Write the definition of wave speed and derive $v = \frac{\omega}{k}$.

(N/A) Wave speed: The distance covered by a wave in unit time is called wave speed.
Its unit is $m/s$ and its dimensional formula is $[M^0 L^1 T^{-1}]$.
Let $\lambda$ be the wavelength (distance covered by the wave in one time period $T$).
By definition,wave speed $v = \frac{\text{distance}}{\text{time}} = \frac{\lambda}{T}$.
Since frequency $f = \frac{1}{T}$,we have $v = f \lambda$.
Multiplying and dividing by $2\pi$,we get $v = \frac{2\pi f \lambda}{2\pi}$.
Using the relations $\omega = 2\pi f$ (angular frequency) and $k = \frac{2\pi}{\lambda}$ (wave number),we substitute these into the equation:
$v = \frac{\omega}{k}$.