Re: The Wave Equation : Mathematica vs. Mathworld

• To: mathgroup at smc.vnet.net
• Subject: [mg47897] Re: The Wave Equation : Mathematica vs. Mathworld
• From: Thomas E Burton <tburton at brahea.com>
• Date: Thu, 29 Apr 2004 19:39:45 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```The traveling-wave solution f[x + c t] to the wave equation in one
dimension is about as "classical" as classical physics gets! It
represents a wave propagating to the left (if c is positive) with speed
|c| and shape f.

You are apparently attempting to satisfy Dirichlet boundary conditions
(f[0]===f[L]===0) with this solution, which will require something like
a method of multiple reflections. If you then expand the function f in
a Fourier series, convert traveling waves Exp[+/-I omega t] to standing
waves Sin[omega t] & Cos[omega t], you'll arrive at a standing-wave
solution somewhat resembling equation (39) in Mathworld's wave equation
intro, with v = c. Note: you have not transcribed equation (39)
accurately into your notebook.

Tom Burton

I'm attempting to duplicate the analysis found in:

http://mathworld.wolfram.com/WaveEquation.html

about how to derive a solution to the Wave Equation. I want to get to
that solution using Mathematica. The solution to the Wave Equation is
given by Eq(39) displayed on the above website. To see my attempt to
solve the Wave Equation using Mathematica v.5, please double-click the
following internet link, and save this notebook into a directory of