Both the intensity and power of a wave are proportional to its _____ ____.

• A. Amplitude
• B. Frequency
• C. Amplitude Squared
• D. Wavelength

Answer: (C)

The energy carried by a wave grows with how big the oscillations are. The oscillation amplitude sets how strong the displacement or field variation is, and the energy stored in that motion scales with the square of that amplitude. Because power is the rate at which energy is transferred and intensity is power per area, both of these quantities end up proportional to the amplitude squared.

Think of a sound wave: the pressure variation is proportional to the amplitude, and the energy flow (intensity) goes as the square of that pressure variation. For light, the electric field strength plays the role of the amplitude, and the energy flux scales with the square of the field. This squared relationship also explains why doubling the amplitude makes the energy—and thus the power and intensity—rise by a factor of four.

Frequency or wavelength doesn’t set this same direct scaling; they influence how often energy passes a point or relate to the wave’s speed, but the fundamental energy transfer for a given wave amplitude is governed by amplitude squared.