Nice superposition da same units correct 1 2 2 3 d

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: b identities: Wednesday, October 9, 2013 Wave equation 1 ∂2 ∂2 1d: ( 2 2 − 2 )ψ (t, x) = 0 v ∂t ∂x Linear 2nd order PDE :-)! Nice! Superposition! DA: Same units. Correct! 1 ∂2 2 3 d: ( 2 2 − ∇ )ψ (t, x) = 0 v ∂t ψ (t, x) = A cos(k (x − vt)) ψ (t, x) = A cos(k (x + vt)) ψ (t, x) = A cos(kx) cos(kvt) Wednesday, October 9, 2013 We’ll discuss 3d case later. This week, just 1d waves. Examples solutions of the 1d wave equation. Superpose for general solution (Fourier). (Aside: Fourier) Math statement: get general functions from a sum (superposition) of sin or cos functions. Physics application: get general solution of the wave equation from a superposition of waves of definite frequency and wavelength Wednesday, October 9, 2013 Wave equation, cont. 1 ∂2 ∂2 ( 2 2− )ψ (t, x) = 0 2 v ∂t ∂x Is solved by: ψ = ψR (x − vt) + ψL (x + vt) Arbitrary functions for right and left moving parts. E.g. right moving y (t, x) = A cos(kx − ω t) Velocity (speed) is the phase velocity: Wednesday, October 9, 2013 ω λ v= = k T Waves on a string y (t, x) x Acceleration in y direction, for fixed posit...
View Full Document

This note was uploaded on 02/11/2014 for the course PHYSICS 2C taught by Professor Hicks during the Fall '09 term at UCSD.

Ask a homework question - tutors are online