Longitudinal waves can be propagated through all media, solid, liquid and gas, but transverse waves can propagate only through solids. Explain why.

A longitudinal wave motion travels in a medium in the form of compressions and rarefactions, which involves changes in volume and density of the medium. Thus longitudinal waves can be transmitted through a medium, which can offer an opposition to changes in volume. Solids, liquids and gases possess this property. Hence longitudinal waves can be propagated through all media.
A transverse wave motion is transmitted through a medium in the form of crests and troughs. This involves changes in the shape of the medium. The transverse waves can be transmitted only through the medium, which offers an opposition or resistance to changes in its shape. Solids possess this property and so the transverse waves can be propagated through them.