they can travel through solids but not liquids
In transverse waves, the constituents of the medium oscillate perpendicular to wave motion subjecting each element of the medium to shearing stress. Solids and strings have shear modulus, that is they sustain shearing stress. Fluids have no shape of their own - they yield to shearing stress. This is why transverse waves are possible in solids and strings (under tension) but not in fluids.
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