Profiles of the parallel and perpendicular velocity as a function of y, for three times. Velocities are normalised with respect to the initial velocity amplitude. Time is normalised by the Alfvén travel time τ_A = 2L/v_A. The solid line represents the perpendicular velocity, which is approximately the same for varying sound speeds. The transverse velocity is taken at x = πL/20 where maximum and the parallel velocity at x = 0 where also maximum. The dotted dashed, dashed and dotted lines are the parallel velocity profiles for c_S/v_A = 0.190, 0.379, 0.602, respectively. The velocity has been multiplied by a factor four for clarity. Left panels: results from the Lare2d numerical simulation. Right panels: analytical solution Eq. (24).