Animate[Plot[{E^(-1/2 (x-v t)^2)*.95,E^(-1/2 (-30+x+v t)^2)*.95,E^(-1/2 (x-v t)^2)+E^(-1/2 (-30+x+v t)^2)},{x,0,30},PlotRange->{0,2}],{t,0,30}]

Animate[Plot[{E^(-1/2 (x-v t)^2)*.95,-E^(-1/2 (-30+x+v t)^2)*.95,E^(-1/2 (x-v t)^2)-E^(-1/2 (-30+x+v t)^2)},{x,0,30},PlotRange->{-1,1}],{t,0,30}]

Animate[Plot[{D[E^(-1/2 (x-v t)^2)*.95,t],-D[E^(-1/2 (-30+x+v t)^2)*.95,t],D[E^(-1/2 (x-v t)^2)-E^(-1/2 (-30+x+v t)^2),t]}/.{t->T},{x,0,30},PlotRange->{-1,1}],{T,0,30}]

k1=1;f1=1;k2=1.1;f2=1.05;

Animate[Plot[Sin[2 π (k1 x-f1 t)]+Sin[2 π (k2 x-f2 t)],{x,0,20},PlotPoints->100,PlotRange->{-2,2}],{t,0,10}]