Answer :
To calculate the wavelength at which the FM radio station is broadcasting, we use the relationship between the speed of light, frequency, and wavelength. The formula we use is:
[tex]\[ \text{Wavelength} = \frac{\text{Speed of light}}{\text{Frequency}} \][/tex]
Here's how we solve it step-by-step:
1. Identify the given values:
- The speed of light is approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second.
- The frequency of the FM radio station is 99.7 MHz.
2. Convert the frequency from MHz to Hz:
- 1 MHz is equal to [tex]\( 10^6 \)[/tex] Hz.
- Therefore, 99.7 MHz equals [tex]\( 99.7 \times 10^6 \)[/tex] Hz, which is 99,700,000 Hz.
3. Calculate the wavelength:
- Use the formula to find the wavelength:
[tex]\[ \text{Wavelength} = \frac{3 \times 10^8 \, \text{m/s}}{99,700,000 \, \text{Hz}} \][/tex]
- This calculation gives a result of approximately [tex]\( 3.009 \)[/tex] meters.
Therefore, the FM radio station broadcasts at a wavelength of approximately 3.01 meters.
[tex]\[ \text{Wavelength} = \frac{\text{Speed of light}}{\text{Frequency}} \][/tex]
Here's how we solve it step-by-step:
1. Identify the given values:
- The speed of light is approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second.
- The frequency of the FM radio station is 99.7 MHz.
2. Convert the frequency from MHz to Hz:
- 1 MHz is equal to [tex]\( 10^6 \)[/tex] Hz.
- Therefore, 99.7 MHz equals [tex]\( 99.7 \times 10^6 \)[/tex] Hz, which is 99,700,000 Hz.
3. Calculate the wavelength:
- Use the formula to find the wavelength:
[tex]\[ \text{Wavelength} = \frac{3 \times 10^8 \, \text{m/s}}{99,700,000 \, \text{Hz}} \][/tex]
- This calculation gives a result of approximately [tex]\( 3.009 \)[/tex] meters.
Therefore, the FM radio station broadcasts at a wavelength of approximately 3.01 meters.
