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We study linear perturbations in cylindrically symmetric fluid filaments, similar to those observed in molecular cloud complexes. We perturb the nonlinear, inhomogeneous, cylindrical equilibrium of a self-gravitating fluid and solve the linearized Euler equations, including the effects of an axial magnetic field. We present numerical solutions and dispersion relations for various barotropic equations of state. In addition to the traditional isothermal equation of state, we also consider the empirical relation $p \sim \log(\rho)$, suggested by velocity dispersions in molecular cloud observations. Studies of Alfv\'{e}n waves in molecular clouds suggest $p \sim \rho^{1/2}$, which is also considered. Finally, we discuss observable characteristics of periodic structure in molecular cloud filaments modelled in this fashion and make comparisons with observations.
