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 ([tex]\(c\)[/tex]): [tex]\(3 \times 10^8 \, \text{m/s}\)[/tex]
- Frequency ([tex]\(f\)[/tex]): [tex]\(100,000,000 \, \text{Hz}\)[/tex]
2. Recall the formula for wavelength ([tex]\(\lambda\)[/tex]):
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
where:
- [tex]\(\lambda\)[/tex] is the wavelength,
- [tex]\(c\)[/tex] is the speed of light,
- [tex]\(f\)[/tex] is the frequency.
3. Plug the values into the formula:
- Speed of light, [tex]\(c = 3 \times 10^8 \, \text{m/s}\)[/tex]
- Frequency, [tex]\(f = 100,000,000 \, \text{Hz}\)[/tex] (which is [tex]\(1 \times 10^8 \, \text{Hz}\)[/tex])
[tex]\[
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{1 \times 10^8 \, \text{Hz}}
\][/tex]
4. Perform the division:
[tex]\[
\lambda = \frac{3 \times 10^8}{1 \times 10^8}
\][/tex]
5. Simplify the expression:
[tex]\[
\lambda = 3 \, \text{meters}
\][/tex]
### Conclusion:
The wavelength of a beam of light with a frequency of 100,000,000 Hz is [tex]\(3\)[/tex] meters.
