problem15_35

University Physics with Modern Physics with Mastering Physics (11th Edition)

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

View Full Document Right Arrow Icon
15.35: The wave equation is a linear equation, as it is linear in the derivatives, and differentiation is a linear operation. Specifically, . ) ( 2 1 2 1 x y x y x y y x y + = + = Repeating the differentiation to second order in both x and t , 2 2 = x y , 2 2 2 2 1 2 x y x y + 2 2 = t y . 2 2 2 2 1 2 t y t y + The functions 1 y and 2 y are given as being solutions to the wave equation; that is, 2 2 = x y 2 2 2 2 1 2 x y
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x y + = 2 1 v + 2 1 2 t y 2 1 v 2 2 2 t y = 2 1 v + 2 2 2 2 1 2 t y t y = 2 1 v 2 2 t y and so 2 1 y y y + = is a solution of Eq. (15.12)....
View Full Document

This document was uploaded on 02/05/2008.

Ask a homework question - tutors are online