The relation between wave speed, wavelength and frequency of the wave is called universal wave equation. This equation applies to all mechanical and electromagnetic waves.

Derivation of the universal wave equation

Consider a wave of wavelength λ, frequency f and moving with speed v. Now if it travels a distance of one wavelength λ, then ΔS = λ. As the time taken for one wavelength is called time period, therefore, the time taken for this distance must by equal to the time period of the wave, T. Now, if v is the speed of the wave, then

Now T and f are related as f = 1/T, so put value of f in the above equation,

This equation is called universal wave equation and relates the wave speed to the frequency and wavelength of the wave.