  Short-duration gamma-ray bursts (SGRBs) are widely believed to be powered by
the mergers of compact binaries, such as binary neutron stars or possibly
neutron star-black hole binaries. Though the prospect of detecting SGRBs with
gravitational wave (GW) signals by the advanced Laser Interferometer
Gravitational-Wave Observatory (LIGO)/VIRGO network is promising, no known SGRB
has been found within the expected advanced LIGO/VIRGO sensitivity range for
binary neutron star systems. We find, however, that the two long-short GRBs
(GRB 060505 and GRB 060614) may be within the horizon of advanced GW detectors.
In the upcoming era of GW astronomy, the merger origin of some long-short GRBs,
as favored by the macronova signature displayed in GRB 060614, can be
unambiguously tested. The model-dependent time lags between the merger and the
onset of the prompt emission of the GRB are estimated. The comparison of such
time lags between model predictions and the real data expected in the era of
the GW astronomy would be helpful in revealing the physical processes taking
place at the central engine (including the launch of the relativistic outflow,
the emergence of the outflow from the dense material ejected during the merger,
and the radiation of gamma rays). We also show that the speed of GWs, with or
without a simultaneous test of Einstein's equivalence principle, can be
directly measured to an accuracy of $\sim 3\times 10^{-8}~{\rm cm~s^{-1}}$ or
even better in the advanced LIGO/VIRGO era. The Astrophysical Journal, Volume
