The energy of a wave can be calculated using the formula:
\[ E = h \cdot f \]
where:
- \(E\) is the energy,
- \(h\) is Planck's constant (approximately \(6.626 \times 10^{-34} \text{ J s}\)),
- \(f\) is the frequency of the wave.
Since energy is directly proportional to frequency, the wave with the lowest frequency will have the lowest energy.
From the given data:
- Wave 1: \(6.66 \times 10^{14} , \text{Hz}\)
- Wave 2: \(5.77 \times 10^{14} , \text{Hz}\)
- Wave 3: \(4.61 \times 10^{14} , \text{Hz}\)
- Wave 4: \(4.28 \times 10^{14} , \text{Hz}\)
Comparing the frequencies, we find that Wave 4 has the lowest frequency (\(4.28 \times 10^{14} , \text{Hz}\)).
Therefore, the wave with the lowest energy is wave 4.