Travelling waves.
Version 0.2 [3-21-07]
restart;
with(plots):
A := 1.2;
k := 2.0;
w := 3.0;
y := (x,t) -> A*cos(k*x-w*t);
plot(y(x,1),x=-4..10);
animate(plot,[y(x,t),x=-4..10],t=0..5);
A1 := 0.3;
A2 := 0.3;
k1 := 2.0;
k2 := 3.0;
w1 := 3.0;
w2 := 5.0;
Deltak := k2 - k1;
Deltaw := w2 - w1;
kbar := (k2 + k1)/2;
wbar := (w2 + w1)/2;
y1 := (x,t) -> A1*cos(k1*x-w1*t);
y2 := (x,t) -> A2*cos(k2*x-w2*t);
env := (x,t) -> 2*A1*cos(Deltak/2*x-Deltaw/2*t);
plot([y1(x,1)+y2(x,1),env(x,1),-env(x,1)],x=-20..20,color=[blue,red,red]);
animate( plot, [[y1(x,t)+y2(x,t),env(x,t),-env(x,t)],x=-20..20,color=[red,blue,blue]], t=0..10 ) ;