485_Physics ProblemsTechnical Physics

485_Physics ProblemsTechnical Physics - Chapter 16 P16.46...

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Chapter 16 487 P16.46 (a) From yx v t =+ 22 2 , evaluate = y x x 2 = 2 2 2 y x = y t vt 2 2 = 2 2 2 2 y t v Does = 2 2 2 1 y tv y t ? By substitution: 2 1 2 2 2 = v v and this is true, so the wave function does satisfy the wave equation. (b) Note 1 2 1 2 xv t t ++− afaf + +− + 1 2 1 2 1 2 1 2 2 2 xx v t v t v t v t t 2 as required. So fx v t x v t += + a f a f 1 2 2 and gx v t t −= a f a f 1 2 2 . (c) yx v t = sin cos makes = y x t cos cos =− 2 2 y x t sin cos y t vxv t sin sin 2 2 2 y t vx v t sin cos Then = 2 2 2 1 y y t becomes sin cos sin cos t v v t 1 2 2 which is true as required. Note sin sin cos cos sin t t t + af sin sin cos cos sin t t t . So sin cos t f x v t g x v t with t t + 1 2 sin and t t 1 2 sin . Additional Problems P16.47 Assume a typical distance between adjacent people ~1 m .
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