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Generally speed of wave depends on the property of medium which it travels. Elasticity and inertia are the properties of the medium which effect the speed of wave.

Elasticity (property of regaining to original shape for applied forces ) is more in solids when compared with liquids and gases. Next best is liquids. so wave travels faster in solids. Similarly Inertia of solids is more so

V solid > V water > V gas

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