In a sinusoidal wave traveling along a rope, which shaded piece of rope has the least amount of energy?

In a sinusoidal wave, the energy transported by the wave is related to the amplitude of the wave and the displacement of the particles in the medium (in this case, the rope). The energy in a wave is highest at the crests and troughs because that is where the displacement of the medium is greatest. This is where the particles of the rope move the most, leading to higher kinetic and potential energy.

In the context of this question, the little blue piece at the top middle represents a point where the displacement is the smallest because it is located at or near the equilibrium position of the wave. At this point, the particles of the rope are not moving up or down significantly, resulting in minimal energy transfer compared to regions near the crests or troughs, where the displacement is maximal.

Thus, that particular shaded piece of rope has the least amount of energy because it experiences little movement and thus little energy transfer in comparison to other parts of the wave.