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Establish a relation between coverage distance and height of transmitting antenna. |
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Answer» Solution :Let `AB` be a T.V. tower of height `h` above the earth. `T.V.` signal is received within a circle of `CQ=QD` on the surface of earth. Let `R` be the radius of the earth. Let `CQ=QD=d` and `AB=h`. `:. OB=R+h` In rt. `/_d` triangle `OCB,` `OB^(2)=OC^(2)+BC^(2)` `(R+h)^(2)=R^(2)+d^(2)` `d^(2)=(R+h)^(2)-R^(2)` `=R^(2)+h^(2)+2Rh-R^(2)` or `d^(2)=h^(2)+2Rh` SINCE `h^(2)` can be neglected as compared to `2hR` `:.d^(2)=2Rh` or `d=sqrt(2hR)` or `h=(d^(2))/(2R).`  AREA covered by T.V. signal `=pid^(2)` `=pi2hR=2pihR` Population covered = Area covered `XX` Population density Since `dpropsqrt(h,)( :.2R` is constant ) So greater the height of T.V. transmitting antenna, grater is its range. |
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