       Re: Phase reversal at fixed boundary

• To: mathgroup at smc.vnet.net
• Subject: [mg107096] Re: Phase reversal at fixed boundary
• From: dh <dh at metrohm.com>
• Date: Tue, 2 Feb 2010 06:53:57 -0500 (EST)
• References: <hk3noo\$aiv\$1@smc.vnet.net>

```Hi Jon,
the solution to the wave equations is the superposition of two arbitrary
waves that move in opposite directions with the phase velocity. You must
choose the two waves to suit your initial and border conditions.
Here is an example:
f[x_] := Exp[-100 (Mod[x, 2] - 0.5)^2];
Manipulate[
Plot[f[x - t] - f[2 - x - t], {x, 0, 1}, PlotRange -> {-1, 1}]
, {t, 0, 4, .01}]

Daniel

Jon Joseph wrote:
> All: I would like to simulate a wave pulse on a string. The end of the
> string is fixed to a wall so when the pulse hits the wall I have perfect
> reflection with a phase reversal. The following code is an attempt and
> if I could figure out how to put the two animations together I would
> just about have it. Any suggestions?
>
>
> =
> Animate[Show[Graphics[Rectangle[{9.5,-1},{10,1}]],Plot[PDF[NormalDistribution[t,.5],x],{x, -4,9.5}, PlotRange->{{-4,10}, {-1,1}}]], {t, 0, 10}]
>
> =
> Animate[Show[Graphics[Rectangle[{9.5,-1},{10,1}]],Plot[-PDF[NormalDistribution[10-t,.5],x],{x, 9.5,-4}, PlotRange->{{-4,10}, {-1,1}}]], {t, 0, 10}]
>
>