(*Define variables*)
ω:=π/2 (*rad/s*)
k:=2π (*rad/m*)
Y:=5 (*m*)
Φ:=0(*rad*)

(*Define individual waves*)
y1[x_,t_]:=Y*Sin[k*x-ω*t]
y2[x_,t_]:=Y*Sin[k*x-ω*t-Φ]

(*Animate individual waves and their sum*)
Animate[
Show[
Plot[{y1[x,t],y2[x,t],y1[x,t]+y2[x,t]},
{x,0,5},
PlotRange-> {-10,10},
AxesLabel-> {"x (m)", "y (m)"},
PlotStyle->{{Blue,Dashed,Thickness[.001]},{Orange,Dashed,Thickness[.001]},Black},
ImageSize->450
]
],
{t,0,8},AnimationRate->1
]