Lec18 - Wave Equations (I) UCF likewise UCF Wave Equations...

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CF Wave Equations (I) UCF likewise
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CF Wave Equations (II) UCF
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CF Scalar Wave Equation UCF q 0 : equation ector wave Consider v 2 2 2 = t με E E uation alar wav tisfy ould eld ectric f mponent ch hen s, coordinate r rectangula In 2 2 2 2 + + = z z y y x E E E a a a x E 1 have we , or or either represent Let equation. e scalar wav satisfy should field electric of component each Then u z y x E E E 0 , 0 = = y x equation. wave 3D a is This . 1 where 0 2 2 = = v u v u p z have we , 0 and 0 or only, z on depends that Assume = = u u u p equation e scalar wav 1D 0 1 2 2 2 2 2 = t u v z u y x p
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CF General Solution to 1D Scalar Wave Equation UCF 0 1 : equation e scalar wav 1D For 2 2 2 2 2 p t u v z u = ). ( ) ( ) , ( : is solution general the p p v z t g v z t f t z u + + = : solution a is ) ( Prove p v z t f 1 . 1 and 1 have we , Let p p u u u u u u t v z v z t = = = ξ 1 1 , 2 2 2 2 p u u u u u u t t v z z
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Lec18 - Wave Equations (I) UCF likewise UCF Wave Equations...

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