Experimental Verification of Negative Phase Velocity in Layered Media
Stress-wave propagation is a generally dispersive phenomenon in elastic layered and periodic media. In the frequency ranges where propagation is possible, pass bands, the wave speed is a function of frequency. In the rest of the frequency spectrum, stop bands, wave propagation is impossible. The band structure of a periodic medium can be calculated using a variety of analytical and computational methods. In this paper we present such calculations for a simple layered sample. The wave propagation through the sample was measured using an ultrasonic experimental setup. The band structure was shown to agree with numerical and analytical predictions. The group velocity was calculated based on time of travel of the pulse through samples with different thicknesses. A measure of energy velocity was introduced and measured based on the mechanical power flux through samples. The phase velocity was measured based on the phase difference observed among the transmitted waves through different thicknesses. It is shown that the phase and group velocity become anti-parallel within specific pass bands as predicted based on theory.
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