  Supercritical state has been viewed as an intermediate state between gases
and liquids with largely unknown physical properties. Here, we address the
important ability of supercritical fluids to sustain collective excitations. We
directly study propagating modes on the basis of correlation functions
calculated from extensive molecular dynamics simulations, and find that the
supercritical system sustains propagating solid-like transverse modes below the
Frenkel line but becomes devoid of transverse modes above the line where it
supports longitudinal modes only. Important thermodynamic implications of this
finding are discussed. We directly detect positive sound dispersion (PSD) below
the Frenkel line where transverse modes are operative, quantitatively explain
its magnitude on the basis of transverse and longitudinal velocities. PSD
disappears above the Frenkel line which therefore demarcates the supercritical
phase diagram into two areas where PSD does and does not operate.
