Topic: Electromagnetics and Antennas
If over the course of a day, the maximum electron density in the ionosphere varies from $10^{11}$ to $10^{12}m^{-3}$ the critical frequency changes approximately from:
- A. 2.2 MHz to 7 MHz
- B. 2.5 MHz to 8 MHz
- C. 2.8 MHz to 9 MHz
- D. 3.2 MHz to 10 MHz
Answer: C. 2.8 MHz to 9 MHz
Explanation: The critical frequency $f_c$ in Hz is related to the maximum electron density $N_{max}$ (in $m^{-3}$) by the formula $f_c \approx 9 \sqrt{N_{max}}$. For $N_{max} = 10^{11}$, $f_c \approx 9 \sqrt{10^{11}} = 9 \times 3.16 \times 10^5 \approx 2.84$ MHz. For $N_{max} = 10^{12}$, $f_c \approx 9 \sqrt{10^{12}} = 9 \times 10^6 = 9$ MHz. Therefore, the frequency changes from approximately 2.8 MHz to 9 MHz.