  It is proved that the acoustic-type dispersion of bending mode in graphene is
generated by the fluctuation interaction between in-plane and out-of-plane
terms in the free energy arising with account of non-linear components in the
graphene strain tensor. In doing so we use an original adiabatic approximation
based on the alleged (confirmed a posteriori) significant difference of sound
speeds for in-plane and bending modes. The explicit expression for the bending
sound speed depending only on the graphene mass density, in-plane elastic
constants and temperature is deduced as well as the characteristics of the
microscopic corrugations of graphene. The obtained results are in good
quantitative agreement with the data of real experiments and computer
simulations.
