Explain which properties are necessary to understand the speed of mechanical waves.

Explanation

Once disturbance is passed through the mean position, restoring force and elasticity are required for string particles to come back to their original position.
Oscillated particle is displacement depends on the inertia of medium.
Thus, for propagation of mechanical waves, elasticity and inertia are needful.
Thus, by using dimensional analysis based on two properties wave speed can be obtained.