# Asmar 3.4-15, D'Alembert's solution of the wave equation, f=pulses,g=0
pulse:=(x,a,b)->piecewise(x<a,0,x<b,1,0);
f:=x->4*x*pulse(x,0,1/4)+(2-4*x)*pulse(x,1/4,1/2);
#plot(f(x),x=0..1);
F0:=x->piecewise(x<0,-f(-x),f(x));F:=x->F0(x-2*floor((x+1)/2));
plot(F(x),x=-1..4);
u:=(x,t)->(1/2)*(F(x+t)+F(x-t));
#plot(u(x,0.7),x=-2..2);
with(plots):
animate( plot, [u(x,t),x=-3..3], t=0..1.5, trace=0, frames=50 );