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What would be the frequency of an electromagnetic wave hav- ing a wavelength equal to Earth's diameter (12,800 km)? In what part of the electromagnetic spectrum would such a wave lie?

What would be the frequency of an electromagnetic wave hav- ing a wavelength equal to Earth's diameter (12,800 km)? In what part of the electromagnetic spectrum would such a wave lie?

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### Electromagnetic Wave Frequency Calculation **Question:** What would be the frequency of an electromagnetic wave having a wavelength equal to Earth's diameter (12,800 km)? In what part of the electromagnetic spectrum would such a wave lie? **Detailed Explanation:** To determine the frequency of an electromagnetic wave, we can use the relationship between the speed of light (c), frequency (f), and wavelength (λ). The speed of light in a vacuum is approximately \( 3 \times 10^8 \) meters per second (m/s). The formula that relates these quantities is: \[ c = f \lambda \] Given: - Wavelength, \( \lambda \) = 12,800 km = \( 12,800 \times 10^3 \) meters We can rearrange the formula to solve for frequency \( f \): \[ f = \frac{c}{\lambda} \] Substituting in the given values: \[ f = \frac{3 \times 10^8 \text{ m/s}}{12,800 \times 10^3 \text{ m}} \] \[ f = \frac{3 \times 10^8}{12,800 \times 10^3} \] \[ f \approx 23.44 \text{ Hz} \] ### Conclusion: The frequency of an electromagnetic wave with a wavelength equal to Earth's diameter is approximately 23.44 Hz. This frequency falls within the Extremely Low Frequency (ELF) range of the electromagnetic spectrum, which typically spans frequencies from 3 Hz to 30 Hz.
Transcribed Image Text:### Electromagnetic Wave Frequency Calculation **Question:** What would be the frequency of an electromagnetic wave having a wavelength equal to Earth's diameter (12,800 km)? In what part of the electromagnetic spectrum would such a wave lie? **Detailed Explanation:** To determine the frequency of an electromagnetic wave, we can use the relationship between the speed of light (c), frequency (f), and wavelength (λ). The speed of light in a vacuum is approximately \( 3 \times 10^8 \) meters per second (m/s). The formula that relates these quantities is: \[ c = f \lambda \] Given: - Wavelength, \( \lambda \) = 12,800 km = \( 12,800 \times 10^3 \) meters We can rearrange the formula to solve for frequency \( f \): \[ f = \frac{c}{\lambda} \] Substituting in the given values: \[ f = \frac{3 \times 10^8 \text{ m/s}}{12,800 \times 10^3 \text{ m}} \] \[ f = \frac{3 \times 10^8}{12,800 \times 10^3} \] \[ f \approx 23.44 \text{ Hz} \] ### Conclusion: The frequency of an electromagnetic wave with a wavelength equal to Earth's diameter is approximately 23.44 Hz. This frequency falls within the Extremely Low Frequency (ELF) range of the electromagnetic spectrum, which typically spans frequencies from 3 Hz to 30 Hz.
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