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The dispersion equation of a waveguide, which relates the wavenumber $k$ to the frequency $\omega$ is

$$k(\omega)= (1/c) \sqrt{\omega^{2}-\omega_{\circ}^{2}}$$

where the speed of light $c= 2 \times 10^{8}\: m/s$ and $\omega_{\circ}$ is a constant . If the group velocity is $2 \times 10^{8}\: m/s$, then the phase velocity is

  1. $1.5 \times 10^{8} \:m/s$
  2. $2 \times 10^{8}\: m/s$
  3. $3 \times 10^{8}\: m/s$
  4. $4.5 \times 10^{8}\: m/s$
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