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

Abstract

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 degrees) into the linear model. Attenuation per wavelength computed with the three-point methods 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.