Give the definition,equation,and unit for wavelength and wave number for a wave.

(N/A) Wavelength: The linear distance between any two consecutive points or particles having a phase difference of $2 \pi \text{ rad}$ is called the wavelength $(\lambda)$ of the wave. Its $SI$ unit is metre $(m)$.
Wave Number: The number of waves per unit distance is called the wave number $(\bar{\nu})$. It is defined as the reciprocal of the wavelength.
Equation for Wavelength: For a wave represented by $y(x, t) = a \sin(kx - \omega t)$,the displacement repeats after a distance $\lambda = \frac{2 \pi}{k}$.
Equation for Wave Number: $\bar{\nu} = \frac{1}{\lambda} = \frac{k}{2 \pi}$.
Units:
- Wavelength $(\lambda)$: $SI$ unit is metre $(m)$.
- Wave Number $(\bar{\nu})$: $SI$ unit is metre$^{-1}$ $(m^{-1})$.