  Inspirals of neutron star-neutron star binaries are a promising source of
gravitational waves for gravitational wave detectors like LIGO. During the
inspiral, the tidal gravitational field of one of the stars can resonantly
excite internal modes of the other star, resulting in a phase shift in the
gravitational wave signal. We compute using a Fisher-matrix analysis how large
the phase shift must be in order to be detectable. For a $1.4 M_\odot, 1.4
M_\odot$ binary the result is $\sim 8.1, 2.9$ and 1.8 radians, for resonant
frequencies of $16, 32$ and 64 Hz. The measurement accuracies of the other
binary parameters are degraded by inclusion of the mode resonance effect.
