Frequency and damping rate of different wave modes in two-fluid MHD vs. the normalized wavenumber a = k_zv_A/ν_in. Frequencies and damping rates are normalized by kv_A. Red asterisks correspond to the fast magneto-acoustic mode and green diamonds correspond to the usual slow magneto-acoustic mode. The mode with the blue squares is the new sort of slow magneto-acoustic wave (“neutral” slow mode), which arises for larger wave numbers. This mode has only an imaginary frequency for small wave numbers, which is not shown in this figure. Frequencies and damping rates are calculated for the waves propagating along the magnetic field. The neutral hydrogen is taken to be 50% (ξ_n = 0.5). Here we consider c_sn/v_A = 0.5.