The wave being done in a stadium is an example of a mechanical wave. In a stadium wave, the  fans interacting are the interacting part of the wave, by interacting with each other  to the flow of the wave. The fans are also the medium of the wave and eventually go back to their original position.

Three types  of mechanical waves exist, Transverse, Longitudinal, and surface waves. Transverse waves cause the medium to vibrate at a right angle to the direction of the wave or energy being carried by the medium. Transverse waves have two parts the crest and the trough. Longitudinal waves cause the medium to vibrate parallel to the direction of the wave. It consits of mutiple compressions and rarefactions. The rarefraction is the farthest distance apart in the longitudinal wave and the compression is the closet distance together. Surface waves travels along a surface of water. An example of a surface wave would be waves in a pool, or in an ocean, lake, or any other type of water body.