Which option correctly describes the relationship between density and speed of sound?

Which option correctly describes the relationship between density and speed of sound?

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

Answer: (C)

The speed of sound depends on both how easily the material compresses (stiffness) and how much inertia it has (density). In a simple view, c is related to the stiffness-to-density ratio, roughly c ≈ sqrt(K/ρ). If you hold stiffness constant, increasing density lowers the speed. But real materials don’t keep stiffness constant when density changes—dense substances can also be very stiff, which can raise the speed, or they may be less stiff, which can lower it. Because density can be linked to different elastic properties across materials, there isn’t a single universal direction of the relationship. Sometimes higher density goes with higher speed, sometimes it doesn’t. That’s why this relationship is best described as sometimes related.

The speed of sound depends on both how easily the material compresses (stiffness) and how much inertia it has (density). In a simple view, c is related to the stiffness-to-density ratio, roughly c ≈ sqrt(K/ρ). If you hold stiffness constant, increasing density lowers the speed. But real materials don’t keep stiffness constant when density changes—dense substances can also be very stiff, which can raise the speed, or they may be less stiff, which can lower it. Because density can be linked to different elastic properties across materials, there isn’t a single universal direction of the relationship. Sometimes higher density goes with higher speed, sometimes it doesn’t. That’s why this relationship is best described as sometimes related.