Stiffness and propagation speed are ______ related.

Stiffness and propagation speed are ______ related.

• A. Directly
• B. Inversely
• C. Not related
• D. Sometimes

Answer: (A)

Stiffness sets how strongly a medium resists being deformed, and that strength directly affects how quickly disturbances move through the material. When a wave travels, neighboring particles are pulled back toward equilibrium by those restoring forces. A stiffer medium provides stronger restoring forces, so the disturbance is passed along more quickly. In solids, the speed of a longitudinal wave is proportional to the square root of the elastic modulus (a measure of stiffness) divided by the density, v ∝ sqrt(E/ρ). With density roughly constant, increasing stiffness increases speed. So stiffness and propagation speed rise together—hence they are directly related. If stiffness decreases, speed decreases as well.

Stiffness sets how strongly a medium resists being deformed, and that strength directly affects how quickly disturbances move through the material. When a wave travels, neighboring particles are pulled back toward equilibrium by those restoring forces. A stiffer medium provides stronger restoring forces, so the disturbance is passed along more quickly. In solids, the speed of a longitudinal wave is proportional to the square root of the elastic modulus (a measure of stiffness) divided by the density, v ∝ sqrt(E/ρ). With density roughly constant, increasing stiffness increases speed. So stiffness and propagation speed rise together—hence they are directly related. If stiffness decreases, speed decreases as well.