Interference from Two Sources

z[x_, y_, t_, x0_, y0_, λ_, v_] := Sin[((2 π)/λ)(Sqrt[(x-x0)^2 + (y-y0)^2] - v t)]

Show the waves propagating outward in time.  The orange lines are nodes, where the intensity is small.  Set a1 and/or a2 to show either or both sources.

λ = 0.5; v = 0.2; Manipulate[DensityPlot[a1 z[x, y, t, 0, 1, λ, v] +  a2 z[x, y, t, 0, -1, λ, v], 
{x, -1, 7}, {y, -4, 4}, PlotPoints -> 64, MaxRecursion-> 1, ImageSize -> 500, AspectRatio -> 1], 
{{a1, 1}, {0, 1}}, {{a2, 1}, { 0, 1}},{t, 0, 10, 0.25, Appearance -> "Open"}]

Show how the angle is inversely related to the spacing ‘d’ between the sources.

v = 0.2; 
Manipulate[DensityPlot[a1 z[x, y, 0, 0, d/2, λ, v] +  a2 z[x, y, 0, 0, -d/2, λ, v], 
{x, -1, 7}, {y, -4, 4}, PlotPoints -> 64, MaxRecursion-> 1, AspectRatio -> 1, ImageSize -> 500], {{a1, 1}, {0, 1}}, {{a2, 1}, { 0, 1}}, {{d, 2}, 0.25, 6, 0.25, Appearance -> "Open"}, {{λ, 0.5}, 0.2, 1.5, 0.1, Appearance->"Open"}]