If you have ten degrees of freedom, you obtain 20 eigenmodes. Out of those 20, ten eigenvectors describe modes that propagate (or decay) in the positive direction (say +x), while the other ten modes correspond to modes that propagate or decay in the negative direction.
How many of those ten modes per direction are propagating ones depends on the frequency. You can look at the dispersion diagrams to see how many propagating modes you would expect at a given frequency. If there is no damping, the propagating modes are represented by real wavenumbers.