Final answer:
To increase the amplitude of a wave on a rope, the student should shake their hand with greater amplitude, as larger movements will result in waves with higher peaks.
Step-by-step explanation:
To increase the amplitude of a wave on a rope, the student could shake their hand back and forth with a greater amplitude. Option II correctly suggests that by moving the hand more vigorously, the wave generated will have a higher peak, therefore a larger amplitude. Options I and III, increasing frequency and tension respectively, would affect other characteristics of the wave, but not directly its amplitude. For example, increasing the frequency would result in a higher number of waves passing a given point per unit of time, leading to a decrease in wavelength, while increasing tension might affect the speed at which the wave travels along the rope but not its amplitude.