TK device, TPU.. Only enter if you seek truth. Cause here it is...

[elementSix]

I was messing with a new yoke i got yesterday.  I used a little wall transformer with a 12V output.  I ran each line thru small caps and into each side of the yoke coils and then hooked the outputs into a small tansformer primary and hooked that secondary to a 13W CFL.   I noticed that the yoke vibrates pretty well under the normal setup.  But I then took a small 3 foot copper unshielded Coax cable and ran each output of the yoke coils into opposite sides of the coax, each on their own wire and took the outputs of the coax and then ran them into the primary of the second transformer.  The vibrations in the yoke magnified by like 10 times.  Is that bemf doing that?

[verpies]

I don't understand the setup you are describing.  Coaxial cables could be introducing phase delays.

If you are experiencing the vibration of the ferrite then you are witnessing magnetostriction.
If the wires are vibrating, then those vibrations are caused by Ampere forces.

Graham Gunderson has a nice patent about energy out of vibrating ferrite. See below:

[verpies]

How the wave acts if the wire is the exact length of say, 1 full wave length.  Does it bounce back and fourth or does it just stop at the zero point at the end of the wire? 

It bounces back. See here and here.

What happens to the wave when a wire is soldered to another wire? Does it disturb the wave any? 

For single wire - almost not at all.
For coaxial shielded wire (or twin-lead) it disturbs the wave very much, especially if the soldering changes the distance of the center wire from the shield (or the other lead)

What happens if you apply a current to a copper ring, by way of which way does the wave move, does it go both ways??

If the current is applied to diametrically opposite points on the ring then the current goes "both ways".

[elementSix]

This is how I had the YOKE hooked up.  I was using a small spring switch to pulse one line of it, just to see what happens.  But I didn't add that to the picture tho.  Doesn't have anything to do with the Yoke Vibrations..

[NickZ]

  That is very similar to my yoke/ferrite core inverters. But mine use one transistor for each of the two inverters to switch the pulses of each of their separate primary coils. And both (two) different inverters core together, are also joint at their secondaries, as well as in parallel at their primaries. Secondaries coils output are both jointed together, then go to the Cfl or incandescent bulbs as the load.
Earth grounding is attached to the negative side of the Cfl.
  The louder the ringing sound coming from the inverter coils, the more draw is being pull through the device. Frequency is less important than the actual louder sound (volume level) being emitted, along with the accompaning vibrations.
  I've also tried different caps on the input side, but have not noticed much difference on my circuit. Maybe I haven't found the right  ones.
What caps are you using?
  Picture below.