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''
The corresponding constraints on the sampled traveling waves are then
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.