1-4 Superposition soln

# 1-4 Superposition soln - Solution Physics 214 Problem 4...

This preview shows pages 1–2. Sign up to view the full content.

Physics 214 Problem 4 Week 1 Superposition and the Wave Equation The wave equation for electromagnetic waves is given by: d 2 y dx 2 = 1 v 2 d 2 y dt 2 with ν = c, the speed of light a) What relation between ω 1 , k 1 and velocity v is needed to make y 1 = A 1 cos( k 1 x 1 t ) a solution to this equation? (In fact, any function of the form y = f( kx t + φ ) is a solution if that relation holds, although we would not usually use the , k notation for other functional forms.). b) Show that the superposition of two solutions, y 3 (x,t) = y 1 (x,t) + y 2 (x,t) is also a solution to this wave equation if each of y 1 (x,t) and y 2 (x,t) is separately a solution. If that seems to abstract, try a specific case: y 3 (x,t) = A 1 cos( k 1 x 1 t ) + A 2 cos( k 2 x 2 t+ ), where the ’s and k ’s satisfy the necessary condition from part (a). ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 1 2 1 2 2 2 3 1 1 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 3 1 1 2 2 2 2 2 2 2 3 1 1 2 2 2

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

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

## This note was uploaded on 10/21/2010 for the course PHYSICS 214 taught by Professor A during the Fall '10 term at University of Illinois, Urbana Champaign.

### Page1 / 2

1-4 Superposition soln - Solution Physics 214 Problem 4...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online