  We study the long wavelength excitations in rotating QCD fluid in presence of
an external magnetic field at finite vector and axial charge densities. We
consider the fluctuations of vector and axial charge currents coupled to energy
and momentum fluctuations and compute the $SO(3)$ covariant dispersion
relations of the six corresponding hydrodynamic modes. Among them, there are
always two scalar Chiral Magnetic-Vortical-Heat (CMVH) waves; In the absence of
magnetic field (vorticity) these waves reduce to CVH (CMH) waves. While CMVH
waves are the mixed of CMH and CVH waves, they have generally different
velocities compared to the sum of velocities of the latter waves. The other
four modes, which are made out of scalar-vector fluctuations, are mixed
Sound-Alfv\'en waves. We show that in the direction parallel to both magnetic
field and vorticity, these four modes are the two ordinary sound modes together
with two Chiral Alfv\'en waves (CAW).
