Final answer:
To increase the amplitude of a transverse wave, you should move your hand with a greater vertical distance and increase the rope tension by creating a tighter rope. When waves traveling in opposite directions meet, they can result in constructive interference with increased amplitude or destructive interference with reduced amplitude.
Step-by-step explanation:
To increase the amplitude of a transverse wave in a jump rope, one could employ a couple of strategies. Firstly, the person creating the wave can move their hand with a greater vertical distance, thereby imparting more energy into the wave and increasing its amplitude. This is like shaking the rope with more significant motion at the point of initiation. Secondly, the tension in the rope can be increased by stepping backwards, creating a tighter rope which allows larger amplitude waves to travel more easily. It's important to note that when two waves traveling in opposite directions meet, such as one person shaking the rope up and down while the other holds it still, they can interfere constructively or destructively. Constructive interference will result in waves with twice the original amplitude, while destructive interference can cancel the waves out, leading to points of equilibrium with no amplitude.
In the context of a returned pulse with differing amplitude, when a pulse of amplitude A and another pulse of amplitude 3A meet, the resulting amplitude when they overlap would be the sum of the two amplitudes if they are in phase, leading to an amplitude of 4A at points of constructive interference. If they are out of phase, they could partially or fully cancel each other, leading to reduced or zero amplitude at points of destructive interference.