Question

A TV transmission tower has a height of $140\text{m}$ and the height of the receiving antenna is $40\text{m}$. What is the maximum distance upto which signals can be broadcasted from this tower in LOS (Line of Sight) mode? (Given : radius of earth $=6.4\times {10}^6\text{m}$).

• A. $80\text{km}$
• B. $65\text{km}$
• C. $40\text{km}$
• D. $48\text{km}$

Answer 1

The correct option is B $65\text{km}$

Given:
Tower height $h_T=140\text{m}$
Height of the receiving antenna $h_R=40\text{m}$
Radius of earth $R=6.4\times {10}^6\text{m}$

We know that,
Maximum distance upto which signal can be broadcasted

$d_{\text{max}}=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}$

where $h_T$ and $h_R$ are heights of transmission tower and receiving antenna respectively.

Putting values $R,h_T$ and $h_R$

$d_{\text{max}}=\sqrt{2\times 6.4\times {10}^6}[\sqrt{140}+\sqrt{40}]$

or, $d_{\text{max}}\simeq 65\text{km}$

Hence, option $\left(A\right)$ is correct.