  We develop a description of spin waves in a $3D$ quantum $XY$ antiferromagnet
(AFM) in terms of macroscopic variables, magnetization and N\'eel vector
densities. We consider a layered AFM with spins located on the honeycomb
lattice. In the discussed system, the spectrum of spin waves consists of four
modes, all well captured by our macroscopic description. The gapless mode of
the spin waves, i.e., magnons, is described by a system of equations, which has
a structure general for the Goldstone mode in AFMs. We demonstrate that the
parameters in the spin Hamiltonian can be evaluated by fitting the experimental
data with the results obtained for the four modes using the macroscopic
variable approach. The description of AFM in terms of macroscopic variables can
be easily extended to the case when the lattice of the magnetic substance is
deformed by an external strain or acoustic wave.
