Gravitational waves (GWs) from inspiralling neutron stars afford us a unique opportunity to infer the as-of-yet unknown equation of state of cold hadronic matter at supranuclear densities. The dominant matter effects are due to the stars response to their companions tidal field, leaving a characteristic imprint in the emitted GW signal. This unique signature allows us to constrain the neutron star equation of state. At GW frequencies above $gtrsim 800$Hz, however, subdominant tidal effects known as dynamical tides become important. In this letter, we demonstrate that neglecting dynamical tidal effects associated with the fundamental ($f$-) mode leads to large systematic biases in the measured tidal deformability of the stars and hence in the inferred neutron star equation of state. Importantly, we find that $f$-mode dynamical tides will already be relevant for Advanced LIGOs and Virgos fifth observing run ($sim 2025$) -- neglecting dynamical tides can lead to errors on the neutron radius of $mathcal{O}(1{rm km})$, with dramatic implications for the measurement of the equation of state. Our results demonstrate that the accurate modelling of subdominant tidal effects beyond the adiabatic limit will be crucial to perform accurate measurements of the neutron star equation of state in upcoming GW observations.
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