Question

Answer the following questions:
(i) A TV transmitter has a range of $50 Km$. What is the height of the TV transmission tower? Radius of earth $R_{e} = 6.4 \times 10^{6} m$
(ii) A $1V$ tower has a height of $500 m$ at a given place. If the radius of earth is $6400Km$. what Is it coverage range?

Answer 1

Hint: For solving the question, we need to know the formula that tells about the relationship between the height of the tower, the covering range of the tower, and the radius of the earth. If two values are given, we can find the third unknown term.

Complete step-by-step solution:
a) Given: Range covered, $d = 50Km = 50000 m$
Radius of earth $R_{e} = 6.4 \times 10^{6} m$
We have to find the height of the TV transmission tower.
Height is related with range and radius of earth by this formula:
$h = \dfrac{d^{2}}{2 R_{e}}$
 Now put the given values in the above formula.
$h = \dfrac{(50000)^{2}}{2 \times 6.4 \times 10^{6}}$
$\implies h = \dfrac{2500}{2 \times 6.4}$
$\times h = 195.3 m$
The height of the TV transmission tower is $195.3 m$.
b) height of the tower, $h = 500 m$
Radius of earth $R_{e} = 6400 Km$
We have to find the range of the tower.
Range is related with height and radius of earth by this formula:
$d = \sqrt {2hR_{e}}$
$\implies d = \sqrt {2 \times 0.5 \times 6400}$
$\implies d = 80Km$
The coverage range is $80 Km$.

Note: Television signal waves possess a frequency range. These waves neither obey the curvature of the earth nor get returned by the ionosphere. The propagation of such waves is probably only via satellite or a tall television antenna, which may directly prevent the transmitted signals from the communications antenna.