Phase velocity: Phase velocity is defined as the rate at which the wave changes its phase in terms of the guide wavelength.

OR

The phase velocity is the velocity with which the wave changes phase in a direction parallel to the conducting surface.

The phase velocity is given by equation

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

Where

Vc is velocity of light.

$\lambda$ is free space wavelength

$\lambda_o$ is cutoff wavelength

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.

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

Guided wavelength of waveguide: It is defined as the distance travelled by the wave in order to undergo a phase shift of 2π radians along the waveguide.

$\lambda_g$ = $\frac{\lambda}{\sqrt{1+ ({\frac{\lambda}{{\lambda}_c}})^2}}$

Cut off wavelength: Cut-off wavelength for a parallel plane waveguide where only side walls are present i.e. only the a dimension is present,and it is given by,

$\lambda_c$ = $\frac{2a}{m}$