Polarization

Manipulate[Show[ParametricPlot[{A1 Cos[-2 π t],A2 Cos[-2 π t+ψ]},{t,0,tf},PlotRange->{{A1+1,-A1-1},{A2+1,-A2-1}},PlotStyle->{RGBColor[0,0,0.6],Thickness[0.005]}],
Graphics[{Thickness[0.005],Arrow[{{0,0},{A1 Cos[-2 π tf],A2 Cos[-2 π tf+ψ]}}]}],Graphics[{Red, Thickness[0.005],Arrow[{{0,0},{A1 Cos[-2 π tf],0}}]}],Graphics[{Red, Thickness[0.005],Arrow[{{0,0},{0,A2 Cos[-2 π tf+ψ]}}]}]],{A1,1,10},{A2,1,10},{tf,0.0001,1,0.001},{ψ,-2 π,2 π,π/10}]

Manipulate[Show[ParametricPlot[{A1 Cos[-2 π x],A2 Cos[-2 π x+ψ]},{x,0,xf},PlotRange->{{A1+1,-A1-1},{A2+1,-A2-1}},PlotStyle->{RGBColor[0,0,0.6],Thickness[0.005]}],
Graphics[{Thickness[0.005],Arrow[{{0,0},{A1 Cos[-2 π xf],A2 Cos[-2 π xf+ψ]}}]}],Graphics[{Red, Thickness[0.005],Arrow[{{0,0},{A1 Cos[-2 π xf],0}}]}],Graphics[{Red, Thickness[0.005],Arrow[{{0,0},{0,A2 Cos[-2 π xf+ψ]}}]}]],{A1,1,10},{A2,1,10},{xf,0.0001,1,0.001},{ψ,-2 π,2 π, RandomReal[{-2 π,2 π},10]}]

Polarization of standing waves

Manipulate[Show[ParametricPlot[{0.5 (A1 Cos[ϕ+2 π t+ψ1]+A1 Cos[ϕ-2 π t]),0.5 (A2 Cos[ϕ+2 π t+ψ2]+A2 Cos[ϕ-2 π t+ψ3])},{t,0,tf},PlotRange->{{A1+1,-A1-1},{A2+1,-A2-1}},PlotStyle->{RGBColor[0,0,0.6],Thickness[0.005]}],Graphics[{Thickness[0.005],Arrow[{{0,0},{A1 Cos[ϕ+2 π tf+ψ1],A2 Cos[ϕ+2 π tf+ψ2]}}]}],Graphics[{Thickness[0.005],Arrow[{{0,0},{A1 Cos[ϕ-2 π tf],A2 Cos[ϕ-2 π tf+ψ3]}}]}]],{A1,1,10},{A2,1,10},{tf,0.0001,1,0.001},{ϕ,-2 π,2 π,π/4},{ψ1,-2 π,2 π,π/4},{ψ2,-2 π,2 π,π/4},{ψ3,-2 π,2 π,π/4}]

Plot standing waves

wave1[A1_,λ1_,x_,f1_, t_] := A1 Cos[2 π /λ1 x+2 π f1 t]
wave2[A2_,λ2_,x_,f2_,t_, ϕ_] := A2 Cos[2 π /λ2 x-2 π f2 t+ϕ]
f=1;
λ = 1;
Manipulate[Show[Plot[{wave1[1,λ,x,f, t],wave2[1, λ,x,f,t, 0]}, {x,0,λ 10},PlotRange->{{0,1/f*10},{-2,2}},PlotStyle->{Gray,Gray,Thickness[0.005]}],
Plot[wave1[1,λ,x,f, t]+wave2[1,λ,x, f,t, 0], {x,0,λ 10},PlotRange->{{0,1/f*10},{-2,2}},PlotStyle->{Blue,Thickness[0.005]}]],
{t,0.0001,1/f*10,0.001}]

Plot waves

wave1[A1_,k1_,x_,v_, t_] := A1 Cos[k1 (x-v t)]
wave2[A2_,k1_,x_,v_, t_, ϕ_] := A2 Cos[k1 (x-v t)+ϕ]
λ1=8 ;
k1=2 π/λ1;
v=1;
Manipulate[Plot[{wave1[1,k1,x,v, t],wave2[1,k1,x,v, t,π]},
 {x,0,2 π/k1 10},PlotRange->{{0, 10},{-2,2}},PlotStyle->{Blue,Red,Thickness[0.005]}],{t,0.0001,10,0.001}]