Low-frequency propagation modes in a liquid-filled elastic tube waveguide

Abstract

Axisymmetric propagation in a liquid-filled elastic tube waveguide is considered, with emphasis on the two modes existing down to zero frequency. Previous work by Del Grosso is used as the basis of the theoretical description of modal phase velocities and particle displacement profiles in such waveguides. It is shown that certain combinations of material properties can produce a mode which, in the zero frequency limit, has plane-wave motion in the liquid. Two examples of waveguides with very different wall compliance, aluminum/water and PVC/water, are studied numerically and experimentally. Numerical calculations are used to show the frequency dependence of phase velocity in all waveguide modes and the radial dependence of complex particle displacement amplitude in the two low-frequency modes (ET0 and ET1). Contrasting behavior in the two waveguides is seen—approximate plane-wave motion in the liquid occurs in the ET0 mode of the aluminum/water waveguide, but in the ET1 mode of the PVC/water waveguide. Experimental measurements of the frequency dependence of phase velocity in the ET0 and ET1 modes of these waveguides are also presented. Good agreement with numerical predictions is obtained in both cases, although experimental difficulties more severely limit the frequency range of measurement in the PVC/water waveguide.