Changes in the of the medium through which a wave travels can cause the wave to either speed up or slow down.

Changes in the elastic properties and density of the medium through which a wave travels can cause the wave to either speed up or slow down.

Elastic properties determine how rigid the material is, and the rigid the material the faster its particles can vibrate, which means that the wave can travel faster trough it. This explain why waves can travel way faster trough iron than trough rubber because iron is far more rigid than rubber.

Density on the other hand, is the mass of a substance per unit volume. The higher the density of a medium the higher the mass of it, and so the wave has to use more energy to travel trough it; thus slowing the wave down.