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 denotes the string wave impedance.

The bridge velocity is given by

so that the

and the bridge

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 where and denote the string tension and slope, respectively.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University