To determine which student is correct about the relationship between wavelength and frequency, we need to understand the fundamental relationship defined by the formula:
\[ v = f \lambda \]
Where:
- \( v \) is the speed of light (a constant),
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.
From this equation, we can derive the relationship between wavelength and frequency:
- If the wavelength (\( \lambda \)) increases, the frequency (\( f \)) must decrease to keep the speed of light constant.
- Conversely, if the wavelength decreases, the frequency must increase.
Now, let's analyze each student's claim:
- Darius: Wavelength increases and frequency increases. (Incorrect)
- Kathryn: Wavelength increases and frequency remains the same. (Incorrect)
- Anya: Wavelength decreases and frequency increases. (Correct)
- Franco: Wavelength remains the same and frequency decreases. (Incorrect)
Only Anya's statement aligns with the established relationship, where a decrease in wavelength corresponds to an increase in frequency. Therefore, Anya is correct.