In this simulation study, we investigate the influence of biomolecular confinement on dynamical processes in water. We compare water confined in a membrane protein nanopore at room temperature to pure liquid water at low temperatures with respect to structural relaxations, intermolecular vibrations, and the propagation of collective modes. We observe distinct potential energy landscapes experienced by water molecules in the two environments, which nevertheless result in comparable hydrogen bond lifetimes and sound propagation velocities. Hence, we show that a viscoelastic argument that links slow rearrangements of the water-hydrogen bond network to ice-like collective properties applies to both, the pure liquid and biologically confined water, irrespective of differences in the microscopic structure.