How Does a Two Atoms Basis Lattice Act Independently?

[CB4]

Homework Statement

For a lattice with a two atoms basis, the two dispersion relations valid for Ka = ±∏

w² = 2C/M₂ and w² = 2C/M₁

Show that under these conditions the lattice acts as two independent lattices (one lattice per each atom) with one of the lattices moving while the other is at rest.

The Attempt at a Solution

I really don't know where to begin when dealing with this problem. I presume it's dependent on an oscillatory function, but I'm completely lost as to what defines two independent lattices.

 

[ehild]

You need to read about lattice vibrations. First see a one-dimensional lattice, a linear chain of two different kinds of atom.

http://users.physik.fu-berlin.de/~pascual/Vorlesung/SS09/slides/EPIV-09SS-SolSt_K3-Lattice%20vibrations.pdf
ehild