Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Solving the Wave Equation

In class, we derived the wave equation for the transverse displacement of a taut elastic string. We found the equation for the displacement, y, of a bit of string at the point x at time t, y(x,t) to be

(a) Change the variables in the equation from x, t to ξ, η ("xi" and "eta") where

ξ = x - v0t
η = x + v0t

(b) Show that any arbitrary pair of functions (as long as they have two well-defined derivatives) f and g lead to a solution of the wave equation

y(ξ, η) = f(ξ) + g(η)

(c) Rewrite y of the solution in part (b) as a function of x and t. Interpret f and g physically, explaining why you interpet them as you do.

RETURNS

University of MarylandPhysics DepartmentPhysics 374 Home

This page prepared by

Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120
Email: redish@umd.edu

Last revision 7. November, 2005.