The paper presents a simplified theoretical analysis of the hydrodynamics of a two-dimensional hexatic phase, based on the more detailed theory of Zippelius et al (Zippelius A, Halperin B I and Nelson D R 1980 Phys. Rev. B 22 2514). The crossover, with increasing frequency, of the hydrodynamic modes from those typical of a hexatic phase to those typical of a solid is studied in a free-dislocation model, and it is discussed whether in practice this crossover is likely to be strongly affected by the presence of dislocation pairs. The theory is applied to a two-dimensional sheet of ions trapped below the free surface of superfluid helium, and the effect of both a magnetic field and a finite ionic mobility is examined. The extent to which this system offers the possibility of experimental verification of the theory is discussed.