If stiffness increases while density remains unchanged, the speed of sound will:

If stiffness increases while density remains unchanged, the speed of sound will:

• A. Decrease
• B. Stay the same
• C. Increase
• D. Random

Answer: (C)

Speed of sound depends on how stiff the material is relative to its inertia. With density held constant, increasing stiffness raises the restoring forces in the medium, so disturbances propagate faster. In simple terms, velocity is proportional to the square root of stiffness divided by density; since density stays the same, a rise in stiffness leads to a higher speed. So the speed increases. The other possibilities don’t fit: decreasing stiffness would slow the wave, keeping density but changing stiffness would still affect speed, and a random value has no physical basis for wave propagation.

Speed of sound depends on how stiff the material is relative to its inertia. With density held constant, increasing stiffness raises the restoring forces in the medium, so disturbances propagate faster. In simple terms, velocity is proportional to the square root of stiffness divided by density; since density stays the same, a rise in stiffness leads to a higher speed. So the speed increases. The other possibilities don’t fit: decreasing stiffness would slow the wave, keeping density but changing stiffness would still affect speed, and a random value has no physical basis for wave propagation.