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PHYS 422 Lecture 9 Superposition I

PHYS 422 Lecture 9 Superposition I - The Superposition of...

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he Superposition of Waves I The Superposition of Waves I
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Principle of Superposition 2 2 2 2 2 2 2 2 2 1 t z y x = + + ψ v Wave equation: n G G ( ) ( ) = = i i i t r C t r 1 , , e solutions of the wave equation then their linear If i are solutions of the wave equation, then their linear combination is also a solution rinciple of uperposition e resultant isturbance at any point Principle of Superposition : the resultant disturbance at any point is the algebraic sum of the separate constituent waves. or d elds it stems from e definition these are forces For E and B fields it stems from the definition: these are forces, and the resultant force is a vector sum of the individual forces.
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Adding Waves of the Same Frequency ( ) ( ) [ ] ξ ω + = kx t E t x E sin , 0 Consider a plane wave: ( ) α kx x , The case of two waves coexisting in space: [ ] ( )( ) ( ) ( ) [ ] 1 1 01 1 01 1 sin cos cos sin sin t t E t E E + = + = [ ] ( ) ( ) ( ) ( ) [ ] 2 2 02 2 02 2 sin cos cos sin sin t t E t E E + = + = Resulting wave: 2 1 E E E + = s n n n s s ( ) ( ) [ ] ( ) ( ) ( ) [ ] ( ) t E E t E E E cos sin sin sin cos cos 2 02
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