Why do sound waves travel through solids as transverse waves?
Are you asking why sound waves travel through solids in either mode? Another way of putting the question that might be easier to answer is, why can’t transverse waves travel through gases and liquids? The answer to that is that all waves require that some part of the system provide an elastic restoring tendency when there is a displacement from the original state, either shape (transverse) or density (longitudinal). Gases, liquids and solids carry longitudinal waves because they all provide an elastic means (bulk modulus, resulting in pressure) to restore the mean density. But neither gases nor liquids have elastic rigidity (shear modulus, resulting in force) to restore a transverse displacement, so only solids carry a transverse wave.
