Speed of sound in a medium is determined by which two properties?

• A. Temperature and Viscosity
• B. Density and Temperature
• C. Viscosity and Temperature
• D. Density and Stiffness

Answer: (D)

The speed of sound in a medium is set by how easily the medium can be compressed (its stiffness) and how much mass there is per unit volume (its density). The wave travels as a sequence of compressions and rarefactions, so a stiffer medium resists compression and passes along the disturbance more quickly, while a denser medium has more inertia to move and slows the wave. This relationship is captured by c ≈ sqrt(K/ρ), where K is the bulk modulus (a measure of stiffness) and ρ is density. Higher stiffness increases speed, higher density decreases it. Viscosity and temperature affect damping and the medium’s state, but the direct determinants of the propagation speed are density and stiffness.