Analysis of Propagation of Ultrasonic Pulses in Dispersive Media Using Group Delay Concept

Abstract

A new analytical technique of the propagation of ultrasonic pulses in dispersive or nondispersive media is proposed. First, on the basis of the concept of group delay, we develop the theory as follows: (1) group delay is deduced directly from the Fourier transform of waveforms, and (2) cross-correlation theory is extended to a total measurement system which may include, for example, a sensor, couplant, amplifier, and A/D converter. Then, a fundamental result that the group delay between wave motions generated in a medium is exactly the same as that of corresponding waveforms observed by an observer is obtained. Next, this result is applied to improve the conventional pulse-echo method, and it is shown that by preparing two specimens of the same material but with different thicknesses, correct group delay in propagation can be obtained even though no physical or mechanical constants of the couplant or sensor may be known. In order to apply the results to the pulse-echo method, measurements of phase and group velocity in synthetic fused silica were also attempted.