Which statement correctly describes the relation between density and propagation speed?

Which statement correctly describes the relation between density and propagation speed?

• A. Speed is faster in denser media
• B. Speed is slower in less dense media
• C. Speed is faster in media of lower density
• D. Speed is independent of density

Answer: (C)

Sound speed in a medium depends on both how stiff the material is and how much mass it has to move. The relationship v = sqrt(B/ρ) shows that, if the stiffness (bulk modulus B) stays roughly the same, lowering density ρ makes the speed higher. In other words, with less inertia to push aside, the wave can travel faster through the material. This is why lower-density media tend to have faster propagation, though the exact speed also depends on how the stiffness changes. The idea stands as a useful general rule of thumb: reducing density (without a proportional drop in stiffness) increases speed.

Sound speed in a medium depends on both how stiff the material is and how much mass it has to move. The relationship v = sqrt(B/ρ) shows that, if the stiffness (bulk modulus B) stays roughly the same, lowering density ρ makes the speed higher. In other words, with less inertia to push aside, the wave can travel faster through the material. This is why lower-density media tend to have faster propagation, though the exact speed also depends on how the stiffness changes. The idea stands as a useful general rule of thumb: reducing density (without a proportional drop in stiffness) increases speed.