Ultrasonic dispersion in suspensions and solids: A study of fundamental dynamics and the Kramers-Kronig relations

This thesis is concerned with the measurement of the phase velocity and attenuation coefficient for ultrasonic waves as well as the connections between dispersion (i.e., the variation of phase velocity with frequency) and attenuation. In the course of this work, the relationships between the attenuation coefficient and phase velocity for solids and suspensions are investigated from the standpoint of the fundamental dynamics specific to each of these systems. The results of the measurements are analyzed in the context of the theory. Kramers-Kronig relations relevant to ultrasonic wave propagation are derived. These relations are applied to the results to study the more general relationship between dispersion and attenuation that arises from causality. The issues that arise when applying the relations to finite-bandwidth data are explored. Good agreement between the measured phase velocities and attenuation coefficients and their Kramers-Kronig predictions is obtained.