To determine which student is correct about the relationship between wavelength and frequency, we need to recall the fundamental relationship between these two properties of waves. The relationship is described by the equation:
\[ v = f \lambda \]
where:
- \( v \) is the speed of the wave (which remains constant in a given medium),
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.
From this relationship, we can deduce that if the wavelength increases, the frequency must decrease (since the speed of the wave is constant) and vice versa.
Now, let's analyze each student's statement based on the given information in the table:
-
Darius: "Wavelength increases - Frequency increases"
- Incorrect: If wavelength increases, frequency should decrease.
-
Kathryn: "Wavelength increases - Frequency remains the same"
- Incorrect: If wavelength increases, frequency cannot remain the same; it must decrease.
-
Anya: "Wavelength decreases - Frequency increases"
- Correct: If wavelength decreases, frequency increases.
-
Franco: "Wavelength remains the same - Frequency decreases"
- Incorrect: If wavelength remains the same, frequency should also remain the same.
Based on this analysis, Anya is correct.