Energy transported by a wave is proportional to its amplitude.

Energy transported by a wave is proportional to its amplitude.

• A. Only for mechanical waves
• B. False
• C. Only for light waves
• D. True

Answer: (D)

Energy carried by a wave scales with how big the oscillations are, and it does so in a squared way. In mechanical waves on a string, the energy density comes from both the motion of the medium and its displacement, and these contributions are proportional to the square of the amplitude. Doubling the amplitude makes the energy transported increase by a factor of four. The same squaring relationship holds for electromagnetic waves: the intensity (energy per unit area per unit time) is proportional to the square of the electric and magnetic field amplitudes. Because of this, energy is not proportional to the amplitude itself but to the amplitude squared. If you see a statement that energy is proportional to amplitude, it’s missing that important square factor.

Energy carried by a wave scales with how big the oscillations are, and it does so in a squared way. In mechanical waves on a string, the energy density comes from both the motion of the medium and its displacement, and these contributions are proportional to the square of the amplitude. Doubling the amplitude makes the energy transported increase by a factor of four. The same squaring relationship holds for electromagnetic waves: the intensity (energy per unit area per unit time) is proportional to the square of the electric and magnetic field amplitudes. Because of this, energy is not proportional to the amplitude itself but to the amplitude squared. If you see a statement that energy is proportional to amplitude, it’s missing that important square factor.