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standing wave - Standing Waves Standing Waves V z = Vo e j...

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Standing Waves
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Standing Waves ( ) ( ) ( ) ( ) ( ) { } ( ) ( ) 1/ 2 * * 1/ 2 2 2 2 ( ) ( ) Let's find ( ) and replace ( ) ( ) ( ) ( ) 1 Since r r r r r j z j z o j z j z o o j j j j z j z j z j z o o j z j z o j V z V e e V I z e e Z V z e V z V z V z V e e e V e e e V z V e e e β β β β θ θ θ β β β β θ β θ β + + + + + + + = + Γ = − Γ Γ = Γ = = + Γ + Γ = + Γ + Γ + Γ ± ± ± ± ± ± ± 1/ 2 2 1/ 2 2 2cos ( ) 1 2 cos( 2 ) Similarly, ( ) 1 2 cos( 2 ) x jx o r o r o e x V z V z V I z z Z θ β θ β + + + = = + Γ + Γ + = − Γ Γ + ± ±
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