The Critical Frequency appears when the bending wavelength is equal to the acoustic wavelength (or the celerity of the bending wave is equal to the sound celerity) :
$$ f_c = \frac{c_0^2}{2\sqrt{\frac{\rho_s}{B_p}}} = \frac{c_0^3}{\sqrt{\pi}} \sqrt{\frac{3\rho_s(1-\nu^2)}{Eh^3}} $$
with :