Manipulate[Graphics[{Thickness[.005],If[pattern=="plane",Table[{ColorData["SouthwestColors"][((n+Mod[t,2])/10)],Circle[{x,0},n+Mod[t,2]]},{n,0,t,2},{x,0,2sources-2,2}],Table[{ColorData["SouthwestColors"][((n+Mod[t,2])/10)],Circle[{Cos[(x+1)π/(2sources)],Sin[(x+1)π/(2sources)]},n+Mod[t,2]]},{n,0,t,2},{x,0,2sources-2,2}]]},PlotRange->{If[pattern=="plane",{-5,2sources-2+5},{-2sources+2-.5,2sources-2+.5}],{-.5,2sources+.5}},ImageSize->{1900,1050}],{{t,8.15,"time"},0,20},{{sources,5},1,10,1,Appearance->"Labeled"},
{pattern,{"plane","circular"}}]

TotalAmplitude[x_,y_,t_,a_,Nmax_,k_,A0_]:=Total[Table[A0 Sin[k (Sqrt[(((n a-x))^2)+(y^2)])-t/k],{n,Range[Nmax]}]]

(Subscript[Ψ, total])(x,y)=(Subscript[A, 0])(∑_(n=0)^(Subscript[N, max]))Sin[k((Sqrt[(((na))^2)+(y^2)])-(t/k)]

wavenumber=0.6;
numberofsources=555;
amplitude=0.1;
spacingbetweensources=2;

maxX=maxY=500;
gridpointsX=gridpointsY=150;
timeinterval=Range[0,20,0.1];

staticwavefield=Flatten[ParallelTable[{xx,yy,TotalAmplitude[xx,yy,timeinterval[[1]],spacingbetweensources,numberofsources,wavenumber,amplitude]},{xx,Range[-maxX,maxX,2 maxX/gridpointsX]},{yy,Range[-maxY,maxY,2 maxY/gridpointsY]}],1];
ListPlot3D[staticwavefield,ImageSize->{1800,1000},AxesLabel->{"X coordinate","Y coordinate","Total Amplitude"},LabelStyle->"Title",PlotLabel->"(Subscript[Ψ, total])(x,y)=(Subscript[A, 0]) (∑_(n = 0)^(Subscript[N, max]))Sin[k(\!\(\*SqrtBox[\(\*SuperscriptBox[\((n\\  a)\), \(2\)] + \*SuperscriptBox[\(y\), \(2\)]\)]\)-(t/k)]"]