Lecture19 - • Last time we started using Newton’s Laws...

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Unformatted text preview: • Last time we started using Newton’s Laws to understand how a wave moves on a string T T dx θ 1 θ 2 T is the tension in the string Lecture 19: The Wave Equation • We found that: • How do we solve this equation? – by “solve” I mean we need to find a function y ( x,t ) for which the wave equation is true for any value of x and t • The wave equation is a 2nd-order partial differential equation – in general, such equations can be a challenge to solve – you’ll probably take a whole course on it • But luckily, this one isn’t so bad • In fact, we already know the answer: T ∂ 2 ψ ∂ξ 2 = μ ∂ 2 ψ ∂τ 2 This is the wave equation Useful for any kind of wave y x , t ( 29 = Ασιν κξ - ϖτ ( 29 • To check if it works, compute the derivatives: • and then plug them into the wave equation: ∂ y ¶ x = Ak cos kx- wt ( ) ∂ 2 y ¶ x 2 = - Ak 2 sin kx- wt ( ) ∂ y ¶ t = - Aw cos kx- wt ( ) ∂ 2 y ¶ t 2 = - Aw 2 sin kx- wt ( ) T ∂ 2 ψ ∂ξ 2 = μ ∂ 2 ψ ∂τ 2...
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This note was uploaded on 08/24/2010 for the course PHYS 142 taught by Professor Staff during the Fall '08 term at Arizona.

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Lecture19 - • Last time we started using Newton’s Laws...

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