[en] In this work we consider the theory of sound amplification under the hopping perpendicular transport in a semiconductor superlattice. It is shown that phonons propagating close to the axis of superlattice demonstrate high values of the increment, exceeding the rates of phonon scattering on natural isotopes. Effects, restricting the value of increment, including the current induced heating of electrons, are discussed. Influence of the phonon spectrum modification in superlattice on the value of increment is examined. (author)