  The speed of sound ($c_s$) is studied to understand the hydrodynamical
evolution of the matter created in heavy-ion collisions. The quark-gluon plasma
(QGP) formed in heavy-ion collisions evolves from an initial QGP to the
hadronic phase via a possible mixed phase. Due to the system expansion in a
first order phase transition scenario, the speed of sound reduces to zero as
the specific heat diverges. We study the speed of sound for systems, which
deviate from a thermalized Boltzmann distribution using non-extensive Tsallis
statistics. In the present work, we calculate the speed of sound as a function
of temperature for different $q$-values for a hadron resonance gas. We observe
a similar mass cut-off behaviour in non-extensive case for $c^{2}_s$ by
including heavier particles, as is observed in the case of a hadron resonance
gas following equilibrium statistics. Also, we explicitly present that the
temperature where the mass cut-off starts, varies with the $q$-parameter which
hints at a relation between the degree of non-equilibrium and the limiting
temperature of the system. It is shown that for values of $q$ above
approximately 1.13 all criticality disappear in the speed of sound, i.e. the
decrease in the value of the speed of sound, observed at lower values of $q$,
disappears completely.
