Which two characteristics of a medium determine the speed of sound?

The speed of sound in a medium is primarily determined by its stiffness (or elasticity) and density. Stiffness refers to how much a medium resists deformation (how "hard" or "rigid" it is), while density is the mass per unit volume of the medium. The relationship can be described by the formula:

[ \text{Velocity} = \sqrt{\frac{\text{Stiffness}}{\text{Density}}} ]

This formula indicates that as stiffness increases, the speed of sound in that medium also increases, given that density remains constant. Conversely, if density increases without a corresponding increase in stiffness, the speed of sound generally decreases. Thus, the interplay between stiffness and density is crucial for understanding how sound travels through different materials.

In this context, the other options do not directly relate to sound speed in the same way. For example, compressibility does influence sound speed, but it is closely associated with stiffness, making them effectively interchangeable in the context of this question. Similarly, while temperature can affect sound speed, it does so through its impact on density, rather than being a primary characteristic of the medium itself.