The dispersion relation for a one-dimensional monoatomic lattice chain is given by the equation, \(\rm \omega=\frac{2}{a}v, \left|\sin \left(\frac{ka}{2}\right)\right|\) where, ‘ a ’ is the interatomic spacing \(\rm K=\frac{2\pi}{\lambda}\) and v, has the dimension of velocity. The relation between the phase velocity V_P and group velocity V_g in the long wavelength limit is given by