Measurement of ultrasonic dispersion by phase comparison of continuous harmonic waves

The method of phase comparison of continuous waves is applied to determine the dispersion relation, phase, and group velocities as a function of frequency of dispersive materials. A combination of the variable frequency method and the variable path-length method is found necessary to eliminate any uncertainty in the dispersion relation determination. Experiments are performed on specimens of various thickness. A constraint equation can be derived since the dispersion relation is unique and independent of the specimen thickness. This equation provides a procedure for determining the absolute number of wavelengths in the specimen. Measurements in unidirectional, fiber-reinforced boron–epoxy specimens show good agreement with results reported previously.