When plucking a string, it is necessary to detect ``collisions''
between the plectrum and string. Also, more complete plucked-string
models will allow the string to ``buzz'' on the frets and ``slap''
against obstacles such as the fingerboard. For these reasons, it is
convenient to choose displacement waves for the waveguide
string model. The reflection and transmission filters for
displacement waves are the same as for velocity, namely,
and
.
As in the mass-string collision case, we obtain the one-filter
scattering-junction implementation shown in Fig.9.23. The filter
may now be digitized using the bilinear transform as
previously (§9.3.1).