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Lecture4 - Proof that f(x vt solves the wave equation u = 1...

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Proof that f ( x ± v t ) solves the wave equation Write f ( x ± v t ) as f ( u ) , where u = x ± v t . So and Now, use the chain rule: So and Substituting into the wave equation: 1 u x = v u t = ± f f u x u x = f f u t u t = f f x u = v f f t u = ±
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