.the dispersion relation ior a lattice wave propagating in a one dimensional chain of atoms of mass m bound together by force constant ß is given by the followi

.The dispersion relation Ior a lattice wave propagating in a one dimensional chain of atoms of mass m bound together by force constant ß is given by the following equation. = 0, sin (ka/2), where a, - Here a is the distance between atoms. (a) For small values of 'K, show that the phase velocity is the same as the group velocity (b) Find the group and phase velocities at k=ada.