  Oscillations of atomic Bose-Einstein condensates in a 1D optical lattice with
a two-point basis is investigated. In the low-frequency regime, four branches
of modes are resolved, that correspond to the transverse in-phase and
out-of-phase breathing modes, and the longitudinal acoustic and optical phonon
modes of the condensates. Dispersions of these modes depend intimately on the
values of two intersite Josephson tunneling strengths, $J_1$ and $J_2$, and the
on-site repulsion $U$ between the atoms. Observation of these mode dispersions
is thus a direct way to access them.
