Here's why:

* Amplitude: The amplitude of a wave is the maximum displacement of a particle from its equilibrium position. In other words, it's the "height" of the wave.

* Energy: The energy of a wave is related to the amount of disturbance or vibration it carries.

The relationship:

* Higher amplitude = Higher energy: A wave with a larger amplitude has more energy. This is because the particles in the wave are moving with greater displacement and velocity, leading to more energy transfer.

* Lower amplitude = Lower energy: A wave with a smaller amplitude has less energy. The particles in the wave are moving with smaller displacements and velocities, resulting in less energy transfer.

Example:

Think of a sound wave. A loud sound has a high amplitude, meaning the air molecules are vibrating with large displacements and transferring more energy to your ear. A soft sound has a low amplitude, meaning the air molecules are vibrating with small displacements and transferring less energy.

Important Note: While amplitude determines the energy of a wave, other factors also play a role, such as:

* Frequency: The frequency of a wave also contributes to its energy. Higher frequency waves typically have more energy.

* Wave type: The type of wave (e.g., electromagnetic, sound, water) also influences the relationship between amplitude and energy.

Let me know if you'd like a more detailed explanation of any of these concepts!