This paper presents a numerical study of the sound generated by turbulent, premixed flames. Direct numerical simulations (DNS) of two round jet flames with equivalence ratios of 0.7 and 1.0 are first carried out. Single-step chemistry is employed to reduce the computational cost, and care is taken to resolve both the near and far fields and to avoid noise reflections at the outflow boundaries. Several significant features of these two flames are noted. These include the monopolar nature of the sound from both flames, the stoichiometric flame being significantly louder than the lean flame, the observed frequency of peak acoustic spectral amplitude being consistent with prior experimental studies and the importance of so-called ‘flame annihilation’ events as acoustic sources. A simple model that relates these observed annihilation events to the far-field sound is then proposed, demonstrating a surprisingly high degree of correlation with the far-field sound from the DNS. This model is consistent with earlier works that view a premixed turbulent flame as a distribution of acoustic sources, and provides a physical explanation for the well-known monopolar content of the sound radiated by premixed turbulent flames.