Question

Derive the relation between the velocity of wave, wavelength and frequency.

Answer 1

Frequency wavelength and wave velocity are related as follows:

Wave length is the distance travelled by the wave during the time a particle of the medium completes one vibration.

Therefore, if $\lambda$ be the wavelength and $T$ the time period then the wave travels a distance $\lambda$ and time $T$

Hence,

Wave velocity $=\frac{Distance}{Time}$

$\Rightarrow v=\frac{\lambda }{T}$

$\therefore v=\nu \lambda$ $[\frac{1}{T}=frequency(\nu \left)\right]$

$\therefore$ Wave velocity$=$ Frequency $\times$ Wavelength

The wave velocity in a medium remains constant under the same physical condition.