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

Also T = 1/f

or,  V(1/f) = λ

or, V = fλ

Therefore,

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