Question
Assertion : Solids can support both longitudinal and transverse waves but only longitudinal waves can propagate in gases.
Reason : For the propagation of transverse waves, medium must also neccessarly have the property of rigidity.

Answer

(a) For the propagation of transverse waves, medium must have the property of rigidity. Because gases have no rigidity, (they do not posses shear elasticity), hence transverse waves cannot be produced is gases. On the other hand, the solids possess both volume and shear elasticity and likewise both the longitudinal and transverse waves can be transmitted through them.

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