The hyperbolic nature of the continuity equation in the melt spinning process causes several kinematic waves to travel in the spinline. Since different trawling waves possess different speeds, the system invariably has many characteristic times. This study computes the traveling times of these waves, finds their interrelationships, and then derives the criterion for the instability of periodic oscillation known as draw resonance The period of oscillation is greater than the fluid residence time, but equal to the time during which both the maximum and minimum spinline cross-sectional area waves travel in sequence from the spinneret to the take-up. The onset of draw resonance occurs when two successive unity-throughput waves are also able to travel the same distance within the same period of oscillation. This happens when the drawdown ratio takes on the critical value of 20.218 for the isothermal spinning of Newtonian fluids, agreeing with the value reported by earlier researchers.