Question

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

Answer 1

Let the velocity of a wave be V, time period T, frequency ν and wavelength λ. By the definition of wavelength,

Wavelength = Distance travelled by the wave in one time period i.e., in T second

Or, wavelength = Wave velocity × Time period

Or, λ = V × T

Or, λ  = V × 1/ ν      ...[As, T = 1/]

Therefore, V = ν λ

Therefore, Wave velocity = Frequency × wavelength