We assume that the dipole wobble excites Alfv¿n waves which propagate outward along the field lines. The plasma density in the outer Jovian magnetosphere is derived from the amplitude of such diurnal magnetic field variations, as measured by Pioneer 10. The number density obtained by this method is of the same order of magnitude as that derived from pressure balance, the dynamic pressure of the outflow being neglected. This result casts some doubt on the existence of a super-Alfv¿nic outflow in the Jovian magnetosphere.