c=1; L=1; u[n_, x_, t_] := Sin[n Pi x/L] Cos[c n Pi t/L]

Animate[Table[
  Plot[{u[n, x, 0], u[n, x, t]}, {x, 0, L}, PlotRange -> {-1, 1}],
    {n, 1, 3}], {t, 0, 2L/c, 0.01}]