In summary, we have characterized the mass on the string in terms of its reflectance and transmittance from either string. For force waves, we have outgoing waves given by
in terms of the incoming waves and , the force reflectance , and the force transmittance . We may say that the mass creates a dynamic scattering junction on the string. (If there were no dependency on , such as when a dashpot is affixed to the string, we would simply call it a scattering junction.) The above form of the dynamic scattering junction is analogous to the Kelly-Lochbaum scattering junction (§C.8.4). The general relation can be used to simplify the Kelly-Lochbaum form to a one-filter scattering junction analogous to the one-multiply scattering junction (§C.8.5):
The one-filter form follows from the observation that appears in both computations, and therefore need only be implemented once:
This structure is diagrammed in Fig.9.20.
Again, the above results follow immediately from the more general formulation of §C.12.