To determine the frequency of a radio wave with a wavelength of 3 meters, we need to make use of the relationship between the speed of light, frequency, and wavelength. The formula connecting these quantities is:
[tex]\[ \text{Frequency} (\nu) = \frac{\text{Speed of light} (c)}{\text{Wavelength} (\lambda)} \][/tex]
where:
- [tex]\(\nu\)[/tex] is the frequency,
- [tex]\(c\)[/tex] is the speed of light, which is approximately [tex]\(300,000,000 \, \text{meters per second}\)[/tex] or [tex]\(3 \times 10^8 \, \text{m/s}\)[/tex],
- [tex]\(\lambda\)[/tex] is the wavelength.
Given:
- [tex]\( c = 3 \times 10^8 \, \text{m/s} \)[/tex]
- [tex]\( \lambda = 3 \, \text{m} \)[/tex]
We substitute these values into the formula:
[tex]\[ \nu = \frac{3 \times 10^8 \, \text{m/s}}{3 \, \text{m}} \][/tex]
Simplifying the above expression:
[tex]\[ \nu = 1 \times 10^8 \, \text{Hz} \][/tex]
Next, we need to convert the frequency from hertz (Hz) to megahertz (MHz). We know that:
[tex]\[ 1 \, \text{MHz} = 1,000,000 \, \text{Hz} = 1 \times 10^6 \, \text{Hz} \][/tex]
So to convert from Hz to MHz:
[tex]\[ \nu_{\text{MHz}} = \frac{1 \times 10^8 \, \text{Hz}}{1 \times 10^6 \, \text{Hz/MHz}} = 100 \, \text{MHz} \][/tex]
Thus, the frequency of the radio wave with a wavelength of 3 meters is:
[tex]\[ 100 \, \text{MHz} \][/tex]
Therefore, the correct answer is:
B. [tex]\( 100 \, \text{MHz} \, \left( 1 \times 10^8 \, \text{Hz} \right) \)[/tex]
