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Shive Wave Machine Allows Visualization of Wave Properties

Posted April 6th, 2012 · 12 Comments · Video

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Posted by Colin Warwick

Mathematics is great, but for me true comprehension only comes with some kind of visual representation. In this 1959, video Dr. John N. Shive of Bell Labs uses his “Shive wave machine” (a mechanical analog of electrical propagation on transmission lines) to demonstrate:

  • Positive and negative reflection of waves from free and clamped ends
  • Superposition
  • Standing waves, standing wave ratio, and resonance
  • Energy loss by impedance mismatching
  • Reduction of energy loss by quarter-wave and tapered-section transformers
It’s a little longer (26 minutes) than most video clips but it’s worth watching the whole thing because he packs so much in it.

Hat tip to my friend Dick Benson for sharing this gem with me.


Update April, 10 2012

Math behind the analogy

I received a message questioning Shive’s analogy between mechanical free end and electrical short. “Doesn’t a short kind of ‘clamp’ the voltage?” True, but Shive chose to make voltage, V, analogous to force, F, (or torque) not displacement, x. This might not sit well with some folks because voltage is (subjectively) more easily visualized than charge, Q, whereas force is less easily visualized than displacement. But once you get past that, his mapping works out quite nicely:

MechanicalElectromagnetic
x (easily visualized)Q (less easily visualized)
F (less easily visualized)V (easily visualized)
mL
Kinetic:
F = ma = m d2x/dt2
Magnetic:
V = L di/dt = L d2Q/dt2
k1/C
Elastic:
F = kx
Electrostatic:
V = (1/C) Q
Substitute for F:
x = m/k d2x/dt2
Substitute for V:
Q = LC d2Q/dt2
Free end
(big displacement, no force)
Short-circuit termination
(big charge motion, no voltage)
Clamped end
(big force, no displacement)
Open termination
(big voltage, no charge motion)

(I haven’t checked the sign convention so I might a minus sign or three off. This is an ODE for a single oscillator. See an EM textbook for the coupled oscillator PDE version.)

Hungry for more?

I also received several emails that this type of material makes a healthy “digital snack break.” Thanks!

I don’t claim these are Shive’s league by any means, but here is a list of my blog postings that aim to record some “A ha!” moment or another:

Enjoy!

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