Abstract The theory of the sibilant fricative [s] is formulated and solved as a mathematical problem of aeroacoustics. Air is forced through the constriction between the tongue blade and the hard palate by intra-oral pressure, forming a jet that strikes the upper incisors and leaves the mouth through a gap between the upper and lower incisors. The principal source of sound is the ‘diffraction’ of jet turbulence pressure fluctuations by the incisors. The spectrum of these pressure fluctuations incident on the teeth is modelled analytically using an empirical formula adapted from turbulent boundary-layer theory. Predictions are made about the far field acoustic pressure spectrum with reference to measured and estimated values of vocal tract dimensions and intra-oral pressure. Predicted spectra compare well with observations. The principal spectral peaks are determined by vocal tract physiology anterior to the tongue–palate constriction. The theory furnishes the first correct prediction of the dependence of the overall sound pressure level on the intra-oral pressure.