One of the key requirements for good thermoelectric materials is a low lattice thermal conductivity. Here we present a combined neutron scattering and theoretical investigation of the lattice dynamics in the type I clathrate system Ba-Ge-Ni, which fulfills this requirement. We observe a strong hybridization between phonons of the Ba guest atoms and acoustic phonons of the Ge-Ni host structure over a wide region of the Brillouin zone, which is in contrast with the frequently adopted picture of isolated Ba atoms in Ge-Ni host cages. It occurs without a strong decrease of the acoustic phonon lifetime, which contradicts the usual assumption of strong anharmonic phonon-phonon scattering processes. Within the framework of ab initio density-functional theory calculations we interpret these hybridizations as a series of anticrossings which act as a low-pass filter, preventing the propagation of acoustic phonons. To highlight the effect of such a phononic low-pass filter on the thermal transport, we compute the contribution of acoustic phonons to the thermal conductivity of Ba8Ge40Ni6 and compare it to those of pure Ge and a Ge-46 empty-cage model system.