Molecular dynamics (MD) simulations have been widely used to study flow at molecular scales. Most of this work is devoted to study the departure from continuum fluid mechanics as the confining dimension decreases. Here, we present MD results under conditions where hydrodynamic descriptions typically apply, but focus on the influence of in-plane wavelengths. Probing the long wavelength limit in thermodynamic equilibrium, we observed anomalous relaxation of the density and longitudinal momentum fluctuations. The limiting behavior can be described by an effective continuum theory that describes a transition to overdamped sound relaxation for compressible fluids.