1. The medium the wave travels through: Different mediums have different properties like density and elasticity. A wave travels faster through a denser medium, but slower through a more elastic medium. For example, sound travels faster in steel than in air because steel is denser.

2. The type of wave: Some waves are transverse, where the particles of the medium move perpendicular to the direction of wave propagation. Others are longitudinal, where the particles move parallel to the direction of propagation. The speed of a wave depends on the type of wave, as well as the properties of the medium.

Let me know if you want more detail about the relationship between wave speed, medium properties, and wave type.