Despite the fact that quantitative experimental data have been available for more than forty years now, nematoacoustics still poses intriguing theoretical and experimental problems. In this paper, we prove that the main observed features of acoustic wave propagation through a nematic liquid crystal cell – namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation – can be explained by properly accounting for two fundamental features of the nematic response: anisotropy and relaxation. The latter concept – new in liquid crystal modelling – provides the first theoretical explanation of the structural relaxation process hypothesised long ago by Mullen and co-workers [Mullen et al., Phys. Rev. Lett., 1972, 28, 799]. We compare and contrast our proposal with an alternative theory where the liquid crystal is modelled as an anisotropic second-gradient fluid.