The time t spent by a charged particle, of mass m and carrying a charge q, inside a dee of a cyclotron is independent of the radius of the path and the speed of the particle so long as m is constant. Then, the periodic time of the charged particle in its nearly circular path is T = 2t, and the frequency of revolution,
f = \(\cfrac 1T\) = \(\cfrac 1{2t}\) = \(\cfrac{qB}{2\pi m}\)
are also independent of the radius and the speed.
