Use the table

Question

Student:
Darius
Kathryn
Anya
Franco

Wavelength:
increase
increase
decrease
remain the same

Frequency:
increase
remain the same
increase
decrease

Four students write their ideas about the relationship between wavelength and frequency. Which student is correct?

Answer 1

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:

1. Darius: Wavelength increases, frequency increases. (This is incorrect because an increase in wavelength means frequency should decrease.)
2. Kathryn: Wavelength increases, frequency remains the same. (This is incorrect because an increase in wavelength should result in a decrease in frequency.)
3. Anya: Wavelength decreases, frequency increases. (This is correct because a decrease in wavelength corresponds to an increase in frequency.)
4. 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.