generators, one of which broadcast a
> > fast wave, the other a slow one. The waves interfere with each other to
> > produce electric pulses, which can be watched using an oscilloscope.
> > Any pulse, whether electrical, light or sound, can be imagined as a
> > of tiny intermingled waves. The energy of this "group pulse" rises and
> > falls over space, with a peak in the middle. The different electrical
> > resistances in the hybrid cable cause the waves in the pulse's rear to
> > reflect off each other, accelerating the pulse's peak forward.
> Jon Ogden
> NA9D (ex: KE9NA)
> Life Member: ARRL, NRA
> Member: AMSAT, DXCC
> "A life lived in fear is a life half lived."
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