  Room temperature simulations of graphene have been performed as a function of
the mechanical tension of the layer. Finite-size effects are accurately
reproduced by an acoustic dispersion law for the out-of-plane vibrations that,
in the long-wave limit, behaves as $\rho\omega^2=\sigma k^2+\kappa k^4$. The
fluctuation tension $\sigma$ is finite ($\sim 0.1$ N/m) even when the external
mechanical tension vanishes. Transverse vibrations imply a duplicity in the
definition of the elastic constants of the layer, as observables related to the
real area of the surface may differ from those related to the in-plane
projected area. This duplicity explains the variability of experimental data on
the Young modulus of graphene based on electron spectroscopy, interferometric
profilometery, and indentation experiments.
