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Wave Optics

Question

A TV tower has a height of 100 m, how much population will be covered by the TV broadcast if the average population density around the tower is 10000 per km²

Solution

Given,
Height of TV tower, h = 100 m
Average population density around the TV tower = 10000 per km^2.Now, range is given by,

d = \sqrt{2 rh} = \sqrt{2 \times 6.4 \times 10^{6} \times 100} = 3.6 \times 10^{4} m

Area = {πd}^{2} = \frac{22}{7} \times {(3.6 \times 10^{6})}^{2} = 4.1 \times 10^{13} m^{2}

Population of the area covered is =

4.1 \times 10^{7} {km}^{2} \times 10000 per {km}^{2} = 4.1 \times 10^{11} .