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 mode of propagation for a signal transmitted from a ground transmitter to a receiving station, we need to analyze the given parameters step by step.

### Step 1: Calculate Maximum Distance for Space Wave Communication
The maximum distance \( D \) for space wave communication can be calculated using the formula:
\[ D = \sqrt{2RH} \]
where:
- \( R \) is the radius of the Earth (\( 6.4 \times 10^6 \) m),
- \( H \) is the height of the transmitter (500 m).

Substituting the values:
\[ D = \sqrt{2 \times (6.4 \times 10^6) \times 500} \]
Calculating this gives:
\[ D = \sqrt{2 \times 6.4 \times 10^6 \times 500} = \sqrt{6.4 \times 10^9} \approx 80 \times 10^3 \text{ m} = 80 \text{ km} \]

### Step 2: Compare Distance with Maximum Distance for Space Waves
The distance between the transmitter and the receiver is given as 100 km. Since the maximum distance for space wave communication is 80 km, the signal cannot propagate via space waves.

### Step 3: Calculate Critical Frequency for Sky Wave Propagation
The critical frequency \( f_c \) can be calculated using the formula:
\[ f_c = 9 \sqrt{n_{max}} \]
where \( n_{max} \) is the maximum number density of electrons in the ionosphere (\( 10^{12} \, m^{-3} \)).

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

### Step 4: Determine the Mode of Propagation
The transmitted signal frequency is 6 MHz. Since 6 MHz is less than the critical frequency of 9 MHz, the signal can be reflected back to the Earth by the ionosphere, allowing for sky wave propagation.

### Conclusion
Thus, the signal is coming via **sky wave propagation**.

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