What does an increase in stiffness do to the speed of sound?

An increase in stiffness in a medium leads to an increase in the speed of sound traveling through that medium. Stiffness is defined as the ability of a material to resist deformation when a force is applied. When stiffness increases, this means the medium is better able to transmit vibrations quickly.

In the context of sound waves, which are mechanical waves traveling through a medium, both stiffness and density influence sound speed. According to the fundamental relationship defined in physics, the speed of sound (v) in a medium is related to its stiffness (K) and density (ρ) by the formula:

[ v = \sqrt{\frac{K}{\rho}} ]

From this equation, it's clear that when stiffness increases while density remains constant, the speed of sound increases as a result. Thus, increasing the stiffness of a medium enhances its ability to transmit sound waves more rapidly, confirming that the correct answer is that an increase in stiffness increases the speed of sound.