To determine which student's idea about the relationship between wavelength and frequency is correct, we need to consider the relationship defined by the wave equation for electromagnetic waves:
\[ c = \lambda \cdot f \]
where:
- \( c \) is the speed of light (a constant),
- \( \lambda \) is the wavelength,
- \( f \) is the frequency.
From the equation, we can deduce that:
- If the wavelength \( \lambda \) increases, the frequency \( f \) must decrease (because the speed of light is constant).
- If the wavelength \( \lambda \) decreases, the frequency \( f \) must increase.
- If the wavelength \( \lambda \) remains the same, the frequency \( f \) will also remain the same.
Now, let's evaluate each student's statement:
- Darius: Wavelength increases (correct) and frequency increases (incorrect).
- Kathryn: Wavelength increases (correct) and frequency remains the same (incorrect).
- Anya: Wavelength decreases (incorrect) and frequency increases (correct).
- Franco: Wavelength remains the same (correct) and frequency decreases (incorrect).
Based on this analysis, all four students have at least one incorrect statement regarding the relationship between wavelength and frequency. However, the correct relationships from the principle above lead us to conclude that none of them are completely correct.
Thus, none of the students are entirely correct based on the established scientific principles. Would you like to explore this further or discuss different scenarios?