  Gravitational-wave signals from coalescing binary neutron stars can yield
important information about the properties of nuclear-matter equation of state
from the early part of the signal through tidal effects to the properties and
oscillation frequencies of the merger product. We investigate a direct link
between the properties of isolated neutron stars and their merger, by comparing
the frequency of the fundamental oscillation mode ($f$-mode) of neutron stars
with the gravitational-wave frequency associated with the merger of two neutron
stars. We calculate the quadrupolar ($l=2$) $f$-mode oscillation ($f_{2f}$) of
non-rotating and rotating neutron stars using a nonlinear hydrodynamics code in
the conformally-flat approximation and obtain the gravitational-wave frequency
associated with the peak amplitude ($f_{\rm max}$) of binary-neutron stars from
a set of publicly available simulations. We find that $f_{\rm max}$ and
$f_{2f}$ differ by about 1\%, on average, across forty-five equal-mass systems
with different total mass and equations of state. Assuming that the
gravitational-wave frequency is still approximately equal to twice the orbital
frequency $\Omega$ near the merger, the result indicates that the condition for
tidal resonance $|m|\Omega = f_{2f}$ is satisfied to high accuracy near the
merger, where $m=2$ is the azimuthal quantum number. Moreover, the well
established universal relation between $f_{\rm max}$ and the tidal
deformability of equal-mass binary systems can now be explained by a similar
relation between $f_{2f}$ and the tidal deformability of isolated neutron
stars, which has been demonstrated to be associated with the nearly
incompressible properties of neutron stars. Our findings suggest that it is
possible to relate the gravitational-wave signal at the merger of a binary
neutron star system directly to the fundamental oscillation modes and the mass
ratio.
