The height of transmission antenna is 600m find the area covered by the antenna in which the signal from the antenna can be received.

To determine the area covered by a transmission antenna, we can use the concept of the radio horizon, which is the maximum distance over which the signal can be received. This distance depends on the height of the antenna and can be calculated using a specific formula. Let's break this down step by step.

Understanding the Radio Horizon

The radio horizon is influenced by the curvature of the Earth. The formula to estimate the distance to the horizon in kilometers is:

D = 3.57 × √h

In this formula, D represents the distance to the horizon in kilometers, and h is the height of the antenna in meters. For your case, the height of the antenna is 600 meters.

Calculating the Distance to the Horizon

Now, let's plug in the height of the antenna into the formula:

D = 3.57 × √600

First, we need to calculate the square root of 600:

√600 ≈ 24.49

Now, substituting this value back into the formula gives:

D ≈ 3.57 × 24.49 ≈ 87.5 kilometers

Determining the Coverage Area

The area covered by the antenna can be visualized as a circle, where the radius is the distance to the horizon we just calculated. The formula for the area of a circle is:

Area = π × r²

Here, r is the radius, which is the distance we found (87.5 km). Now, let's calculate the area:

Area ≈ π × (87.5)²

Calculating the square of the radius:

(87.5)² ≈ 7656.25

Now, substituting this into the area formula:

Area ≈ 3.14 × 7656.25 ≈ 24040.5 square kilometers

Final Thoughts

Therefore, the area covered by the transmission antenna with a height of 600 meters is approximately 24040.5 square kilometers. This means that, under ideal conditions, the signal can be received within this expansive area, allowing for effective communication over a vast distance.