(* 1D - cosine/sin functions *)
n = 5 (* pick @ antinodes *)
w =  Pi n;
f[x_] = If[EvenQ[n],Sin[x],Cos[x] ];
Animate[
Plot[f[w x] Cos[w t], {x,-0.5,0.5},PlotRange-> {-1,1},AspectRatio->1/3],{t,0, 2 Pi/w}]

(* 2D circular - Bessel functions *)
(* first, no angular dependence *)
n = 3(* pick # antinodes *)
w = BesselJZero[0,n]//N;
Animate[
ParametricPlot3D[{r Cos[theta], r Sin[theta],
BesselJ[0,w r] Cos[w t]}, 
{r,0,1}, {theta,0,2 Pi}, PlotRange->{-1,1},BoxRatios->{1,1,1/3}, Mesh-> 8, PlotPoints -> 25],{t,0, 2 Pi/w}]

(* now, with angular dependence *)
m = 3(* pick # angular antinodes *)
n = 2 (* pick # radial antinodes *)
w = BesselJZero[m,n]//N;
Animate[
ParametricPlot3D[{r Cos[theta], r Sin[theta],
BesselJ[m,w r] Cos[w t] Cos[m theta]}, 
{r,0,1}, {theta,0,2 Pi}, PlotRange->{-1,1},BoxRatios->{1,1,1/3}, Mesh-> 8, PlotPoints -> 25],{t,0, 2 Pi/w}]