Using one-dimensional waveguide resonators to measure phase velocities in bubbly liquids.

Resonator techniques can be successfully used to extract effective medium properties from dispersive materials. However, in some cases the dispersion can cause modes to repeat. If repeated modes are not taken into account, the useful range of the resonator technique is limited. A resonance tube containing tethered balloons is used to create a dispersive effective medium. Resonator measurements show that modes do repeat. Direct measurement of the mode shapes allows exploitation of all longitudinal radially symmetric modes and expands the frequency range of the technique. A theoretical model is also used to predict when modes repeat. For the presented data set this method increases the measurement range from below 160 Hz to 3000 Hz excluding the stop band where resonances are damped. A means to account for non-ideal resonator boundary conditions often found in highly dispersive systems is discussed.