Here's why:

* Energy in a wave: The energy carried by a wave is related to the amount of disturbance it creates.

* Amplitude and disturbance: The amplitude of a wave represents the maximum displacement from its resting position. A larger amplitude means a greater disturbance.

* Energy and amplitude: The energy of the wave is directly proportional to the square of the amplitude. This means that doubling the amplitude quadruples the energy.

Example:

Imagine a rope tied to a post. If you give it a small shake, the rope will oscillate with a small amplitude and low energy. If you shake it harder, the amplitude increases, and so does the energy of the wave traveling down the rope.

Important Note: This relationship holds true for various types of waves, including:

* Mechanical waves: Waves that require a medium to travel, like sound waves or waves on a string.

* Electromagnetic waves: Waves that can travel through a vacuum, like light waves.

Let me know if you'd like to explore this further!