  We develop the theory of acoustic wave propagation in a waveguide containing
an array of time modulated digital meta-atoms, showing the equivalence between
this array and a homogeneous, time varying, dispersive material. In the limit
of an adiabatic time variation we find some choices of meta-atom coupling
strength lead to exceptional points, where one mode is exponentially amplified
and the adiabatic approximation breaks down. In the highly non--adiabatic limit
we derive the analogue of reflection coefficients for an abrupt change in the
meta-atom coupling. Due to dispersion we have both conversion between different
types of modes, and different directions of propagation, which can be tuned
through modifying the programmed response of the digital meta--atoms.
