The UN regulation R51-03 on vehicle sound emissions enters its third phase in July 2024, with the challenging level of 68 dB(A) to achieve for most of passenger cars and light commercial vehicles. The Lurban indicator, as calculated in the regulation, is a weighted average of acceleration and constant rolling speed tests. Thus, the tire sound emissions represent by far the first contributor to the vehicle compliance. Therefore, it is crucial to understand how tire sound changes under the effects of speed, acceleration, or temperature. In this paper, a study on tire sound behavior is presented. It is based on repeated measurements of pass-by sound emissions of a set of tires, under various conditions of speed, acceleration, and ambient temperature. Among a huge variety of tire sound emission models, a regression algorithm is used to identify the model that fits the best to the measured tire sound emissions data. This tire sound emission model is then used to foresee the impacts of Regulation R51-03 updates, aiming at reducing the uncertainties induced by temperature and test track discrepancies, by correcting the tire sound contribution. The effects of this correction on the uncertainties can be anticipated by the model.