PHYS 422 Lecture 10 Superposition II

# PHYS 422 Lecture 10 Superposition II - The Superposition of...

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Unformatted text preview: The Superposition of Waves II Standing Wave In general: ( ) ( ) ( ) t x g C t x f C t x v v + + − = 2 1 , ψ two waves traveling in opposite direction Consider 2 waves, incident and reflected: ( ) I I I t kx E E ξ ω + − = sin ( ) R R R t kx E E ξ ω + + = sin n n ( ) ( ) [ ] R I I t kx t kx E E ξ ω ξ ω + + + + − = sin sin ( ) ( ) 2 cos 2 sin 2 sin sin β α β α β α − + = + ⎞ ⎛ − ⎞ ⎛ + + = cos sin I R R I kx ξ ξ ξ ξ ⎟ ⎠ ⎜ ⎝ ⎟ ⎠ ⎜ ⎝ 2 2 I ω an select rigin and that: s n Can select x origin and t= 0 so that: ( ) ( ) t kx E E I ω cos sin 2 = (Typically E =0 on the surface of a metal mirror) Standing Wave s n ( ) ( ) t kx E E I ω cos sin 2 = λ Animation courtesy of Dr. Dan Russell, Kettering University Standing Wave and Resonance If the number of λ /2 is integer in example above, the string can oscillate forever (if there are no losses) - resonance. Standing Electromagnetic Wave 890 tto Wiener experiment 1890 - Otto Wiener experiment Where is the energy when E is zero?...
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PHYS 422 Lecture 10 Superposition II - The Superposition of...

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