Carbon nanostructures are under deep investigation due their peculiar properties and possible applications. In particular, development of new methods for the synthesis of these materials and their mechanism of formation represent interesting research fields. Arc discharge allows to produce different forms of carbon nanostructures. The parameters involved in the process, voltage, current density, type and pressure of the surrounding gas can be controlled especially for achieving high quantity of material with enhanced characteristics in terms of purity while the use of transition metal-graphite mixtures has been used to produce single wall structures. Moreover direct current (DC) and alternating current (AC) are suitable for producing carbon nano-materials, but different results can be obtained. In this work the effect of the power frequency in an AC arc discharge technique on the synthesis of carbon nanostructures is reported. Pure graphite electrodes have been arched in air in an homemade apparatus where the material can be collected directly on a cylindrical collector fixed near the arc. In order to avoid the formation of deposits under the arc a symmetrical configuration of the electrodes has been set. The production of carbon soot containing Single Wall Nanohorns (SWNH) and highly convoluted graphene sheets is optimized. The range of power frequencies 32-1000Hz has been investigated and the arcs have been ignited fixing the voltage at 28 V. The materials has been analyzed by field emission scanning electron microscope and high resolution transmission electron microscope. The microstructure of the material synthesized by this apparatus is affected by the power frequency, as the experimental results demonstrate. The samples produced at low frequency presented high amounts of single wall structures, SWNH-type. More compact structures, similar to large onion-like structures, have been found in samples synthesized at high frequency values.