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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?
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