  We study the gravitational wave signal from eight new 3D core-collapse
supernova simulations. We show that the signal is dominated by $f$- and
$g$-mode oscillations of the protoneutron star and its frequency evolution
encodes the contraction rate of the latter, which, in turn, is known to depend
on the star's mass, on the equation of state, and on transport properties in
warm nuclear matter. A lower-frequency component of the signal, associated with
the standing accretion shock instability, is found in only one of our models.
Finally, we show that the energy radiated in gravitational waves is
proportional to the amount of turbulent energy accreted by the protoneutron
star.
