Why does a longitudinal wave need a medium?

Answer 1

A mechanical wave (like a sound wave) requires a medium for propagation because the medium must carry the energy of the wave. With a mechanical wave, the source puts the energy into the medium, and the medium transports it. In contrast, and electromagnetic wave (like light) can travel in a vacuum; it needs no medium to support its propagation. To keep it simple there has to be energy that's all

Answer 2

Material medium is so important only for mechanical waves such as sound waves. But for electromagnetic wave even space is also a medium. Space is immaterial. For waves to get propagated we could imagine the secondary sources of waves and secondary wavelets right from those. Hence there becomes a chance for waves to change their direction at the edges of the obstacles.

Answer 3

It is not so much longitudinal vs. transverse - it is the type of wave. Mechanical waves, by definition, travel through matter. That includes sound waves. Mechanical waves, however, can be both longitudinal and transverse - and both require a medium.