The velocity of a transverse wave in a stretched string is given by

v = √(F/m)

where F is tension in the string and m is mass per unit length of the wire.

The velocity of longitudinal waves in an elastic medium is given by

v = √(E/ρ)

where E is elasticity.

Since the value of elasticity is more in solids, the velocity of longitudinal waves in solids is greater than that in gases and liquids.

v_{g} < v_{l} < v_{s}