CDNSWC, Bethesda, MD 20084-5000
In one approach, the response is given by the superposition of two terms. The first is merely the response of the unbeaded infinite string. The remaining terms involve elements of the first term mingled with parameters that describe the beads; e.g., the impedance that each bead presents to the infinite string and the position of that bead on the string. In the other approach, the bays (portions of the string that lie between adjacent beads) are treated as individual dynamic systems. These dynamic systems are coupled at the beads. The model is then a cascade of coupled one-dimensional dynamic systems. In this approach, the response is a vector composed of the response in each bay. The response vector is composed of the superposition of a direct response vector and a reverberant response vector. The reverberant response itself is composed of two distinct terms. The formalisms in the two approaches appear very different although they yield identical responses when subjected to the same external drive. This identity in the responses is illustrated by computations. Unlike the Sommerfeld--Watson transformation that relates the modal and the wave approaches to describing the response of a finite string, as yet, no analogeous analytical transformation is found to relate the two approaches of concern here.