We study coherent phonon oscillations in GaAs/AlGaAs superlattices and multiple quantum wells as a function of the barrier width. Strong, bulklike screened LO phonons accompany bare LO phonons for thin barrier samples, whereas for thicker barrier samples, only the bare LO phonons exist. These results strongly indicate that the coherent interwell plasmons oscillating across the barrier couple to LO phonons. The technique applied is a very sensitive way of probing the superlattice-multiple quantum well transition of collective charge oscillations.