  Black holes are superb sources of gravitational wave signals, for example
when they are born in stellar collapse. We explore the subtleties that may
emerge if mass accretion events increase significantly the mass of the black
hole during its gravitational wave emission. We find the familiar
damped-oscillatory radiative decay but now both decay rate and frequencies are
modulated by the mass accretion rate. Any appreciable increase in the horizon
mass during emission reflects on the instantaneous signal frequency, which
shows a prominent negative branch in the dot[f](f) evolution diagram. The
features of the frequency evolution pattern reveal key properties of the
accretion event, such as the total accreted mass and the accretion rate. For
slow accretion rates the frequency evolution follows verbatim the accretion
rate, as expected from dimensional arguments. In view of the possibility of
detection of black hole ``ringing'' by the upcoming gravitational wave
experiments, the deciphering of the late time frequency dynamics may provide
direct insight into otherwise obscured aspects of the black hole birth process.
