This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 2ndorder 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...
View
Full
Document
This note was uploaded on 08/24/2010 for the course PHYS 142 taught by Professor Staff during the Fall '08 term at Arizona.
 Fall '08
 STAFF
 Thermodynamics

Click to edit the document details