Which statement best describes the effect of density and stiffness on propagation speed?

Which statement best describes the effect of density and stiffness on propagation speed?

• A. Increased density increases speed; Increased stiffness decreases speed
• B. Increased density decreases speed; Increased stiffness increases speed
• C. Increased density increases speed; Increased stiffness increases speed
• D. Increased density decreases speed; Increased stiffness decreases speed

Answer: (B)

Propagation speed of a wave in a medium depends on the balance between inertia and restoring forces. In many cases the speed is proportional to the square root of stiffness divided by density (v ≈ sqrt(stiffness/density)). That means higher density adds inertia and slows the wave, while higher stiffness strengthens the restoring forces and speeds the wave up. In ultrasound terms, denser or more massive tissues slow the wave, whereas stiffer tissues transmit it faster. For example, soft tissues have moderate density and stiffness, giving speeds around typical ultrasound values, while bone is very stiff (and relatively dense) and conducts the wave much faster. So the correct characterization is that increasing density decreases speed, and increasing stiffness increases speed.

Propagation speed of a wave in a medium depends on the balance between inertia and restoring forces. In many cases the speed is proportional to the square root of stiffness divided by density (v ≈ sqrt(stiffness/density)). That means higher density adds inertia and slows the wave, while higher stiffness strengthens the restoring forces and speeds the wave up. In ultrasound terms, denser or more massive tissues slow the wave, whereas stiffer tissues transmit it faster. For example, soft tissues have moderate density and stiffness, giving speeds around typical ultrasound values, while bone is very stiff (and relatively dense) and conducts the wave much faster. So the correct characterization is that increasing density decreases speed, and increasing stiffness increases speed.