Which statement about wave speed is true?

Which statement about wave speed is true?

• A. Wave speed is independent of density
• B. Increasing density always increases speed
• C. Increasing bulk modulus and decreasing density increases speed
• D. Decreasing stiffness decreases speed

Answer: (C)

Wave speed reflects how fast a disturbance travels, determined by how stiff the material is against compression and how much inertia the medium has. For compressional waves, speed is proportional to the square root of stiffness divided by density. So increasing the bulk modulus (stiffness against compression) makes waves propagate faster, while decreasing density reduces inertia, also making waves travel faster. When both happen—bulk modulus goes up and density goes down—the speed increases the most. If stiffness drops, speed drops as well, since the medium offers less resistance to compression. The statement that increasing bulk modulus and decreasing density increases speed directly matches this relationship, which explains why it is the true choice.

Wave speed reflects how fast a disturbance travels, determined by how stiff the material is against compression and how much inertia the medium has. For compressional waves, speed is proportional to the square root of stiffness divided by density. So increasing the bulk modulus (stiffness against compression) makes waves propagate faster, while decreasing density reduces inertia, also making waves travel faster. When both happen—bulk modulus goes up and density goes down—the speed increases the most. If stiffness drops, speed drops as well, since the medium offers less resistance to compression. The statement that increasing bulk modulus and decreasing density increases speed directly matches this relationship, which explains why it is the true choice.