You are creating transverse waves in a rope by shaking your hand from side to side. Without changing the distance your hand moves, you begin to shake it faster and faster. What happens to the amplitude of the wave?
When you shake your hand from side to side to create transverse waves in a rope, the rope moves up and down in a wave-like motion. The amplitude of a wave is defined as the maximum displacement of the particles from their equilibrium position.
As you begin to shake your hand faster and faster while keeping the distance your hand moves constant, the amplitude of the wave remains the same. The amplitude is determined by the energy you put into shaking your hand, which does not change regardless of the speed of shaking.
So, in this scenario, the increased speed of shaking your hand only affects the frequency of the wave. The frequency refers to the number of cycles or oscillations of the wave that occur per unit of time. By shaking your hand faster, you increase the frequency of the wave, but the amplitude remains unchanged.