Propagation speed increases most when which combination of material properties occurs?

Propagation speed increases most when which combination of material properties occurs?

• A. Increasing stiffness and increasing density
• B. Increasing stiffness and decreasing density
• C. Decreasing stiffness and increasing density
• D. Decreasing stiffness and decreasing density

Answer: (B)

Wave speed for mechanical signals in a material depends on how stiff the material is and how much inertia (density) it has. The speed is proportional to the square root of stiffness divided by density, roughly v ~ sqrt(E/ρ) (or sqrt(K/ρ) for fluids). When stiffness increases, the material resists deformation more and can push the wave front faster. When density decreases, there’s less inertia to move, so particles can accelerate more quickly and the wave travels faster. The combination that makes the speed largest is higher stiffness with lower density. The other scenarios either raise density or lower stiffness, both of which tend to slow the wave compared with the best case.

Wave speed for mechanical signals in a material depends on how stiff the material is and how much inertia (density) it has. The speed is proportional to the square root of stiffness divided by density, roughly v ~ sqrt(E/ρ) (or sqrt(K/ρ) for fluids). When stiffness increases, the material resists deformation more and can push the wave front faster. When density decreases, there’s less inertia to move, so particles can accelerate more quickly and the wave travels faster. The combination that makes the speed largest is higher stiffness with lower density. The other scenarios either raise density or lower stiffness, both of which tend to slow the wave compared with the best case.