Answer :
To determine the wavelength of the FM radio waves broadcast by the station, you can use the formula that relates the frequency and speed of light to the wavelength. The formula is:
[tex]\[ \text{wavelength} = \frac{\text{speed of light}}{\text{frequency}} \][/tex]
Given data:
- Frequency (\(f\)) = \(9.23 \times 10^7\) Hz
- Speed of light (\(c\)) = \(3.00 \times 10^8\) m/s
Now, plug these values into the formula:
[tex]\[ \text{wavelength} = \frac{3.00 \times 10^8 \, \text{m/s}}{9.23 \times 10^7 \, \text{Hz}} \][/tex]
Carrying out the division:
[tex]\[ \text{wavelength} = \frac{3.00 \times 10^8}{9.23 \times 10^7} = 3.2502708559046587 \, \text{meters} \][/tex]
Rounding the result to two decimal places, we get:
[tex]\[ \text{wavelength} \approx 3.25 \, \text{meters} \][/tex]
Thus, the wavelength of these radio waves is approximately \(3.25 \, \text{meters}\). Therefore, the correct answer from the options provided is:
[tex]\[3.25 m\][/tex]
[tex]\[ \text{wavelength} = \frac{\text{speed of light}}{\text{frequency}} \][/tex]
Given data:
- Frequency (\(f\)) = \(9.23 \times 10^7\) Hz
- Speed of light (\(c\)) = \(3.00 \times 10^8\) m/s
Now, plug these values into the formula:
[tex]\[ \text{wavelength} = \frac{3.00 \times 10^8 \, \text{m/s}}{9.23 \times 10^7 \, \text{Hz}} \][/tex]
Carrying out the division:
[tex]\[ \text{wavelength} = \frac{3.00 \times 10^8}{9.23 \times 10^7} = 3.2502708559046587 \, \text{meters} \][/tex]
Rounding the result to two decimal places, we get:
[tex]\[ \text{wavelength} \approx 3.25 \, \text{meters} \][/tex]
Thus, the wavelength of these radio waves is approximately \(3.25 \, \text{meters}\). Therefore, the correct answer from the options provided is:
[tex]\[3.25 m\][/tex]
