Question

which wave has more energy? why? pick the answer the correctly answers both questions
wave e
wave f
both waves have the same amount of energy.
wave f: even though they have the same amplitude, wave f has a greater frequency.
wave e: even though they have the same frequency, wave e has a greater amplitude.
wave f: even though they have the same frequency, wave f has a greater amplitude.

Explanation:

Step1: Understand the relationship between wave energy and amplitude

The energy of a wave is directly proportional to the square of its amplitude ($E\propto A^{2}$). A larger amplitude means more energy.

Step2: Compare the amplitudes of Wave E and Wave F

Looking at the displacement - position graphs (which show amplitude as the maximum displacement from the equilibrium position). Wave E has a greater maximum displacement (amplitude) than Wave F. Since they have the same frequency (number of cycles in a given position range is the same), and energy depends on amplitude (for waves of the same type, when frequency is constant, higher amplitude means more energy).

Answer:

Wave E: Even though they have the same frequency, Wave E has a greater amplitude.