Which statement about density and propagation speed is correct?

Which statement about density and propagation speed is correct?

• A. Increasing density increases speed
• B. Increasing density decreases speed
• C. Density has no effect on speed
• D. Density doubles speed

Answer: (B)

Density influences how fast a wave can move through a medium because the wave’s speed depends on how easily the medium can be restored after being displaced relative to how much inertia the particles have. When the restoring forces (the stiffness or modulus) are held constant, increasing density makes the particles heavier to move, so the disturbance propagates more slowly. This gives the general relationship that, for a given stiffness, the propagation speed decreases as density increases (v is roughly proportional to the square root of stiffness divided by density). So the statement that increasing density decreases speed matches this intuition: more inertia means a slower wave front. A note for intuition: if you doubled density while keeping the restoring force the same, the speed would drop by about a factor of 1/√2 (roughly 30% slower).

Density influences how fast a wave can move through a medium because the wave’s speed depends on how easily the medium can be restored after being displaced relative to how much inertia the particles have. When the restoring forces (the stiffness or modulus) are held constant, increasing density makes the particles heavier to move, so the disturbance propagates more slowly. This gives the general relationship that, for a given stiffness, the propagation speed decreases as density increases (v is roughly proportional to the square root of stiffness divided by density). So the statement that increasing density decreases speed matches this intuition: more inertia means a slower wave front.

A note for intuition: if you doubled density while keeping the restoring force the same, the speed would drop by about a factor of 1/√2 (roughly 30% slower).