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.