Question

is it possible for a transverse mechanical wave to move through air?
multiple choice
yes, this is a disturbance that causes a back - and - forth motion in the direction the wave is moving.
no, transverse waves are not strong enough to move through solids or fluids.
yes, this is a disturbance that causes motion perpendicular to the direction the wave is moving.
no, there is no force acting on the air to return it to its original position.

Explanation:

Transverse mechanical waves require a restoring force to return the medium to its original position. In air (a gas), there is no significant shear - like restoring force for transverse motion. For a transverse wave, the particles of the medium move perpendicular to the wave direction. In solids, there are forces (like elastic forces) that can support this perpendicular motion (shear forces). But in gases like air, when a transverse - like displacement is attempted, there is no analogous force to bring the air particles back to their original position in the way required for a transverse wave.

Answer:

No, there is no force acting on the air to return it to its original position.