Answer :
To calculate the wavelength of a radio station broadcasting at a frequency of 101.2 MHz, we can use the formula that relates the speed of light, frequency, and wavelength:
[tex]\[ \text{Wavelength} = \frac{\text{Speed of Light}}{\text{Frequency}} \][/tex]
### Step-by-Step Solution:
1. Identify the Given Frequency:
- The frequency of the radio station is 101.2 MHz.
2. Convert Frequency to Hertz (Hz):
- Since 1 MHz is [tex]\(1 \times 10^6\)[/tex] Hz, we need to convert 101.2 MHz to Hz:
[tex]\[
101.2 \, \text{MHz} = 101.2 \times 10^6 \, \text{Hz}
\][/tex]
3. Use the Speed of Light:
- The speed of light is approximately [tex]\(3 \times 10^8\)[/tex] meters per second (m/s).
4. Apply the Wavelength Formula:
- Substitute the values into the formula:
[tex]\[
\text{Wavelength} = \frac{3 \times 10^8 \, \text{m/s}}{101.2 \times 10^6 \, \text{Hz}}
\][/tex]
5. Calculate the Wavelength:
- Performing the division gives us the wavelength in meters:
[tex]\[
\text{Wavelength} \approx 2.964 \, \text{m}
\][/tex]
6. Select the Closest Answer Choice:
- The calculated wavelength is approximately 2.964 m, which matches option (D).
Therefore, the correct answer is (D) 2.964 m.
[tex]\[ \text{Wavelength} = \frac{\text{Speed of Light}}{\text{Frequency}} \][/tex]
### Step-by-Step Solution:
1. Identify the Given Frequency:
- The frequency of the radio station is 101.2 MHz.
2. Convert Frequency to Hertz (Hz):
- Since 1 MHz is [tex]\(1 \times 10^6\)[/tex] Hz, we need to convert 101.2 MHz to Hz:
[tex]\[
101.2 \, \text{MHz} = 101.2 \times 10^6 \, \text{Hz}
\][/tex]
3. Use the Speed of Light:
- The speed of light is approximately [tex]\(3 \times 10^8\)[/tex] meters per second (m/s).
4. Apply the Wavelength Formula:
- Substitute the values into the formula:
[tex]\[
\text{Wavelength} = \frac{3 \times 10^8 \, \text{m/s}}{101.2 \times 10^6 \, \text{Hz}}
\][/tex]
5. Calculate the Wavelength:
- Performing the division gives us the wavelength in meters:
[tex]\[
\text{Wavelength} \approx 2.964 \, \text{m}
\][/tex]
6. Select the Closest Answer Choice:
- The calculated wavelength is approximately 2.964 m, which matches option (D).
Therefore, the correct answer is (D) 2.964 m.
