An ultrasonic frequency sweep interferometer for liquids at high temperature: 1. Acoustic model

[1] A general acoustic model for a frequency sweep rod-liquid-rod interferometer applicable to high-temperature silicate liquids is presented. The wave propagations in the acoustic model are solved according to the accurate elastic wave equation and the acoustic wave equation. The solutions indicate that when a pulsed wave is sent down a buffer rod, which is partially immersed in a silicate liquid, the return signal consists of a series of plane waves (mirror reflections from the liquid) and two series of interfering pulses (modes A and B), which are propagating disturbances guided by the cylindrical surface of the upper rod. The acoustic model gives mathematical expressions for the time delays between the various interfering pulses and between the mirror reflections, which are predicted to vary according to the material and dimensions of the upper buffer rod and liquid. These predictions are verified by experiments on molybdenum and aluminum rods of varying dimensions in air, water, and silicate liquid. These results demonstrate that mirror reflections from the liquid can be isolated from the interfering pulses in the return signal by appropriate choice of the dimensions and material of the upper rod. This theoretical model provides a critical foundation for construction of an acoustic interferometer that is uniquely able to measure relaxed sound speeds in silicate liquids at high temperature and high pressure by the frequency sweep method.