Group velocity: Group velocity is defined as the rate at which the wave propagates through waveguide .

Group velocity is given by equation

$v_g$ = $v_c{\sqrt{1- ({\frac{\lambda}{{\lambda}_c}})^2}}$

Where

Vc is velocity of light.

$\lambda$ is free space wavelength

$\lambda o$ is cutoff wavelength

The group velocity is also can be defined as the velocity of energy flow in the waveguide system.

Cut-off frequency: It is the frequency of the signal above which propagation of waves occur.

$f_c = \frac{c}{2}{\sqrt{({\frac{m}{a})^2}+ ({\frac{n}{b}})^2}}$