This paper describes a novel approach for analyzing ultrasonic signals to permit an experimental determination of the relations between elastic wave phenomena and the properties of a source of sound in a material. It is demonstrated that an adaptive learning system comprising an associative memory can be used to map source and waveform data and vice versa with the auto- and cross-correlation portions of the associative memory. Experiments are described which utilize such an adaptive system, running on a laboratory minicomputer, to process the data from a transient ultrasonic pulse in a plate specimen. In the learning procedure, the system learns from experimental pattern vectors, which are formed from the ultrasonic waveforms and, in this paper, encoded information about the source. The source characteristics are recovered by the recall procedure from detected ultrasonic signals and vice versa. Furthermore, from the discrepancy between the presented and the learned signals, the changes in the wave phenomenon, corresponding, for example, to changes in the boundary conditions of a specimen, can be determined.