The individual waves, having the average of two k's correspond to the first cosine term in equation and their phase velocity(wave velocity) is given by

        

ie. the velocity is nearly the same as that of component waves. The envelope of modulation (wave packet) is given by the second cosine term. The wave vector for this is the difference of wave vector of two waves and is small, which corresponds to a larger wavelength. The velocity of the wave packet (group velocity) is given by

         

The wave velocity and group velocity are related as

        

where is the actual wavelength in the medium. For light waves traveling in vacuum there is no dispersion. (all waves move with same velocity), the wave and groups velocity is same.