Large panel: normalized amplitudes of velocity fluctuations as a function of ξ = x/L for waves incident on the right side of a core with the density profile given by Eq. (35) for various values of the nondimensional wave frequency W. No dissipation is included. The dashed red line shows the WKB solution. Small panel: the red line shows the normalized density profile, and the black line the normalized Alfvén speed.