Ultrasonic Dispersion (AV/V) Determined from Mechanical Resonance Frequency Shifts

With standing wave ultrasonic techniques, small changes in phase velocity which result from changes in some external parameter (e.g., temperature or magnetic field) have traditionally been determined by observing shifts in the mechanical resonance frequency of a composite resonator. Some previous investigators have assumed that the fractional change in velocity is equal to the fractional change in frequency. We discuss quantitatively the errors involved in such an approach, showing that it leads to substantial inaccuracies when the loading effect of the transducer(s) cannot be neglected. Substantially improved formulas for determining the dispersion are presented and one of these is shown to be much more accurate than all previous approximations. The results of simulated and actual experiments over wide ranges of dispersion, transducer loading parameter, and frequency are analyzed in order to compare the errors inherent in the various approximations.