Acoustic Band Structure in 2d

Hi Folks - Ive posted a couple of questions to some related discussion but it looks like they haven't been visited in a while so I thought I would make a new discussion group.

I am interested in finding out whether or not it is possible to calculate acoustic band structures using a reciprocal lattice simulation and periodic boundary conditions. I understand this is typically done by solving for eigan solutions to the helmholtz equation as you vary the direction of the plane wave vector. My question is... while performing an eigan value analysis and say, computing 100 eigan values in the vicinity of the stop band, how does one back out the wave vector direction related to the given eigan values

Thanks

Sean