Question

A wave is propagated in a waveguide at frequency of 9 GHz and separation is 2 cm between walls Calculate group velocity for dominant mode.

Answer 1

We know that

$$v_g\cdot v_p=c^2,\\\space\\ v_p=\frac{c}{\sqrt{1-(f_c/f)^2}}=5\cdot10^7\text{ m/s},\\\space\\ v_g=\frac{c^2}{v_p}=\frac{(3\cdot10^8)^2}{5\cdot10^8}=1.8\cdot10^8\text{ m/s}.$$