It is instructive to study the ``waveguide equivalent circuit'' of the simple case of a rigidly terminated ideal string with its left endpoint being moved by an external force, as shown in Fig.6.4. This case is relevant to bowed strings (§9.6) since, during time intervals in which the bow and string are stuck together, the bow provides a termination that divides the string into two largely isolated segments. The bow can therefore be regarded as a moving termination during ``sticking''.
Referring to Fig.6.4, the left termination of the
rigidly terminated ideal string is set in motion at time
with a
constant velocity
. From Eq.(6.5), the wave impedance of
the ideal string is
, where
is tension and
is mass density. Therefore, the upward force applied by the moving
termination is initially
. At time
, the
traveling disturbance reaches a distance
from
along the
string. Note that the string slope at the moving termination is given
by
, which derives
the fact that force waves are minus tension times slope waves.
(See §C.7.2 for a fuller discussion.)