To determine which student is correct, we need to consider the relationship between wavelength and frequency in waves, specifically electromagnetic waves. The key relationship is given by the formula:
\[ c = \lambda \cdot f \]
where:
- \( c \) is the speed of the wave (constant in a given medium),
- \( \lambda \) is the wavelength, and
- \( f \) is the frequency.
From this equation, we can see that if the speed of the wave is constant, the wavelength (\( \lambda \)) is inversely proportional to the frequency (\( f \)). This means:
- If the wavelength increases, the frequency must decrease,
- If the wavelength decreases, the frequency must increase,
- If the wavelength remains the same, the frequency remains the same.
Now, let's analyze the students' statements:
- Darius: Wavelength increases, frequency increases. (This is incorrect because an increase in wavelength means frequency should decrease.)
- Kathryn: Wavelength increases, frequency remains the same. (This is incorrect because an increase in wavelength should result in a decrease in frequency.)
- Anya: Wavelength decreases, frequency increases. (This is correct because a decrease in wavelength corresponds to an increase in frequency.)
- Franco: Wavelength remains the same, frequency decreases. (This is incorrect because if wavelength remains the same, frequency should also remain the same.)
Based on the analysis, Anya is correct.