As a field expert in wave physics, I can explain the behavior of transverse waves in different states of matter. Transverse waves are characterized by the motion of particles in the medium being perpendicular to the direction of the wave's travel. This type of wave requires a medium that can resist shearing forces, which is a type of deformation that occurs when adjacent layers of the medium move parallel to each other. Solids have a rigid structure where particles are closely packed together and maintain a fixed position relative to each other. This rigidity allows for the particles to move up and down (or in any perpendicular direction) as the wave passes through, thus facilitating the propagation of transverse waves. Liquids, on the other hand, do not have the same rigid structure as solids. In liquids, particles are free to move over one another, which means they cannot maintain the perpendicular motion required for transverse waves. The particles in a liquid can move in parallel layers, which is necessary for the propagation of longitudinal waves (like sound waves in water), but not for transverse waves. Gases are even less capable of supporting transverse waves than liquids because the particles are further apart and the intermolecular forces are weaker. This makes it even more difficult for the particles to interact in a way that would allow for the perpendicular motion of transverse waves. In summary, the key factor is the rigidity and resistance to shearing deformation that solids provide, which is necessary for the propagation of transverse waves. read more >>

Simple. Transverse-waves need a medium rigid enough to propagate, which liquids can't provide. ... 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.read more >>