Abstract The effects of both density stratification and magnetic field expansion on torsional Alfvén waves in magnetic flux tubes are studied. The frequencies, the period ratio P of the fundamental and its first-overtone, and eigenfunctions of torsional Alfvén modes are obtained. Our numerical results show that the density stratification and magnetic field expansion have opposite effects on the oscillating properties of torsional Alfvén waves. 1 /P 2
