  We study the universality in gravitational waves emitted from non-rotating
neutron stars characterized by different equations of state (EOS). We find that
the quasi-normal mode frequencies of such waves, including the $w$-modes and
the $f$-mode, display similar universal scaling behaviours that hold for most
EOS. Such behaviours are shown to stem from the mathematical structure of the
axial and the polar gravitational wave equations, and the fact that the mass
distribution function can be approximated by a cubic-quintic polynomial in
radius. As a benchmark for other realistic neutron stars, a simple model of
neutron stars is adopted here to reproduce the pulsation frequencies and the
generic scaling behaviours mentioned above with good accuracy.
