Sure, let's calculate the wavelength of a beam of light with a frequency of 100,000,000 Hz (100 MHz). Here are the steps we need to follow:
### Step-by-Step Solution:
1. Identify the necessary constants and values:
- Speed of light (\(\(c\)\)): \(\(3 \times 10^8 \, \text{m/s}\)\)
- Frequency (\(\(f\)\)): \(\(100,000,000 \, \text{Hz}\)\)
2. Recall the formula for wavelength (\(\(\lambda\)\)):
\(\[
\lambda = \frac{c}{f}
\]\)
where:
- \(\(\lambda\)\) is the wavelength,
- \(\(c\)\) is the speed of light,
- \(\(f\)\) is the frequency.
3. Plug the values into the formula:
- Speed of light, \(\(c = 3 \times 10^8 \, \text{m/s}\)\)
- Frequency, \(\(f = 100,000,000 \, \text{Hz}\)\) (which is \(\(1 \times 10^8 \, \text{Hz}\)\))
\(\[
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{1 \times 10^8 \, \text{Hz}}
\]\)
4. Perform the division:
\(\[
\lambda = \frac{3 \times 10^8}{1 \times 10^8}
\]\)
5. Simplify the expression:
\(\[
\lambda = 3 \, \text{meters}
\]\)
### Conclusion:
The wavelength of a beam of light with a frequency of 100,000,000 Hz is \(\(3\)\) meters.
