In simplest terms, the energy of a wave is directly proportional to the square of Its

Options

A. amplitude
B. refraction
C. reflection
D. length.

Explanation

To solve the question "In simplest terms, the energy of a wave is directly proportional to the square of its...", we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Wave Energy**: The energy carried by a wave can be expressed in terms of its physical properties. For a mechanical wave, the energy is related to the mass of the medium, the angular frequency (ω), and the amplitude (A).

2. **Energy Formula**: The energy (E) of a wave can be given by the formula:
\[ E \propto \frac{1}{2} m \omega^2 A^2 \]
Here, \(m\) is the mass of the medium, \(ω\) is the angular frequency, and \(A\) is the amplitude of the wave.

3. **Identifying Proportionality**: From the formula, we can see that the energy (E) is directly proportional to the square of the amplitude (A):
\[ E \propto A^2 \]

4. **Relating Energy to Intensity**: We can also relate energy to intensity. Intensity (I) of a wave is defined as power per unit area. The power can be expressed in terms of intensity and area:
\[ P = I \times A \]
Thus, energy can also be expressed as:
\[ E \propto I \times t \]
where \(t\) is time.

5. **Intensity and Amplitude**: The intensity of a wave is also related to the square of the amplitude:
\[ I \propto A^2 \]
Therefore, we can conclude that energy is directly proportional to the intensity, which in turn is directly proportional to the square of the amplitude.

6. **Conclusion**: Thus, we can summarize that the energy of a wave is directly proportional to the square of its amplitude:
\[ E \propto A^2 \]

### Final Answer:
The energy of a wave is directly proportional to the square of its **amplitude**.