Transverse and Longitudinal Waves

The speed of a transverse wave depends on the intrinsic properties of the medium it propagates through. These could be elastic and inertial properties. For a transverse wave on a string, we need to know factors such as tension (a common force) in the string, and its linear mass density. 

Transverse waves can travel through solids or any medium that can withstand shearing strain. Fluids, including liquids and gases, cannot sustain shear force, so such types of mechanical waves cannot travel through them. 

Longitudinal waves can travel through all elastic media that can sustain compressive strain. That means, these mechanical waves can travel through solids, liquids, and gases.  

Sound waves and water waves are mechanical waves, which always require a medium to travel. Light, however, does not require a medium to propagate, as it is electromagnetic.  Light can travel through vacuum, while sound and water waves cannot travel through vacuum.