  A Bose-Einstein condensate (BEC) with periodically modulated interactions
(PMI) has emerged as a novel kind of periodic superfluid, which has been
recently experimentally created using optical Feshbach resonance. In this
paper, we are motivated to investigate the superfluidity of a BEC with PMI
trapped in an optical lattice (OL). In particular, we explore the effects of
PMI on the sound speed and the dynamical structure factor of the model system.
Our numerical results, combined with the analytical results in both the
weak-potential limit and the tight-binding limit, have shown that the PMI can
strongly modify the sound speed of a BEC. Moreover, we have shown that the
effects of PMI on sound speed can be experimentally probed via the dynamic
structure factor, where the excitation strength toward the first Bogoliubov
band exhibits marked difference from the non- PMI one. Our predictions of the
effects of PMI on the sound speed can be tested using the Bragg spectroscopy.
