Math 2280-2
Friday April 20
Wave games
> restart:with(plots):
Warning, the name changecoords has been redefined
> #play this movie to illustrate the fact that
#vibrating strings with fixed endpoints are
#really the sum of waves traveling to the left
#and right with speed c:
animate({sin(x-.5*t),sin(x+.5*t),2*sin(x)*cos(.5*t)},
x=-4*Pi..4*Pi,t=0..4*Pi, color=black,frames = 64);
2
1
–5
–10
x
5
10
–1
–2
> #since I can’t bring the movie to class, here are some stills:
t:=0:
plot({sin(x-.5*t),sin(x+.5*t),2*sin(x)*cos(.5*t)},
x=-2*Pi..2*Pi,color=black);
2
1
–6
–4
–2
2
x
4
–1
–2
> t:=Pi/2:
plot({sin(x-.5*t),sin(x+.5*t),2*sin(x)*cos(.5*t)},
x=-2*Pi..2*Pi,color=black);
6
1
0.5
–6
–4
–2
0
x
2
4
6
–0.5
–1
> t:=Pi:
plot({sin(x-.5*t),sin(x+.5*t),2*sin(x)*cos(.5*t)},
x=-2*Pi..2*Pi,color=black);
#why do you only see two plots?
1
0.5
–6
–4
–2
x
2
4
6
–0.5
–1
> t:=3*Pi/2:
plot({sin(x-.5*t),sin(x+.5*t),2*sin(x)*cos(.5*t)},
x=-2*Pi..2*Pi,color=black);
1
0.5
–6
–4
–2
0
2
x
4
–0.5
–1
> t:=2*Pi:
plot({sin(x-.5*t),sin(x+.5*t),2*sin(x)*cos(.5*t)},
x=-2*Pi..2*Pi,color=black);
#now we’re through half a period of the wave
6
2
1
–6
–4
–2
2
–1
–2
x
4
6