  We present a combination of theoretical and simulation-based examinations of
the role of two-fluid ambipolar drift on molecular line widths. The dissipation
provided by ion-neutral interactions can produce a significant difference
between the widths of neutral molecules and the widths of ionic species,
comparable to the sound speed. We demonstrate that Alfven waves and certain
families of magnetosonic waves become strongly damped on scales comparable to
the ambipolar diffusion scale. Using the RIEMANN code, we simulate two-fluid
turbulence with ionization fractions ranging from 10^{-2} to 10^{-6}. We show
that the wave damping causes the power spectrum of the ion velocity to drop
below that of the neutral velocity when measured on a relative basis. Following
a set of motivational observations by Li & Houde (2008), we produce synthetic
line width-size relations that shows a difference between the ion and neutral
line widths, illustrating that two-fluid effects can have an observationally
detectable role in modifying the MHD turbulence in the clouds.
