The effects of triaxial softness on wobbling motion are investigated within the framework of the core-quasiparticle coupling model. By coupling a high-$j$ valence nucleon located in low shell or middle shell to a $\gamma$-rigid and $\gamma$-soft core, we compare energy spectra and electromagnetic transitions of odd-mass nuclei in the four characteristic scenarios. It is revealed that the wobbling motion also appears in nuclei with $\gamma$-soft cores, however, exclusively as longitudinal wobbling. Only a rigid triaxial core supports the appearance of transverse wobbling at low spin which changes to longitudinal wobbling at higher spin states. The differences in interband $B{\left(E2\right)}_{\text{out}}$ transitions provide clear signatures for distinguishing the softness of core, which may serve as the experimental probes. These findings offer clearer light on wobbling motion, thereby expanding our understanding of this fundamental collective mode.

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• Collective levels
• High spin states
• 90 ≤ A ≤ 149
• Collective models