Plotting complicated Bessel functions expression

Question

I am trying to plot this function

f[X_,Y_]=-(1/Sqrt[2])(√((1/2 - 0.500013 BesselJ[0, 0.01 X] + 
   100.001 BesselJ[1, 0.01 X] Cos[Y])^2/((1/2 - 
    0.500013 BesselJ[0, 0.01 X] + 
    100.001 BesselJ[1, 0.01 X] Cos[Y])^2 + 
  10000.3 BesselJ[1, 0.01 X]^2 Sin[Y]^2) + (
 10000.3 BesselJ[1, 0.01 X]^2 Sin[
   Y]^2)/((1/2 - 0.500013 BesselJ[0, 0.01 X] + 
    100.001 BesselJ[1, 0.01 X] Cos[Y])^2 + 
  10000.3 BesselJ[1, 0.01 X]^2 Sin[
    Y]^2) + (√((1/2 - 0.500013 BesselJ[0, 0.01 X] + 
        100.001 BesselJ[1, 0.01 X] Cos[Y])^2 ((1/2 - 
          0.500013 BesselJ[0, 0.01 X] + 
          100.001 BesselJ[1, 0.01 X] Cos[Y])^2 + 
        10000.3 BesselJ[1, 0.01 X]^2 Sin[Y]^2)))/((1/2 - 
      0.500013 BesselJ[0, 0.01 X] + 
      100.001 BesselJ[1, 0.01 X] Cos[Y])^2 + 
    10000.3 BesselJ[1, 0.01 X]^2 Sin[Y]^2)))

But I get this plot.

Plot[f[X, π/2], {X, 1, 10^4}]

I was expecting more regular oscillations, whereas I see in the lower part certain irregularities, and this make me think of some plotting error. Is there anything I can do to make the bessel function be plotted right?

Thanks!

Answer 1

You can see the effect that changing the number of plotted points has by

plotlist = 
  Table[Plot[f[X, \[Pi]/2], {X, 1, 10^4}, PlotPoints -> n, 
    PlotLabel -> "PlotPoints = " <> IntegerString[n]], {n, {30, 40, 
     100, 200, 400, 800}}];
ListAnimate[plotlist]