To determine which student's explanation about the relationship between wavelength and frequency is correct, we need to recall the fundamental relationship between wavelength (λ) and frequency (f) in the context of electromagnetic waves (including light).
The relationship is defined by the equation:
\[ c = \lambda \cdot f \]
where \( c \) is the speed of light. According to this equation:
- If the wavelength (λ) increases, the frequency (f) must decrease in order to keep the product \( λ \cdot f \) equal to the speed of light.
- Conversely, if the wavelength (λ) decreases, the frequency (f) must increase.
Now, let's assess each student's statement based on the understanding of this relationship:
- Darius: Increase wavelength -> increase frequency (Incorrect)
- Kathryn: Increase wavelength -> remain the same frequency (Incorrect)
- Anya: Decrease wavelength -> increase frequency (Correct)
- Franco: Remain the same wavelength -> decrease frequency (Incorrect)
Only Anya correctly states that a decrease in wavelength leads to an increase in frequency.
Therefore, the correct student is Anya.