How are the wave velocity V, frequency f and wavelength λ of a wave related? Derive the relationship.

The relation between wave velocity V, frequency f and wavelength λ of a wave is —

V = f λ

Derivation

Let velocity of a wave be V, time period T, frequency f, and wavelength λ.

By definition,

Wavelength λ = Distance travelled by the wave in one time period i.e., in T second
= wave velocity x time period
= V x T
or VT = λ     [Equation 1]

But, T = $\dfrac{1}{f}$

∴ From Equation 1

V x ($\dfrac{1}{f}$) = λ

or V = fλ

Therefore,

Wave velocity (V) = Frequency (f) x Wavelength (λ)