Answer :
To find the wavelength of an AM radio wave in a vacuum when its frequency is 810 kHz, we can use the relationship between speed, frequency, and wavelength. The formula is:
[tex]\[ \text{wavelength} = \frac{\text{speed of light}}{\text{frequency}} \][/tex]
Step-by-step:
1. Speed of Light: In a vacuum, the speed of light is approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second.
2. Frequency Conversion: The frequency given is 810 kHz. We need to convert this frequency into hertz (Hz):
[tex]\[
\text{Frequency in Hz} = 810 \times 10^3 = 810,000 \text{ Hz}
\][/tex]
3. Calculate Wavelength: Now, using the formula for wavelength:
[tex]\[
\text{wavelength} = \frac{3 \times 10^8 \text{ m/s}}{810,000 \text{ Hz}} \approx 370.37 \text{ meters}
\][/tex]
We can conclude that the wavelength of the AM radio wave is approximately 370 meters.
Therefore, the correct choice is:
○ 370 m
[tex]\[ \text{wavelength} = \frac{\text{speed of light}}{\text{frequency}} \][/tex]
Step-by-step:
1. Speed of Light: In a vacuum, the speed of light is approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second.
2. Frequency Conversion: The frequency given is 810 kHz. We need to convert this frequency into hertz (Hz):
[tex]\[
\text{Frequency in Hz} = 810 \times 10^3 = 810,000 \text{ Hz}
\][/tex]
3. Calculate Wavelength: Now, using the formula for wavelength:
[tex]\[
\text{wavelength} = \frac{3 \times 10^8 \text{ m/s}}{810,000 \text{ Hz}} \approx 370.37 \text{ meters}
\][/tex]
We can conclude that the wavelength of the AM radio wave is approximately 370 meters.
Therefore, the correct choice is:
○ 370 m
