n=0;
T=1;
v=0.5;
nm=6;
xmin=-3; xmax=3; ymin=-3; ymax=3;
gifs={};(*gifsを初期化*)
i=Table[Random[Real,{xmin,xmax}],{nm}];
j=Table[Random[Real,{ymin,ymax}],{nm}];
Do[{If[n<nm&&Random[]<0.7,{n=n+1,t[n]=time}],
f[x_,y_]:=
Table[Which[(x-i[[k]])^2+(y-j[[k]])^2≤time -t[k],-Sin[2Pi/T(time-t[k]-(Sqrt[(x-i[[k]])^2+(y-j[[k]])^2])/v)]Exp[-(time-t[k]+2)],(x-i[[k]])^2+(y-j[[k]])^2>time-t[k],0],{k,1,n}],
AppendTo[gifs,(*AppendToでgifsに追加*)
Plot3D[Apply[Plus,f[x,y]],{x,xmin,xmax},{y,ymin,ymax},Mesh->False, Axes->False, Boxed->False, PlotPoints->100,PlotRange->{-3,3}]]}

,{time,0,6,T/4}];

ListAnimate[gifs]