A *rigid termination* is the simplest case of a string termination. It
imposes the constraint that the string cannot move at all at the
termination. Let denote the transverse displacement of an ideal
vibrating string at time , with denoting position along the length
of the string. If we terminate a length ideal string at and
, we then have the ``boundary conditions''

where ``'' means ``identically equal to,'' i.e., equal for all .

The corresponding constraints on the sampled traveling waves are then

where is the time in samples to propagate from one end of the string to the other and back, or the total ``string loop'' delay. The loop delay is also equal to twice the number of spatial samples along the string. A digital simulation diagram for the rigidly terminated ideal string is shown in Fig. 4. A ``virtual pick-up'' is shown at the arbitrary location .

Note that rigid terminations reflect traveling displacement, velocity, or acceleration waves with a sign inversion. Slope or force waves reflect with no sign inversion. Since here we have displacement waves, the rigid terminations are inverting. This result may also be obtained from the reflection coefficient formula on the previous page by setting the terminating impedance to infinity in that formula.

Download swgt.pdf

Copyright ©

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

[Automatic-links disclaimer]