  We probe the collective magnetic modes of La$_2$CuO$_4$ (LCO) and underdoped
La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) by momentum resolved Resonant Inelastic X-ray
Scattering (RIXS) at the Cu $L_3$ edge. In LCO the single magnon dispersion
measured by RIXS coincides with the one determined by inelastic neutron
scattering. For LSCO the spin dynamics shows a branch dispersing up to
$\sim$400 meV coexisting with a branch at lower energy. Only the latter has
been observed with neutrons so far and is considered a key signature of doped
cuprates. The presence of the high-energy branch indicates that LSCO is in a
dynamic inhomogeneous spin state.
