We use data from the Cluster satellites to study waves in the frequency range of ~2--150 Hz at the magnetopause. In addition to broad band wave turbulence we identify lower hybrid drift waves and whistler waves. Wave amplitudes maximize within narrow current sheets that are associated with density gradients and electron beams and that can be the separatrices of the reconnection. The dispersion properties of lower hybrid drift waves are studied using interferometric measurements of electric field. A direct estimate of the wave role in the particle diffusion across the magnetopause shows that their importance is limited only to the narrow current sheet.