  We investigate the amplitude modulation of acoustic waves in accelerating
flows, a problem that is still not fully understood, but essential to many
technical applications, ranging from medical imaging to acoustic remote
sensing. The proposed modeling framework is based on a convective form of the
Kuznetsov equation, which incorporates the background flow field and is solved
numerically by a finite-difference method. Using acoustic black and white hole
analogues as model systems, we identify a modulation of the wave amplitude,
that is shown to be driven by the divergence/convergence of the acoustic wave
characteristics in an accelerating/decelerating flow, and which is distinct
from the convective amplification accompanying an acoustic emitter moving at a
constant velocity. To rationalize the observed amplitude modulation, a
leading-order model is derived from first principles, leveraging a similarity
of the wave characteristics and the wave amplitude with respect to a modified
Helmholtz number. This leading-order model may serve as a basis for the
numerical prediction and analysis of the behavior of acoustic waves in
accelerating flows, by taking advantage of the notion that any accelerating
flow field can be described locally as a virtual acoustic black or white hole.
