Influence of geometric taper on the derivation of the true propagation coefficient using a three point method

We studied the effect of geometric taper on the derivation of the true propagation coefficient from three pressures determined 10 cm apart ('three-point method'). For this purpose the true propagation coefficients of a uniform latex tube (length 50 cm, outer diameter 12.73 mm, Womersley phase velocity 6.23-6.42 ms-1 (1-10 Hz), Womersley damping coefficient 0.05-0.14 m-1 (1-10 Hz) and of a tapered latex tube (length 50 cm, outer diameter varying from 15.88 to 9.45 mm, in the middle section with same properties as the uniform tube) were determined. The real part of the true propagation coefficient (the damping coefficient) was compared with apparent damping, and with the damping coefficient calculated using Womersley's theory. The imaginary part of the true propagation coefficient (the phase coefficient) was expressed in terms of phase velocity. True phase velocity was compared with measurements of apparent phase velocity, foot-to-foot velocity, and calculations of phase velocity parameters Womersley's theory and the Moens-Korteweg equation. The results show that in the uniform tube the three-point propagation coefficient is in agreement with all other estimates. Taper causes an error in the three-point propagation coefficient. At some frequencies the damping is reversed to amplification (values up to -2 m-1) and the phase velocity may be both overestimated or underestimated (up to 50%). The overestimation of true damping as reported in the literature cannot be explained from vessel taper.