1. The properties of the medium:

* Elasticity: This refers to how easily a medium can be deformed and then return to its original shape. A more elastic medium will allow the wave to travel faster. Think of a taut string versus a loose string – the taut string will transmit vibrations quickly.

* Density: The denser the medium, the slower the wave will travel. This is because particles in a denser medium have more inertia, meaning they resist changes in motion.

2. The type of wave:

* Transverse waves: In transverse waves, the displacement of the medium is perpendicular to the direction of wave propagation. An example is a wave on a string. The speed of a transverse wave on a string is determined by the tension in the string and the mass per unit length of the string.

* Longitudinal waves: In longitudinal waves, the displacement of the medium is parallel to the direction of wave propagation. An example is sound waves. The speed of a longitudinal wave in a solid is determined by the elastic modulus of the material and its density.

In summary:

* Higher elasticity, faster wave speed.

* Higher density, slower wave speed.

Important Note: Mechanical waves require a medium to travel through. They cannot travel in a vacuum like electromagnetic waves (e.g., light).