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Answer :
To calculate the distance between adjacent crests of the radio waves, which is called the wavelength, we can use the formula:
[tex]\[ \text{Wavelength} = \frac{\text{Speed of light}}{\text{Frequency}} \][/tex]
1. Given information:
- Speed of light: [tex]\(3 \times 10^8 \, \text{m/s}\)[/tex]
- AM frequency: 913 KHz, which is [tex]\(913 \times 10^3\)[/tex] Hz
- FM frequency: 9.9 MHz, which is [tex]\(9.9 \times 10^6\)[/tex] Hz
2. Calculate the wavelength for AM radio:
- Use the formula for wavelength.
- Substitute the speed of light ([tex]\(3 \times 10^8\)[/tex] m/s) and the frequency of the AM station ([tex]\(913 \times 10^3\)[/tex] Hz) into the formula:
[tex]\[
\text{Wavelength}_{\text{AM}} = \frac{3 \times 10^8}{913 \times 10^3}
\][/tex]
- This calculation will give us the wavelength for the AM radio station, which is approximately 328.59 meters.
3. Calculate the wavelength for FM radio:
- Again, use the formula for wavelength.
- Substitute the speed of light ([tex]\(3 \times 10^8\)[/tex] m/s) and the frequency of the FM station ([tex]\(9.9 \times 10^6\)[/tex] Hz) into the formula:
[tex]\[
\text{Wavelength}_{\text{FM}} = \frac{3 \times 10^8}{9.9 \times 10^6}
\][/tex]
- This calculation will give us the wavelength for the FM radio station, which is approximately 30.30 meters.
Therefore, the distance between adjacent crests (or wavelengths) is approximately 328.59 meters for the AM radio and 30.30 meters for the FM radio.
[tex]\[ \text{Wavelength} = \frac{\text{Speed of light}}{\text{Frequency}} \][/tex]
1. Given information:
- Speed of light: [tex]\(3 \times 10^8 \, \text{m/s}\)[/tex]
- AM frequency: 913 KHz, which is [tex]\(913 \times 10^3\)[/tex] Hz
- FM frequency: 9.9 MHz, which is [tex]\(9.9 \times 10^6\)[/tex] Hz
2. Calculate the wavelength for AM radio:
- Use the formula for wavelength.
- Substitute the speed of light ([tex]\(3 \times 10^8\)[/tex] m/s) and the frequency of the AM station ([tex]\(913 \times 10^3\)[/tex] Hz) into the formula:
[tex]\[
\text{Wavelength}_{\text{AM}} = \frac{3 \times 10^8}{913 \times 10^3}
\][/tex]
- This calculation will give us the wavelength for the AM radio station, which is approximately 328.59 meters.
3. Calculate the wavelength for FM radio:
- Again, use the formula for wavelength.
- Substitute the speed of light ([tex]\(3 \times 10^8\)[/tex] m/s) and the frequency of the FM station ([tex]\(9.9 \times 10^6\)[/tex] Hz) into the formula:
[tex]\[
\text{Wavelength}_{\text{FM}} = \frac{3 \times 10^8}{9.9 \times 10^6}
\][/tex]
- This calculation will give us the wavelength for the FM radio station, which is approximately 30.30 meters.
Therefore, the distance between adjacent crests (or wavelengths) is approximately 328.59 meters for the AM radio and 30.30 meters for the FM radio.
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