To solve the problem of finding the wavelength associated with a frequency of 100.7 MHz (a typical frequency for FM radio broadcasting), you can follow these detailed steps:
1. Convert the frequency from megahertz (MHz) to hertz (Hz):
- Frequency in MHz: 100.7 MHz
- Conversion factor: 1 MHz = 1,000,000 Hz (or [tex]\( 10^6 \)[/tex] Hz)
- Therefore, [tex]\( 100.7 \times 10^6 = 100700000 \)[/tex] Hz
2. Use the formula that relates the speed of light, frequency, and wavelength:
- The speed of light [tex]\( c \)[/tex] is approximately [tex]\( 299,792,458 \)[/tex] meters per second (m/s).
- The formula to find the wavelength [tex]\( \lambda \)[/tex] is:
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
where [tex]\( \lambda \)[/tex] is the wavelength in meters, [tex]\( c \)[/tex] is the speed of light in m/s, and [tex]\( f \)[/tex] is the frequency in Hz.
3. Substitute the known values into the formula:
- Speed of light [tex]\( c = 299792458 \)[/tex] m/s
- Frequency [tex]\( f = 100700000 \)[/tex] Hz
[tex]\[
\lambda = \frac{299792458}{100700000}
\][/tex]
4. Calculate the wavelength:
[tex]\[
\lambda \approx 2.97708498510427 \ \text{meters}
\][/tex]
5. Round the wavelength to four significant figures:
- The value [tex]\( \lambda \approx 2.97708498510427 \)[/tex] meters rounds to [tex]\( 2.977 \)[/tex] when considering four significant figures.
Hence, the wavelength associated with a frequency of 100.7 MHz is approximately [tex]\( 2.977 \)[/tex] meters.
The final result should be presented as:
The wavelength corresponding to a frequency of 100.7 MHz is [tex]\( 2.977 \)[/tex] meters when expressed to four significant figures.
