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Question

A TV transmission tower has a height of $$140\ m$$ and the height of the receiving antenna is $$40\ m$$. 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
80 km
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B
48 km
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C
40 km
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D
65 km
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Solution

The correct option is C $$65\ km$$
Maximum distance upto which signal can be broadcasted is
$$d_{max} = \sqrt {2Rh_{T}} + \sqrt {2Rh_{R}}$$
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, $$d_{max} = 65\ km$$.

Physics

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