Explanation

The wave velocity in any medium depends on all of the above:

Elasticity:

A medium's elasticity determines how easily it can resist deformation and return to its original shape when force is applied.

Higher elasticity means the wave can travel faster through the medium. 

Density:

The density of a medium also affects wave velocity.

Denser media tend to slow down wave propagation. 

Homogeneity:

A homogeneous medium has consistent properties throughout, meaning the wave velocity will be uniform in all directions.