An analytic approach to the generation of torsional magnetic tube waves in stellar convection zones is presented. The waves are produced in a thin, vertically oriented magnetic flux tube embedded in a magnetic field-free, turbulent and compressible external medium and are excited by external turbulent flows. A theory for this interaction is developed and used to compute the wave energy spectra and fluxes carried by torsional tube waves in the solar atmosphere. We find that these tube waves have a characteristic cutoff frequency.