D'Alembert's Solution

D'Alembert's Solution - D’Alembert’s Solution There is...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: D’Alembert’s Solution There is an elegant approach to solve the wave equation by introducing new variables: { } , , ( , ) ( , ) The use of these variables is because that the solution of the wave equation behaves in specific fashion that its spatial movement is related to the temporal variation throu v x ct z x ct u x t u v z = + =- = gh the constant . Using these new variables, the derivative w.r.t x & t can be rewritten as ( ) ( ) Label = , , , x v z c u u v u z u x ct u x ct u u x v x z x v x z x v z u u u u u u etc x v z ∂ ∂ ∂ ∂ ∂ ∂ ∂ + ∂ ∂- ∂ ∂ = + = + = + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ = = ∂ ∂ ∂ 2 Similarly, u u u u u u u ( ) ( ) [ ] t t t Continue to convert all derivatives in x & t into derivatives in & , the wave equation to obtain the following equation: v z c c c v z v z v z v z u u z v z v ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ = + = +- =- ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ = ∂ ∂ ∂ ∂ 0, this equation can be integrated twice ( ), ( , ) ( ) ( ) ( ) ( ) ( , ) ( ) ( ) : D'Alembert's solution u f v v u v z f v dv z v z u x y...
View Full Document

This note was uploaded on 11/27/2011 for the course EML 3050 taught by Professor Staff during the Fall '09 term at FSU.

Page1 / 11

D'Alembert's Solution - D’Alembert’s Solution There is...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online