A bending wave in a metal bar or string is simply called a transverse wave because the macroscopic oscillation is transverse. However, paradoxically, in a frame co-moving with the atoms, the atoms are oscillating longitudinally. The outer boundary of a curved section is being stretched, while the inner boundary is being compressed, somewhat like a bimetal.
Is the longitudinal motion in the co-moving frame really irrelevant to the term 'transverse wave'? Or is there a less paradoxical terminology?