The relationship between wavelength and frequency is described by the formula:
\[ c = \lambda \cdot f \]
where \( c \) is the speed of light, \( \lambda \) is the wavelength, and \( f \) is the frequency. According to this relationship:
- If the wavelength increases, the frequency must decrease (because the speed of light is constant).
- If the wavelength decreases, the frequency must increase.
- If the wavelength remains the same, the frequency remains the same.
Now let's evaluate each student's statement:
- Darius (increase, increase): Incorrect. If the wavelength increases, the frequency decreases.
- Kathryn (increase, remain the same): Incorrect. If the wavelength increases, the frequency decreases.
- Anya (decrease, increase): Correct. If the wavelength decreases, the frequency increases.
- Franco (remain the same, decrease): Incorrect. If the wavelength remains the same, frequency must remain the same as well.
Therefore, the correct answer is Anya.