What should be height of transmitting antenna if the T.V. telecast is to cover a radius of 128 km128 km ?(Radius of Earth = 6400 km)
Question
What should be height of transmitting antenna if the T.V. telecast is to cover a radius of 128 km128 km ?(Radius of Earth = 6400 km)
Solution
The height of the transmitting antenna can be calculated using the formula for the line of sight distance or the radio horizon of the antenna. The formula is:
d = √(2 * r * h)
where:
- d is the distance to the horizon (or the coverage radius),
- r is the radius of the Earth, and
- h is the height of the antenna.
We can rearrange this formula to solve for h:
h = (d² / (2 * r))
Given that d = 128 km and r = 6400 km, we can substitute these values into the formula:
h = (128 km)² / (2 * 6400 km) h = 16384 km² / 12800 km h = 1.28 km
So, the height of the transmitting antenna should be approximately 1.28 km to cover a radius of 128 km.
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