Consider the special case of a reflection and transmission at a
yielding termination, or ``bridge'', of an ideal vibrating
string on its right end, as shown in Fig.C.28. Denote the
incident and reflected velocity waves by
and
,
respectively, and similarly denote the force-wave components by
and
. Finally, denote the velocity of the
termination itself by
, and its force-wave
reflectance by
where
The bridge velocity is given by
so that the bridge velocity transmittance is given by
and the bridge force transmittance is given by
where the bridge force is defined as ``up'' so that it is given for small displacements by the string tension times minus the string slope at the bridge. (Recall from §C.7.2 that force waves on the string are defined by