Traveling Wave Example

Animate[Plot[Exp[-(x-t+10)^2],{x,-10,10},PlotRange->{-1,2},AxesLabel->Automatic],{t,0,20}]

Plot3D[Exp[-(x-t+10)^2],{x,-10,10},{t,0,20},PlotRange->{-1,2},AxesLabel->Automatic]

Manipulate[Show[{
Plot3D[Exp[-(x-t+10)^2],{x,-10,10},{t,0,20},PlotRange->{-1,2},AxesLabel->Automatic,PlotStyle->Opacity[0.5],PerformanceGoal->"Quality"],
Graphics3D[{Opacity[0.9],InfinitePlane[{0,s,0},{{1,0,0},{0,0,1}}]}]
}],{s,0,20}]

Example 3

Animate[Plot[Exp[-(x-t)^2]+Exp[-(x+t)^2],{x,-10,10},PlotRange->{-1,3},AxesLabel->Automatic],{t,0,15},AnimationRate->2]

Plot3D[Exp[-(x-t)^2]+Exp[-(x+t)^2],{x,-10,10},{t,0,15},PlotRange->{-1,3},AxesLabel->Automatic]

Manipulate[Show[{
Plot3D[Exp[-(x-t)^2]+Exp[-(x+t)^2],{x,-10,10},{t,0,15},PlotRange->{-1,3},AxesLabel->Automatic,PlotStyle->Opacity[0.5],PerformanceGoal->"Quality"],
Graphics3D[{Opacity[0.9],InfinitePlane[{0,s,0},{{1,0,0},{0,0,1}}]}]
}],{s,0,20}]

Here is the solution from Problem 3 in class

Animate[Plot[(1/(1+(((x-2t))^2))),{x,-10,40},PlotRange->{-1,2},AxesLabel->Automatic,PerformanceGoal->"Quality"],{t,0,20}]