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[Phys-L] types of mechanical waves

Working on content for the fall semester. When it comes to mechanical waves, the general consensus is there are at least two important types based on disturbance vs propagation directions: transverse and longitudinal. Some sources mention "surface waves" but this seems to me to be a combination of transverse and longitudinal and not a distinct type.

Another: a torsional wave seems to me to be a distinct type.

I've also seen the term axial wave. Is that yet another type or not?

Comments, please.