Mechanisms of cavity resonance and antenna resonance and their coupling effect on mode transition in argon helicon plasma excited by a half-helical antenna (14 cm in length) were investigated in this paper. Cavity length was changed to distinguish the effects of cavity and antenna resonances. Plasma parameters in various conditions such as input power (0-2500 W), magnetic field (0-1000 G) and cavity length (10-42 cm) were measured. Characteristics of helicon discharges and mode transitions in cases of fixed and continuously changed cavity lengths were compared. The results show that multiple axial eigenmodes (at least five in the present work) were observed in both cases. In fixed-length cavity, helicon discharge changes abruptly during mode transitions, while in changeable-length cavity, discharge features can change continuously (e.g. in large range of density from 1.7×1012 to 1.3×1013 cm-3) without mode transition. Mode transitions also occur as the cavity length increasing at fixed input power and magnetic field with periodical variations of plasma parameters. Cavity resonance plays a dominant role in formation of standing helicon wave of eigenmodes and mode transition, while antenna resonance affects significantly the transition from inductively coupled mode to helicon wave mode. Enhanced inter-coupling of cavity resonance and antenna resonance appears at specific axial wavelengths of eigenmodes. Threshold conditions for mode transitions were deduced and the overall transition path and the corresponding density were predicted quantitatively, which shows that cavity resonance determines the transition path, while antenna resonance gives the lower limit of the path. Axial wavenumber is closely related to the helicon discharge characteristics. Cavity and antenna resonances influence the helicon discharge and mode transition by determining the axial wavenumber of eigenmodes.