  We theoretically investigate the critical behavior of second sound mode in a
harmonically trapped ultracold atomic Fermi gas with resonant interactions.
Near the superfluid phase transition with critical temperature $T_{c}$, the
frequency or the sound velocity of second sound mode depends crucially on the
critical exponent $\beta$ of superfluid fraction. In an isotropic harmonic
trap, we predict that the mode frequency diverges like
$(1-T/T_{c})^{\beta-1/2}$ when $\beta<1/2$. In a highly elongated trap, the
speed of second sound reduces by a factor $1/\sqrt{2\beta+1}$ from that in a
homogeneous three-dimensional superfluid. Our prediction could be readily
tested by measurements of second sound wave propagation in a setup such as that
exploited by Sidorenkov \textit{et al.} {[}Nature \textbf{498}, 78 (2013){]}
for resonantly interacting lithium-6 atoms, once the experimental precision is
improved.
