We study an initial boundary-value problem for a wave
equation with time-dependent sound speed. In the control problem,
we wish to determine a sound-speed function which damps the
vibration of the system. We consider the case where the sound speed can
take on only two values, and propose a simple control law. We show
that if the number of modes in the vibration is finite, and none of
the eigenfrequencies are repeated, the proposed
control law does lead to energy decay. We illustrate the rich behavior
of this problem in numerical examples.
