Small amplitude axisymmetric sinusoidal waves in an orthotropic, viscoelastic, rough pipe carrying a compressible liquid in turbulent flow are considered. The wall behaviour is described after Kuiken (1984) and the turbulent flow is described by means of an eddy viscosity profile model. We use a four-region model presented by Ohmi & Usui (1976), slightly modified in order to take into account the wall roughness. A one-dimensional dispersion equation is derived, which can predict the two lowest modes of propagation for waves of low frequency. The effects of Reynolds number, pipe roughness or wall viscoelasticity on phase velocity and attenuation factor are presented.