  We investigate the propagation of acoustic singular surfaces, specifically,
linear shock waves and nonlinear acceleration waves, in a class of
inhomogeneous gases whose ambient mass density varies exponentially. Employing
the mathematical tools of singular surface theory, we first determine the
evolution of both the jump amplitudes and the locations/velocities of their
associated wave-fronts, along with a variety of related analytical results. We
then turn to what have become known as Krylov subspace spectral (KSS) methods
to numerically simulate the evolution of the full waveforms under
consideration. These are not only performed quite efficiently, since KSS allows
the use of `large' CFL numbers, but also quite accurately, in the sense of
capturing theoretically-predicted features of the solution profiles more
faithfully than other time-stepping methods, since KSS customizes the
computation of the components of the solution corresponding to the different
frequencies involved. The presentation concludes with a listing of possible,
acoustics-related, follow-on studies.
