Consider a linear diatomic lattice. Use the amplitude equations
A[2μ−mω²]=2μBcos(ka/2)
and
B[2μ−Mω²]=2μAcos(ka/2)
at the Brillouin zone boundary to show that the amplitude of oscillation for the smaller atoms, A, is zero at in the acoustic branch. You may use the result for the maximum frequency of the acoustic branch.
