Which statement about density and speed of sound is most accurate?

Which statement about density and speed of sound is most accurate?

• A. Higher density yields faster speed
• B. Lower density yields slower speed
• C. Lower density yields faster speed
• D. Density has no effect

Answer: (C)

The main idea is that how fast a sound wave travels depends on the medium’s stiffness relative to its density. The speed is governed by a relation like v ≈ sqrt(stiffness/density). So, if the stiffness stays about the same and density decreases, the speed increases. This means a less dense medium tends to transmit sound waves more quickly because there’s less inertia to move per unit of wavefront. That’s why lower density yields faster speed is the best statement. It aligns with the general trend that, for similar stiffness, decreasing density raises the speed of sound. Real-world examples illustrate this too: sound moves faster in helium than in air at the same temperature, since helium is less dense. Note that in practice both density and stiffness change between media, so density isn’t the sole factor, but the relationship described is the most accurate general principle.

The main idea is that how fast a sound wave travels depends on the medium’s stiffness relative to its density. The speed is governed by a relation like v ≈ sqrt(stiffness/density). So, if the stiffness stays about the same and density decreases, the speed increases. This means a less dense medium tends to transmit sound waves more quickly because there’s less inertia to move per unit of wavefront.

That’s why lower density yields faster speed is the best statement. It aligns with the general trend that, for similar stiffness, decreasing density raises the speed of sound. Real-world examples illustrate this too: sound moves faster in helium than in air at the same temperature, since helium is less dense. Note that in practice both density and stiffness change between media, so density isn’t the sole factor, but the relationship described is the most accurate general principle.