Dispersion relation for composite waveguide with application to measurements in acoustic impedance tube

The amplitude and phase of the reflected wave in an acoustic impedance tube are related to the speed and attenuation of sound in the sample material. It is usually assumed without justification that the pertinent propagation speed is the dilatational speed. To investigate this an analysis was performed on the propagation of axially symmetric waves in a composite waveguide consisting of a solid cylinder immersed in a fluid bounded by a concentric rigid wall. The roots of the ensuing dispersion relation were computed for various materials. The results show that the sound speed in the waveguide may vary between the dilatational and the bar speed, depending on the size of the fluid gap and the elastic properties of solid and fluid. Experiments are designed to verify this effect by changing the sample radius and by excluding the fluid from the gap between sample and wall.