File talk:Standing waves on a string.gif
I generated this in Mathematica. Here's the code for anyone who wants to improve it.
f = .5*Sin[n*t]*Sin[n*x]/n; point = Graphics[Point[{{0, 0}, {Pi, 0}}]]; range = .51; animation = Table[GraphicsGrid[{{Show[{Plot[f /. n -> 1, {x, 0, Pi}, PlotRange -> range, Axes -> False], point}], Show[{Plot[f /. n -> 2, {x, 0, Pi}, PlotRange -> range, Axes -> False], p}]}, {Show[{Plot[f /. n -> 3, {x, 0, Pi}, PlotRange -> range, Axes -> False], point}], Show[{Plot[f /. n -> 4, {x, 0, Pi}, PlotRange -> range, Axes -> False], p}]}, {Show[{Plot[f /. n -> 5, {x, 0, Pi}, PlotRange -> range, Axes -> False], point}], Show[{Plot[f /. n -> 6, {x, 0, Pi}, PlotRange -> range, Axes -> False], p}]} }], {t, 0, 2*Pi, .1}]; Export["anim.gif", animation, AnimationRate -> 10] SystemOpen["anim.gif"]