Period, damping time, and ratio of the damping time to period versus the wavenumber for magnetoacoustic waves in a PIP with . 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 the interval of observed wavelengths in prominence oscillations.