John J. McCoy
Xingfu Chen
School of Eng., The Catholic Univ. of America, Washington, DC 20064
At the ASA meeting in Salt Lake City, the windowed Fourier transform (WFT) was presented as providing the bases for phase-space representations for acoustic signals. For pulsed signal propagation in a one-dimensional waveguide, the sonogram---a description of the signal in a combined time/frequency space---was shown to be a representation of the signal that can be ``propagated.'' That is, this description of the acoustic signal as input to a propagation/scattering event provides the necessary information for determining this description at the completion of the event. It was further shown that propagation/scattering events are described when using this representation, by operators that might be termed, ``propagator-filters.'' Thus, the framework is an alternative, to both an ``impulse-response function'' and a ``transfer function,'' as quantitative descriptors of propagation/scattering events. The issue of the convenience of this descriptions is to be addressed. Using a moderately thick rod theory due to Mindlin and McNiven, this issue is addressed in the context of two propagation/scattering events for moderately broadband signals. One is the propagation of these signals through dispersive waveguides. The second in the phenomenon referred to as an end resonance. In our numerical experiment, this phenomenon applies when a broadband forcing is applied to the end of the rod. It manifests itself in a strongly frequency-dependent input of significant acoustic energy to a vibration confined to the end of the rod, a consequence of higher-order propagation modes below cut-off, with the subsequent ``leaking'' of this energy to the lowest order mode, which has no cut-off. The efficacy of the phase-space description is clearly evident.