A TV tower has a height of 200 m. How much population is covered by TV transmission if the average population density around the tower is 1000/km$^2$? (Radius of the Earth = 6.4$ imes$10$^6$ m)

Question

A TV tower has a height of 200 m. How much population is covered by TV transmission if the average population density around the tower is 1000/km$^2$? (Radius of the Earth = 6.4$	imes$10$^6$ m)

Accepted Answer

First find the range using $d=\sqrt{2Rh}$ with $h=200$ m and $R=6.4\times10^{6}$ m: $d=\sqrt{2\times6.4\times10^{6}\times200}=\sqrt{2.56\times10^{9}}\approx50596$ m $\approx50.6$ km. The area covered is that of a circle of radius $d$ : $\text{Area}=\pi d^{2}=\pi\times(50.6)^{2}\ \text{km}^2\approx\pi\times2560\ \text{km}^2\approx8043\ \text{km}^2$ . Multiplying by the given population density of 1000 people per km$^ …

Start your 14-day free trial to unlock the full solution →

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2022Set TERM21 markMCQ
$Q. The maximum distance upto which TV transmission from a TV tower of height h can be received is proportional to:$
(a) h^(1/2)
(b) h
(c) h³
(d) h²
›Reveal solutionSolution

Line-of-sight TV signals are limited by the curvature of the Earth; the range to the horizon from a tower of height $h$ is $d=\sqrt{2Rh}$ .

TV signals (very high / ultra-high frequency) travel by line-of-sight propagation and are not reflected by the ionosphere, so their range is limited by the visible horizon from the transmitting tower. For a tower of height $h$ on a spherical Earth of radius $R$ , geometry gives the maximum …

Start your 14-day free trial to see the full solution →
CBSE 2018Set ANNUAL1 markMCQ
$Q. The height of a T.V. tower is 100 m. If radius of earth is 6400 km, then what is the maximum distance of transmission from it? (A) 100 km (B) 64\sqrt10 km (C) 6.4\sqrt10 km (D) 8\sqrt20 km$
›Reveal solutionSolution

The line-of-sight range from a tower of height $h$ on the Earth (radius $R$ ) is $d_T = \sqrt{2Rh}$ , giving $d_T = 8\sqrt{20}$ km here. Note: this topic (range of a transmitting antenna) belongs to the Communication Systems chapter, which is not in the current Haryana syllabus.

For a transmitting antenna/tower of height $h_T$ mounted on the (locally flat, curved) Earth of radius $R$ , the maximum line-of-sight distance to the horizon is

$d_T = \sqrt{2Rh_T}$ …

Start your 14-day free trial to see the full solution →
CBSE 2017Set ANNUAL1 markMCQ
$Q. The distance to which a TV tower can broadcast program is, given by (given height of tower h and radius of earth R): (A) \sqrt(2Rh) (B) \sqrt(Rh) (C) \sqrt(R/h) (D) \sqrt(h/R)$
›Reveal solutionSolution

Line-of-sight range from a tower of height $h$ on Earth of radius $R$ is $d=\sqrt{2Rh}$ , from simple geometry.

Note: This question is from the Communication Systems chapter, which was removed from the current CBSE/Haryana Class-12 syllabus in the 2023 rationalisation. It is answered here for completeness since it appeared in this 2017 paper.

…

Start your 14-day free trial to see the full solution →

Q.A TV tower has a height of 200 m. How much population is covered by TV transmission if the average population density around the tower is 1000/km $^2$ ? (Radius of the Earth = 6.4 $\times$ 10 $^6$ m)

Concept understanding — Space Wave Propagation and Range of Transmission

Q.A TV tower has a height of 200 m. How much population is covered by TV transmission if the average population density around the tower is 1000/km2^22? (Radius of the Earth = 6.4×\times×106^66 m)

🎓Unlock everything free for 14 days

Q.A TV tower has a height of 200 m. How much population is covered by TV transmission if the average population density around the tower is 1000/km $^2$ ? (Radius of the Earth = 6.4 $\times$ 10 $^6$ m)

Unlock everything free for 14 days