Individual longitudinal Pochhammer-Chree modes in observed experimental signals

Plane waves and the Pochhammer-Chree solutions are both used to describe longitudinal axially symmetric wave propagation in solid cylinders. For interpreting experiments, plane waves provide a physical explanation for signals with multiple distinct arrivals. For signals without distinct arrivals the Pochhammer-Chree solutions are often used for interpretation, but the complexity of the solutions makes accurate interpretations difficult. This paper discusses some previous misinterpretations and shows how the Pochhammer-Chree solutions relate to signals with and without distinct arrivals by considering more than just the dispersion curves from the solutions.