I have a function that reads:

f[P_?NumericQ, 
Ob_?NumericQ] := -Sqrt[P/Ob^2 + Sqrt[P^2 + Ob^2 w^2]/Ob^2] Tan[
 Sqrt[-(P/Ob^2) + Sqrt[P^2 + Ob^2 w^2]/Ob^2]] + 
 Sqrt[-(P/Ob^2) + Sqrt[P^2 + Ob^2 w^2]/Ob^2]
 Tanh[Sqrt[P/Ob^2 + Sqrt[P^2 + Ob^2 w^2]/Ob^2]]

For each pair of numerical values of P and Ob, there are infinitely many solutions for w (denoted as w0, w1, w2, w3, ...).

I want to write a concise code that does the following:

1. Loops over values of Ob from 0 to 1.
2. For each value of Ob, finds a critical value of P (Pcr) that makes the ratio of w2/w1 approximately equal to 3 (with reasonable tolerance).
3. Stores or outputs these critical values of P for each Ob. I tried but couldn't come up with a successful one. Thanks for any help in advance.

Below is one of my trials:

results = 
Table[Pcr = 
 P /. FindRoot[
  w2/w1 /. NSolve[f[P, Ob] == 0 && 0 < w < 20, w, Reals] == 
    3, {P, .1}], {Ob, 0, 1, .1}];