The magnetic excitations in multiferroic TbMnO3 have been studied by inelastic neutron scattering in the spiral and sinusoidally ordered phases. At the incommensurate magnetic zone center of the spiral phase, we find three low-lying magnons whose character has been fully determined using neutron-polarization analysis. The excitation at the lowest energy is the sliding mode of the spiral, and two modes at 1.1 and 2.5 meV correspond to rotations of the spiral rotation plane. These latter modes are expected to couple to the electric polarization. The 2.5 meV mode is in perfect agreement with recent infrared-spectroscopy data giving strong support to its interpretation as a hybridized phonon-magnon excitation.