f[x_,t_,n_]=Cos[n t] Sin[n x]

f[x_,y_,t_,nx_,ny_]=Cos[Sqrt[nx^2+ny^2] t] Sin[nx x]Sin[ny y]

Do[
Plot3D[f[x,y,t,5,7],{x,0,π},{y,0,π},PlotRange->{-1,1}] //Print;
,{t,0,1,1/25}]

Plot[f[x,0,1],{x,0,π}]

Plot[Table[1/n f[x,0,n],{n,1,10,1}] //Evaluate,{x,0,π}]

n=3;
Do[
Plot[f[x,t,n],{x,0,π},PlotRange->{-1,1}] //Print
,{t,0,π(1-1/16)(2/n),(2/n)π/16}]