A so-called Kelly-Lochbaum scattering junction [17,29] can be introduced into the string at the fourth sample by the following perturbation
A single time-varying scattering junction provides a reasonable model for plucking, striking, or bowing a string at a point. Several adjacent scattering junctions can model a distributed interaction, such as a piano hammer, finger, or finite-width bow spanning several string samples.
Note that scattering junctions separated by one spatial sample (as typical in ``digital waveguide filters'' ) will couple the formerly independent subgrids. If scattering junctions are confined to one subgrid, they are separated by two samples of delay instead of one, resulting in round-trip transfer functions of the form (as occurs in the digital waveguide mesh). In the context of a half-rate staggered-grid scheme, they can provide general IIR filtering in the form of a ladder digital filter [17,29].