x[amplitude_,omega_,phase_,time_] := 
amplitude*Cos[omega*time + phase]

Manipulate[
{Plot[
x[A1,w1,p1,t],
{t,0,If[w1≠  w2,4*Pi/Abs[w1-w2],4*Pi/w1]},
AxesLabel -> {"t","(Subscript[x, 1])"},
PlotRange -> {-2,2},
PlotLabel -> "Wave 1",
PlotStyle -> {Red,Thick}
],
Plot[
x[A2,w2,p2,t],
{t,0,If[w1≠  w2,4*Pi/Abs[w1-w2],4*Pi/w1]},
AxesLabel -> {"t","(Subscript[x, 2])"},
PlotRange -> {-2,2},
PlotLabel -> "Wave 2",
PlotStyle -> {Blue,Thick}
],
Plot[
x[A1,w1,p1,t]+x[A2,w2,p2,t],
{t,0,If[w1≠  w2,4*Pi/Abs[w1-w2],4*Pi/w1]},
AxesLabel -> {"t","x = (Subscript[x, 1]) + (Subscript[x, 2])"},
PlotRange -> {-2,2},
PlotLabel -> "Supperposition of Two Waves",
PlotStyle -> {Green,Thick}
]},
{{A1,0.5,Dynamic["Amplitude (Subscript[A, 1])"]},0,1,Appearance -> "Labeled"},
{{A2,0.5,Dynamic["Amplitude (Subscript[A, 2])"]},0,1,Appearance -> "Labeled"},
{{w1,5,Dynamic["Angular Frequency (Subscript[ω, 1])"]},0.1,10,Appearance -> "Labeled"},
{{w2,5,Dynamic["Angular Frequency (Subscript[ω, 2])"]},0.1,10,Appearance -> "Labeled"},
{{p1,Pi,Dynamic["Phase Angle (Subscript[α, 1])"]},0,2 Pi,Appearance -> "Labeled"},
{{p2,Pi,Dynamic["Phase Angle (Subscript[α, 2])"]},0,2 Pi,Appearance -> "Labeled"}
]