Period, damping time, and ratio of the damping time to period versus the horizontal wavenumber for magnetoacoustic waves in a PIP with and k_z = 1.57 × 10^-5 m^-1. Slow waves (short-dashed and dot-dashed lines), fast waves (continuous and long-dashed lines), thermal wave (dotted line). The location of the critical wavenumbers is defined by the presence of peaks and bifurcations in the plots. The background flow speed is 15 km s^-1 and the shaded region corresponds to an interval of horizontal wavelengths coincident with observed wavelengths in prominence oscillations.