Question

A TV transmission tower at a particular station has a height of 160 m. Radius of earth is 6400 km and the population density is $\rho =1200\text{ }k{{m}^{-2}}$.
i. the range it covers is 45255 m
ii. The population it covers is 77.42 lakhs.
iii. the height of the antenna should be increased by 480 m to double the coverage range.
A. i and ii are true.
B. ii and iii are true
C. i and iii are true
D. i, ii and iii are true

Answer 1

Hint: TV transmission is a broadcast transmission where the wave propagates through space. Obtain the equation that gives the range of space wave propagation and put the given values to find the required answer.

Complete answer:
Given in the question that,
The height of the tv transmission tower is, ${{h}_{t}}=160m$
The radius of the earth is, $R=6400km=6.4\times {{10}^{6}}m$
Tv transmission is a broadcast transmission system. It is done by the sky wave propagation. a space wave propagates from the transmitting antenna in a straight line of sight. The range of the transmission tower is given by,
$\begin{align}
  & \text{Range}=\sqrt{2R{{h}_{t}}} \\
 & \text{Range}=\sqrt{2\times 6.4\times {{10}^{6}}\times 160} \\
 & \text{Range}=45255m \\
\end{align}$
The area covered has been mentioned as,
$A=\pi {{d}_{T}}^{2}$
Substituting the values in it will give,
$\begin{align}
  & A=3.14\times {{\left( 45255 \right)}^{2}}\text{ }{{m}^{2}} \\
 & \Rightarrow A=6.431\times {{10}^{9}}\text{ }{{m}^{2}} \\
 & \therefore A=6431\text{ }k{{m}^{2}} \\
\end{align}$
Therefore the population covered will be given as,
$P=\pi {{d}_{T}}^{2}\times \rho $
Substituting the values in the equation will be written as,
$P=6431\times 1200=77.42\text{ lakhs}$
If the height of the transmission tower is increased by 480m, the new height of the tower will be,
${{h}_{t}}=160+480=640m$
So, the range of the tower for this height of the transmission tower will be,
$\begin{align}
  & \text{Range}=\sqrt{2R{{h}_{t}}} \\
 & \text{Range}=\sqrt{2\times 6.4\times {{10}^{6}}\times 640} \\
 & \text{Range}=90510m \\
\end{align}$
So, the transmission tower will double the coverage range if the height of the tower is increased by 640 m.
So, from the given data in the question, we can say that all the options are correct.

The correct option is (D).

Note:
In a point to point communication system we have only one sender and receiver. But in broadcast communication we have more than one receiver with one sender. So, with the broadcast system we can send the same signal to more than one receiver. Sky wave propagation is used by short wave broadcast services in the frequency range of a few MHz to 40 MHz, long distance communication can be achieved by ionospheric reflection of radio waves. This is called sky wave propagation.