The fine atomization of liquids by means of low-frequency ultrasonic atomizers (about 50 kHz) results from unstable surface waves generated on the free surface of a thin liquid film. This thin liquid film develops as the liquid spreads fast over the atomizing surface of the atomizer. The displacement amplitude of the atomizing surface must be greater than 2 μm to initiate the atomization process. This may be achieved using a displacement amplitude transformer. The present study focuses on an analytical analysis of the longitudinal oscillations stimulated by the piezoelectric elements in a stepped horn which operates as an amplitude transformer. A sizing method of the stepped horn is established and experimentally tested. The influence of the materials’ mechanical damping on the displacement amplitude of the atomizing surface is investigated. The comparison between theoretical and experimental results allows the determination of the internal damping coefficient.