  We consider acoustic wave propagation through a periodic array of the
inclusions of arbitrary shape. The inclusion size is much smaller than the
array period while the wavelength is fixed. We derive and rigorously justify
the dispersion relation for general frequencies and show that there are
exceptional frequencies for which the solution is a cluster of waves
propagating in different directions with different frequencies so that the
dispersion relation cannot be defined uniquely. Examples are provided for the
spherical inclusions.
