Answer :
Sure, let's solve this step by step!
To find the frequency of radio waves, we use the relationship between the speed of light, frequency, and wavelength. The formula to calculate the frequency ([tex]\( f \)[/tex]) is:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
Where:
- [tex]\( c \)[/tex] is the speed of light in a vacuum ([tex]\( 3.00 \times 10^8 \)[/tex] meters per second, m/s).
- [tex]\( \lambda \)[/tex] is the wavelength in meters (0.500 meters in this case).
Let's plug in the values:
[tex]\[ f = \frac{3.00 \times 10^8 \, \text{m/s}}{0.500 \, \text{m}} \][/tex]
First, divide the speed of light by the wavelength:
[tex]\[ f = \frac{3.00 \times 10^8}{0.500} \][/tex]
[tex]\[ f = 6.00 \times 10^8 \, \text{Hz} \][/tex]
The frequency we found is in Hertz (Hz). To convert this into Megahertz (MHz), we need to divide the frequency by [tex]\( 10^6 \)[/tex] because 1 MHz = [tex]\( 10^6 \)[/tex] Hz:
[tex]\[ f_{\text{MHz}} = \frac{6.00 \times 10^8 \, \text{Hz}}{10^6} \][/tex]
[tex]\[ f_{\text{MHz}} = 600 \, \text{MHz} \][/tex]
So, the frequency of the radio waves is [tex]\( 600 \, \text{MHz} \)[/tex].
To summarize, the correct answer from the given options is:
600. MHz
To find the frequency of radio waves, we use the relationship between the speed of light, frequency, and wavelength. The formula to calculate the frequency ([tex]\( f \)[/tex]) is:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
Where:
- [tex]\( c \)[/tex] is the speed of light in a vacuum ([tex]\( 3.00 \times 10^8 \)[/tex] meters per second, m/s).
- [tex]\( \lambda \)[/tex] is the wavelength in meters (0.500 meters in this case).
Let's plug in the values:
[tex]\[ f = \frac{3.00 \times 10^8 \, \text{m/s}}{0.500 \, \text{m}} \][/tex]
First, divide the speed of light by the wavelength:
[tex]\[ f = \frac{3.00 \times 10^8}{0.500} \][/tex]
[tex]\[ f = 6.00 \times 10^8 \, \text{Hz} \][/tex]
The frequency we found is in Hertz (Hz). To convert this into Megahertz (MHz), we need to divide the frequency by [tex]\( 10^6 \)[/tex] because 1 MHz = [tex]\( 10^6 \)[/tex] Hz:
[tex]\[ f_{\text{MHz}} = \frac{6.00 \times 10^8 \, \text{Hz}}{10^6} \][/tex]
[tex]\[ f_{\text{MHz}} = 600 \, \text{MHz} \][/tex]
So, the frequency of the radio waves is [tex]\( 600 \, \text{MHz} \)[/tex].
To summarize, the correct answer from the given options is:
600. MHz
