To determine the accurate ranking of the waves from the lowest energy wave to the highest energy wave, we need to understand how wave energy is calculated. The energy \( E \) of a wave is proportional to the square of its amplitude \( A \). In simpler terms, if we know a wave's amplitude, we can compute its energy using the formula:
[tex]\[ E = A^2 \][/tex]
Let's analyze the information provided for each wave in the table and calculate their energies step-by-step:
1. Wave 1:
- Given amplitude: \(3 \, cm\)
- Energy: \( E_1 = 3^2 = 9 \, (cm^2) \)
2. Wave 2:
- Given distance from the midpoint to the crest: \(6 \, cm\)
- This distance is the amplitude of the wave.
- Energy: \( E_2 = 6^2 = 36 \, (cm^2) \)
3. Wave 3:
- Given distance from the midpoint to the trough: \(12 \, cm\)
- The distance from the midpoint to the trough is the amplitude of the wave.
- Energy: \( E_3 = 12^2 = 144 \, (cm^2) \)
4. Wave 4:
- Given amplitude: \(4 \, cm\)
- Energy: \( E_4 = 4^2 = 16 \, (cm^2) \)
Now, let's list the calculated energies for each wave:
- Wave 1: \(9 \, (cm^2)\)
- Wave 2: \(36 \, (cm^2)\)
- Wave 3: \(144 \, (cm^2)\)
- Wave 4: \(16 \, (cm^2)\)
To rank the waves from the lowest energy to the highest energy, we sort the energies in ascending order:
- \(9 \, (cm^2)\) (Wave 1)
- \(16 \, (cm^2)\) (Wave 4)
- \(36 \, (cm^2)\) (Wave 2)
- \(144 \, (cm^2)\) (Wave 3)
Thus, the correct ranking of the waves from the lowest energy to the highest energy is:
[tex]\[ 1 \rightarrow 4 \rightarrow 2 \rightarrow 3 \][/tex]
Therefore, the last option,
[tex]\[ 1 \rightarrow 4 \rightarrow 2 \rightarrow 3 \][/tex]
is the accurate ranking of the waves based on their energies.
