Physics: Why Waves in Fluids are Longitudinal

[Rashid101]

Homework Statement

Both longitudinal and transverse waves can propagate through a solid. A wave on the surface of a liquid can involve both longitudinal and transverse motion of elements of the medium. On the other hand, a wave propagating through the volume of a fluid must be purely longitudinal, not transverse. Why?

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

What do you think might be different between the two cases, to prompt the question in the first place?