Which statement describes the relationship among amplitude, power, and intensity?

• A. They are inversely related
• B. They are independent
• C. They are directly related; power and intensity relate to amplitude squared
• D. They are equal to each other

Answer: (C)

Energy carried by a wave grows with the square of its amplitude. In acoustics, the power delivered by a sound wave is proportional to the square of the pressure (or displacement) amplitude, and intensity is power per unit area. So when the amplitude increases, both power and intensity rise, and they do so as the amplitude squared. For a sinusoidal wave in a medium, the relationship is typically written as I ∝ p^2/(ρc), meaning the exact factor depends on the medium, but the key idea is the quadratic (square) dependence. This is why doubling the amplitude makes power and intensity increase by a factor of four.