To determine which student is correct regarding the relationship between wavelength and frequency, we can refer to the fundamental relationship described by the equation:
\[ \text{Speed of Wave} = \text{Wavelength} \times \text{Frequency} \]
In most cases (especially in a vacuum), the speed of a wave is constant. This means that if the wavelength increases, the frequency must decrease to maintain the constant wave speed. Conversely, if the wavelength decreases, the frequency must increase.
Let's analyze the statements from the students based on this principle:
- Darius: Wavelength increases → Frequency increases (This is incorrect; if the wavelength increases, frequency should decrease).
- Kathryn: Wavelength increases → Frequency remains the same (This is incorrect; if the wavelength increases, frequency should decrease).
- Anya: Wavelength decreases → Frequency increases (This is correct; if the wavelength decreases, frequency increases).
- Franco: Wavelength remains the same → Frequency decreases (This is incorrect; if the wavelength remains the same, frequency must remain the same).
Thus, the correct statement comes from Anya, who correctly states that as wavelength decreases, frequency increases.