  The recent detection of gravitational waves (GWs) from the neutron star
binary inspiral GW170817 has opened a unique avenue to probe matter and
fundamental interactions in previously unexplored regimes. Extracting
information on neutron star matter from the observed GWs requires robust and
computationally efficient theoretical waveform models. We develop an
approximate frequency-domain GW phase model of a main GW signature of matter:
dynamic tides associated with the neutron stars' fundamental oscillation modes
($f$-modes). We focus on nonspinning objects on circular orbits and demonstrate
that, despite its mathematical simplicity, the new "$f$-mode tidal" (fmtidal)
model is in good agreement with the effective-one-body dynamical tides model up
to GW frequencies of $\gtrsim 1$ kHz and gives physical meaning to part of the
phenomenology captured in tidal models tuned to numerical-relativity. The
advantages of the fmtidal model are that it makes explicit the dependence of
the GW phasing on the characteristic equation-of-state parameters, i.e., tidal
deformabilities and $f$-mode frequencies; it is computationally efficient; and
it can readily be added to any frequency-domain baseline waveform. The fmtidal
model is easily amenable to future improvements and provides the means for a
first step towards independently measuring additional fundamental properties of
neutron star matter beyond the tidal deformability as well as performing novel
tests of general relativity from GW observations.
