f[r_,t_]:=5 (BesselJ[0,r] Cos[t]+BesselY[0,r] Sin[t]);
t = 3Pi/2;
ParametricPlot3D[{r Cos[θ], r Sin[θ], f[r, t]}, {r, .5, 20}, {θ, 0, 2π}, Axes -> False, Boxed -> True, PlotRange ->{{-20, 20}, {-20, 20}, {-5,5}}]
Plot[f[r, t], {r, 0, 20}]

Animate[ParametricPlot3D[{r Cos[θ], r Sin[θ], f[r, t]}, {r, .5, 20}, {θ, 0, 2π}, Axes -> False, Boxed -> True, PlotRange ->{{-20, 20}, {-20, 20}, {-5,5}}], {t, 0, 2π}]

Animate[Plot[f[r, t], {r, 0, 20}, PlotRange ->{{0, 20},{-5,5}}], {t, 0, 2Pi}]