(*Based on the Group and Phase Velocity demonstration submitted by Enrique Zeleny to the Wolram Demonstrations Project*)
Manipulate[
Plot[{Cos[(k1)*x - (ω1)*t] + Cos[(k2)*x - (ω2)*t], 
    2*Cos[-(k1-k2)/2*x + (ω1-ω2)/2*t],
 -2*Cos[-(k1-k2)/2*x + (ω1-ω2)/2*t]}, {x, 0, 30}, 
ImageSize -> {700,200},
AspectRatio -> 1/4,
Frame -> True, 
   PlotRange -> {{0, 30}, {-2, 2}},
PlotStyle -> {Automatic, Dashed, Dashed},
PlotLabel -> Row[{"t = ", NumberForm[t, 3]}], 
AxesLabel->{"x","y"},
   Epilog -> {Black, PointSize[0.01],
Table[
Point[{(Pi*n - (ω1-ω2)/2*t + Pi/2)/((k2-k1)/2), 0}], {n, -15, 15}], Red, Point[{ (ω1+ω2)/(k1+k2)*t, Cos[(k1)* (ω1+ω2)/(k1+k2)*t - (ω1)*t] + Cos[(k2)* (ω1+ω2)/(k1+k2)*t - (ω2)*t]}]}], 
  {{t,0,"t"}, 0., 10., Appearance ->"Labeled"},
{{k1, 5.8, "(Subscript[k, 1])"}, 3, 9,Appearance ->"Labeled"}, 
{{k2, 6.2, "(Subscript[k, 2])"},3,9,Appearance ->"Labeled"},
{{ω1, 5.8, "(Subscript[ω, 1])"}, 3, 9, Appearance ->"Labeled"},
{{ω2, 6.2, "(Subscript[ω, 2])"}, 3, 9, Appearance ->"Labeled"}]