Wave Propagation in a Fluid‐Filled Tube

A circular cylindrical viscoelastic solid tube filled with a compressible viscous fluid is considered. The outer surface of the tube is assumed to be constrained so that it cannot move freely. Axially symmetric wave solutions are obtained for the linearized equations governing the motion of the fluid and the solid. The solutions lead to a complicated transcendental dispersion equation relating the wave frequency and the propagation constant. This equation is simplified by taking the fluid to be inviscid and the tube to be thin. Then it is studied by both analytical and numerical means. Formulas and graphs are given for the propagation constant, the phase velocity, the group velocity, etc., as functions of the frequency for various sets of parameter values. There are infinitely many modes of propagation, two of which are “tube modes” and the rest of which are acoustic modes. The case of a viscous fluid and a tube of any thickness are to be treated in a subsequent paper.