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Answer :
Certainly! Let's solve the problem step-by-step:
1. Convert the Speed of Light:
- Radio waves travel at the speed of light, which is given as [tex]\( c = 300,000 \)[/tex] km/s.
- To convert this to meters per second (m/s), multiply by 1,000 (since 1 kilometer = 1,000 meters).
[tex]\[
c = 300,000 \times 1,000 = 300,000,000 \text{ m/s}
\][/tex]
2. Convert the Frequency:
- The frequency [tex]\( f \)[/tex] of the radio wave is given as [tex]\( 150 \)[/tex] MHz.
- To convert megahertz (MHz) to hertz (Hz), multiply by [tex]\( 1,000,000 \)[/tex] (since 1 MHz = 1,000,000 Hz).
[tex]\[
f = 150 \times 1,000,000 = 150,000,000 \text{ Hz}
\][/tex]
3. Calculate the Wavelength:
- The wavelength [tex]\( \lambda \)[/tex] of a wave is related to its speed and frequency by the formula:
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
- Plugging in the converted values:
[tex]\[
\lambda = \frac{300,000,000 \text{ m/s}}{150,000,000 \text{ Hz}}
\][/tex]
[tex]\[
\lambda = 2 \text{ m}
\][/tex]
Therefore, the wavelength [tex]\(\lambda\)[/tex] of the radio wave is [tex]\( 2.0 \)[/tex] meters.
1. Convert the Speed of Light:
- Radio waves travel at the speed of light, which is given as [tex]\( c = 300,000 \)[/tex] km/s.
- To convert this to meters per second (m/s), multiply by 1,000 (since 1 kilometer = 1,000 meters).
[tex]\[
c = 300,000 \times 1,000 = 300,000,000 \text{ m/s}
\][/tex]
2. Convert the Frequency:
- The frequency [tex]\( f \)[/tex] of the radio wave is given as [tex]\( 150 \)[/tex] MHz.
- To convert megahertz (MHz) to hertz (Hz), multiply by [tex]\( 1,000,000 \)[/tex] (since 1 MHz = 1,000,000 Hz).
[tex]\[
f = 150 \times 1,000,000 = 150,000,000 \text{ Hz}
\][/tex]
3. Calculate the Wavelength:
- The wavelength [tex]\( \lambda \)[/tex] of a wave is related to its speed and frequency by the formula:
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
- Plugging in the converted values:
[tex]\[
\lambda = \frac{300,000,000 \text{ m/s}}{150,000,000 \text{ Hz}}
\][/tex]
[tex]\[
\lambda = 2 \text{ m}
\][/tex]
Therefore, the wavelength [tex]\(\lambda\)[/tex] of the radio wave is [tex]\( 2.0 \)[/tex] meters.
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