A ground receiver station is receiving a signal at (a) 5 MHz and (b) 100MHz.transmitted from a ground transmitter at a height of 400 m located at a distance of 125 km on whether coming via space wave of sky wave propagation or satellite transponder Radius of earth=`6.4 xx10^(6)` m, maximum number density of electrons in lonosphere =`10^(12) m^(-3)`

Answer

To solve the problem, we need to determine whether the signals at 5 MHz and 100 MHz are being transmitted via space wave, sky wave propagation, or satellite transponder. We will also calculate the critical frequency for ionospheric propagation.

### Step-by-Step Solution:

1. **Understanding the Parameters**:
- Height of the transmitter (H) = 400 m
- Distance from the receiver (D) = 125 km = 125,000 m
- Radius of the Earth (R) = 6.4 x 10^6 m
- Maximum electron density in the ionosphere (N_max) = 10^12 m^(-3)

2. **Calculate the Maximum Distance for Space Wave Propagation**:
The maximum distance (D_max) for space wave propagation can be calculated using the formula:
\[ D_{max} = \sqrt{2RH} \]
Substituting the values:
\[ D_{max} = \sqrt{2 \times (6.4 \times 10^6) \times 400} \]
\[ D_{max} = \sqrt{5.12 \times 10^9} \approx 71.6 \text{ km} \]

Since the distance (125 km) is greater than D_max (71.6 km), the signal cannot be received via space wave propagation.

3. **Determine the Critical Frequency for Ionospheric Propagation**:
The critical frequency (f_c) for ionospheric propagation can be calculated using the formula:
\[ f_c = 9 \sqrt{N_{max}} \]
Substituting the value of N_max:
\[ f_c = 9 \sqrt{10^{12}} = 9 \times 10^6 \text{ Hz} = 9 \text{ MHz} \]

4. **Comparison of Frequencies**:
- For the signal at 5 MHz: This frequency is less than the critical frequency (9 MHz), so it can be received via sky wave propagation.
- For the signal at 100 MHz: This frequency is greater than the critical frequency (9 MHz), so it cannot be received via sky wave propagation and is likely transmitted via satellite transponder.

### Final Conclusion:
- The signal at **5 MHz** is received via **sky wave propagation**.
- The signal at **100 MHz** is received via a **satellite transponder**.