Fundamental aspects of pulse phase-locked loop technology-based methods for measurement of ultrasonic velocity

A new instrument based on a constant frequency pulse phase-locked loop concept has been developed to accurately measure the ultrasonic phase velocity in condensed matter. Measurements of the sound velocity in ultrapure water are reported in which both damped and undamped transducers are used with the instrument together with reflectors of various thicknesses placed in the sound propagation path. An analysis of measurements made with the new instrument and similar measurements, taken under identical experimental conditions, using a popular variable frequency pulsed-phase-locked loop instrument is reported. Uncertainties in both measurement systems are analyzed and discussed. A method for measuring inherent phase shifts, not addressed by previous investigators, within the variable frequency pulsed phase-locked loop system and a derivation of the equations that govern the overall use of variable frequency systems using phase-sensitive comparisons are presented. The effects of a finite pulse length on the measurements of phase velocity in dispersive media are addressed in detail.