Question

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

• A. $80km$
• B. $48km$
• C. $40km$
• D. $65km$

Answer 1

Answer: (D)

$65km$

Maximum distance upto which signal can be broadcasted is
$d_{max}=\sqrt{2R{h}_T}+\sqrt{2R{h}_R}$
where $h_R$ and $h_R$ are heights of transmitter tower and height of receiver respectively.
Putting all values -
$d_{max}=\sqrt{2\times 6.4\times 106}[\sqrt{104}+\sqrt{40}]$
on solving, $d_{max}=65km$.