  In relativistic hydrodynamics with spin, following de Groot--van Leeuwen--van
Weert's energy-momentum and spin tensor definitions, we analyze the propagation
of spin degrees of freedom. We deduce an analytical formula for spin wave
velocity, finding that it approaches half the speed of light in the
ultra-relativistic limit. Only transverse degrees of freedom propagate, similar
to electromagnetic waves. Additionally, we explore dissipative effects and
determine the damping coefficients for Maxwell-J\"uttner statistics.
