We perform first-principles calculations to investigate liquid iron-sulfur alloys (Fe, Fe56S8, Fe52S12, and Fe48S16) under high-pressure and high-temperature (150-300 GPa and 4000-6000 K) conditions corresponding to the Earth's outer core. Considering only the density profile, the best match with the preliminary reference Earth model is by liquid Fe-14 wt % S (Fe50S14), assuming sulfur is the only light element. However, its bulk sound velocity is too high, in particular in the deep outer core, suggesting that another light component such as oxygen is required. An experimental check using inelastic X-ray scattering shows good agreement with the calculations. In addition, a present study demonstrates that the Birch's law does not hold for liquid iron-sulfur alloy, consistent with a previous report on pure liquid iron.