Wave Propagation in the Silicon Tube: Comparison of the Two-Point and Three-Point Pressure Methods

The values of the propagation coefficient measured on a silicon rubber tube in the frequency range 1–15 Hz were compared, using four different equations. The first formula is based on three simultaneous pressure measurements performed at equidistant points; the remaining three equations are original, and make use of only two of the three pressure measurements together with a no-flow condition at the terminal tube section.

The results of our trials demonstrate that the experimental phase velocity, obtained with all equations, settles at a value about 25% in excess of the theoretical one computed with a classic linear mathematical model. This result may be explained by an increase in the dynamical Young modulus with respect to that measured in static conditions. However, the three-point method introduces great errors in the results in the frequency range 11–14 Hz where the spectrum of the second signal becomes minimum.

In all cases, the experimental value of attenuation per wavelength at mid-high frequencies is greater than the theoretical one valid for a purely elastic tube. The attenuation values obtained with the two-point method can be explained by introducing a small contribution of wall viscoelasticity (2–3°) into the linear model. Attenuation per wavelength computed with the three-point method turns out about threefold that computed with each of the two-point formulas. This result supports the idea that the accuracy of the three-point method may be insufficient to achieve correct estimation of wave attenuation, especially when the distance between transducers is small compared to wavelength.