Literature shows a lack of works based on non-invasive methods for computing the propagation coefficient γ, a complex number related to dynamic vascular properties. Its imaginary part is inversely related to the wave speed C through the relationship $C=\omega/{\rm Im}(\gamma)$, while its real part a, called attenuation, represents loss of pulse energy per unit of length. In this work an expression is derived giving the propagation coefficient when assuming a pulsatile flow through a viscoelastic vessel. The effects of physical and geometrical parameters of the tube are then studied. In particular, the effects of increasing the reflection coefficient, on the determination of the propagation coefficient are investigated in a first step. In a second step, we simulate a variation of tube length under physiological conditions. The method developed here is based on the knowledge of instantaneous velocity and radius values at only two sites. It takes into account the presence of a reflection site of unknown reflection coefficient, localised in the distal end of the vessel. The values of wave speed and attenuation obtained with this method are in a good agreement with the theory. This method has the advantage to be usable for small portions of the arterial tree.