  The long life-time of the quark-gluon plasma likely to be created in the
relativistic heavy ion collisions at RHIC and LHC energies renders it sensitive
to the details of the equation of state of the quark-matter. We show that the
$p_T$ dependence of the survival probability of the directly produced $J/\psi$
at RHIC energies and that of the directly produced $\Upsilon$ at LHC energies
is quite sensitive to the speed of sound in the quark matter, which relates the
pressure and the energy density of the plasma. The transverse expansion of the
plasma is shown to strongly affect the $J/\psi$ suppression at LHC energies.
