Wave Propagation in Fluid-Filled Tubes

Abstract

The mechanism of wave propagation in fluid-filled tubes is well known for tube walls having large radial impedances; in this case, energy propagates in discrete modes whose order numbers are defined as the number of nodal circles in their pressure distributions. The propagation phenomena are reviewed here for wall reactance values extending from −∞ through the pressure release condition characterizing tube resonance to +∞. It is shown that the modes lose their identity in this process, viz., that a transition occurs from the nth to the (n−1)th mode as the tube wall changes from a slightly massive to a slightly stiffness-controlled condition. A paradoxical situation arises in that the propagation mechanism of a given mode in a pressure release tube depends upon whether this condition is approached through positive or negative reactance values; this difficulty is purely semantic and connected with the mode number definition. All modes, including the zero mode in massive tubes, have cut-off frequencies, determined by the wall reactance. For the zero mode in slightly stiffness-controlled tubes, wave propagation is a skin effect in the fluid layer nearest the wall, buut distingished from R thayighele waves by absence of a nodal circle.