As the frequency of an electromagnetic wave increases, which of the following occurs?

• A. The energy of the wave decreases.
• B. The speed of the wave increases.
• C. The amplitude of the wave increases.
• D. The wavelength decreases.

Answer: (D)

Verified step by step guidance

1. Recall the fundamental relationship between the frequency (\(f\)), wavelength (\(\lambda\)), and speed (\(v\)) of an electromagnetic wave, which is given by the equation: \[v = f \times \lambda\]
2. Understand that for electromagnetic waves traveling in a vacuum (or air), the speed (\(v\)) is constant and equal to the speed of light (\(c\)), approximately \$3.00 \times 10^{8}$ m/s.
3. Since \(v\) is constant, if the frequency (\(f\)) increases, the wavelength (\(\lambda\)) must adjust to keep the product \(f \times \lambda\) equal to \(v\). This means wavelength and frequency are inversely proportional.
4. Mathematically, rearrange the equation to solve for wavelength: \[\lambda = \frac{v}{f}\]
5. From this equation, as frequency (\(f\)) increases, the wavelength (\(\lambda\)) decreases, which explains why the correct answer is that the wavelength decreases when frequency increases.