Period, damping time, and ratio of the damping time to period versus the wavenumber for the long (solid) and short (dashed) period Alfvén waves in a PIP with . In all the panels, the location of the critical wavenumber, k_c, is defined by the vertical dotted line. The background flow speed is 15 km s^-1 and the shaded region corresponds to the interval of observed wavelengths in prominence oscillations.