Weak pressure wave in a gas filled elastic tube

The propagation of a small but finite shock disturbance through gas contained within a cylindrical tube is examined theoretically for the case where both the hoop elasticity and radial inertia of the tube are taken into account. Governing equations so derived are found to admit a non-dispersive wave of variable pressure behind the advancing shock front in direct contrast with the situation existing for an initially sharp-fronted infinitesimal disturbance where no steady wave form is possible. Detailed calculations are carried out for the case where the gas filling the tube is air. Results show that increases in either the tube or shock strength are sufficient to make the pressure distribution behind the wave front approach that which would exist in a rigid tube under similar conditions.