question_answer

In communication system the range is R, if the height of antenna is doubled, then what will be the increase in range?

Answer:

41.4% Transmission range \[d=\sqrt{2hR}\] where, h is the height of antenna and R is the radius of earth. \[\therefore \]      \[d\propto \sqrt{h}\] If the height of antenna is doubled, \[d'\propto \sqrt{2h}\] \[\frac{d'}{d}=\frac{\sqrt{2h}}{\sqrt{h}}=\sqrt{2}=1414\] \[d'=1.414\,d=d\,(1+0.414)=d+0.414\,d\]           \[=d+\frac{41.4}{100}d=d+41.4%\,d\] i.e. the range is increased by 41.4%.