We investigate acousto-optic long period grating resonances in a fluid-filled solid-core photonic bandgap fiber (PBGF). The acoustic grating design enables electrically tunable notches in each of the PBGF transmission bands, where both the center frequency and depth of the resonances can be varied. The measured intermodal beat length and resonance bandwidth are in good agreement with numerical simulations based on multipole method. We show that the highly dispersive nature of PBGF modes results in very narrow-band rejection for a given grating pitch.