Fortschreitende und stehende Wellen

Fortschreitende Wellen

sin(x-t)

Manipulate[
Plot[Sin[x-t],{x,-10,10},PlotRange->{-1.1,1.1},AspectRatio->0.2,ImageSize->600],{t,0,2π,Appearance->"Labeled"}]

sin(x+t)

Manipulate[
Plot[Sin[x+t],{x,-10,10},PlotRange->{-1.1,1.1},AspectRatio->0.2,ImageSize->600],{t,0,2π,Appearance->"Labeled"}]

Stehende Welle

sin(x-t)-sin(x+t)

Manipulate[
GraphicsGrid[{
{Plot[Sin[x-t],{x,-10,10},PlotRange->{-1.1,1.1},AspectRatio->0.2]},
{Plot[Sin[x+t],{x,-10,10},PlotRange->{-1.1,1.1},AspectRatio->0.2]},
{Plot[Sin[x+t]+Sin[x-t],{x,-10,10},PlotRange->{-2.1,2.1},AspectRatio->0.2,PlotStyle->Red]}
},ImageSize->600],{t,0,2π,Appearance->"Labeled"}]

Begründung durch Rechnung:
	sin(x-t)+sin(x+t)=2 cos t  sin x

Sin[x-t]+Sin[x+t]//TrigExpand