Question

Why liquids and gases cannot propagate transverse waves?

Answer 1

The particles in transverse waves move perpendicularly to the direction of propagation so it cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave.

Detail Explanation

First i will explain why transverse wave propagate in solids

A transverse wave propagates in a solid because each atom of the solid has an "equilibrium location" where the forces on it from all its neighboring atoms balance. If one atom gets pulled out of its equilibrium location by a disturbance, it will tend to be pulled back to that location. However, when it's out of its equilibrium location it pulls its neighbors out of their equilibrium locations too, and so on down the line; the end result is that a transverse wave disturbance propagates through the material.

In fluids (liquids and gases), atoms have no "equilibrium location"; they can move freely past each other. So if one atom gets moved by a disturbance, there's no restoring force to pull it back to its equilibrium location, because there is no equilibrium location. Instead each atom is driven by the forces of neighboring atoms to maintain a given average distance between itself and its neighbors, but nothing else; so if one atom is disturbed, it will move to restore its average distance to its neighbors (and they will move in turn in response to the first one moving), but the atom won't be in the same place it was before when it's done equilibrating again. This allows longitudinal waves to propagate in fluids, but not transverse waves.