The Coriolis force is a key ingredient of large scale dynamics of the Earth’s fluid core, where the waves that are the more important in the dynamo process and have periods on the order of the magnetic diffusion time are strongly influenced by rotation. An exact balance between the Coriolis and pressure forces set apart the geostrophic motions, which are readily accelerated by Lorentz and other forces. They can form fast Alfve´n waves, weakly influenced by magnetic diffusion. These transverse waves propagate in the directions perpendicular to the rotation axis. Their frequency is linearly dependent on the intensity of the

magnetic field transverse to the wave motions (Roberts, 1967). Their study, which was initiated by Braginsky (1970), has thus the potential to give precious information on the otherwise hidden magnetic field within the core (Zatman and Bloxham, 1998).