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 You had written: 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 your choice: http://www.tilmarlily.netfirms.com/download/wave.nb The solution given by Out[2](in the notebook) is very different from Eq(39). My question is, why is the solution given by Mathematica so different than the classical result given by Eq(39)in the Mathworld website?