A ground receiving station is receiving a signal at 6MHz transmitted from a ground transmitter at a height of 500m located at a distance of 100km. If radius of earth is `6.4xx10^(6)`m, maxim um number density of electron in ionosphere is `10^(12)m^(-3)`. the signal is coming via:

Options

A. ground wave
B. spac e wave
C. Sky wave propagation is useful in the range of 30 to 40 MHz.
D. satellite transponder

Explanation

To determine the type of signal propagation for a signal transmitted at 6 MHz from a height of 500 m and received at a distance of 100 km, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Types of Propagation**:
The three types of propagation are:
- Ground wave propagation
- Sky wave propagation
- Space wave propagation

2. **Calculate Maximum Distance for Space Wave Propagation**:
The formula for the maximum distance \( d \) for space wave propagation is given by:
\[ d = \sqrt{2Rh} \]
where \( R \) is the radius of the Earth and \( h \) is the height of the transmitter.

Given:
- Radius of Earth \( R = 6.4 \times 10^6 \) m
- Height \( h = 500 \) m

Substituting the values:
\[ d = \sqrt{2 \times (6.4 \times 10^6) \times 500} \]

3. **Calculate the Value**:
\[ d = \sqrt{2 \times 6.4 \times 10^6 \times 500} = \sqrt{6400000000} \approx 80000 \text{ m} = 80 \text{ km} \]

4. **Compare Distance with Transmission Distance**:
The maximum distance for space wave propagation is 80 km. The transmitter is located 100 km away from the receiver. Since 100 km > 80 km, space wave propagation is not possible.

5. **Calculate the Critical Frequency for Sky Wave Propagation**:
The critical frequency \( f_c \) for sky wave propagation can be calculated using the formula:
\[ f_c = 9 \sqrt{N} \]
where \( N \) is the maximum electron density in the ionosphere.

Given:
- Maximum electron density \( N = 10^{12} \, \text{m}^{-3} \)

Substituting the value:
\[ f_c = 9 \sqrt{10^{12}} = 9 \times 10^6 \, \text{Hz} = 9 \, \text{MHz} \]

6. **Compare the Signal Frequency with Critical Frequency**:
The transmitted signal frequency is 6 MHz, which is less than the critical frequency of 9 MHz. Therefore, sky wave propagation is possible.

7. **Conclusion**:
Since the signal cannot propagate as a space wave (due to distance limitations) but can propagate as a sky wave (since 6 MHz < 9 MHz), the signal is coming via **sky wave propagation**.

### Final Answer:
The signal is coming via **sky wave propagation**.