Propagation speed ____ with increased density.

Propagation speed ____ with increased density.

• A. Increases
• B. Remains the same
• C. Decreases
• D. Doubles

Answer: (C)

Propagation speed is set by how easily the medium can restore itself after being disturbed compared with how much mass must be moved. In elastic media, the speed of a wave scales with the square root of the stiffness (or bulk modulus) divided by density. If density increases while stiffness stays the same, the ratio becomes smaller, so the wave travels more slowly. A helpful picture is a chain of masses connected by springs: heavier masses (higher density) require more inertia to accelerate, which slows the propagation of the disturbance. Therefore, increasing density decreases propagation speed. (Note that if stiffness increased proportionally with density, the speed could remain the same, but with density rising and stiffness unchanged, the speed falls.)

Propagation speed is set by how easily the medium can restore itself after being disturbed compared with how much mass must be moved. In elastic media, the speed of a wave scales with the square root of the stiffness (or bulk modulus) divided by density. If density increases while stiffness stays the same, the ratio becomes smaller, so the wave travels more slowly. A helpful picture is a chain of masses connected by springs: heavier masses (higher density) require more inertia to accelerate, which slows the propagation of the disturbance. Therefore, increasing density decreases propagation speed. (Note that if stiffness increased proportionally with density, the speed could remain the same, but with density rising and stiffness unchanged, the speed falls.)