A TV transmission tower of antenna is at a height of 20 m. How much service area can it cover if the receiving antenna is (i) at ground level (ii) at a height of 25 m ? Calculate the percentage increase in area covered in case (ii) relative to case (i).
Answers
Key concept : Distance or range of transmission tower, dT = √2RhT
Where, R is the radius of the earth (approximately 6400 km), hT is the height of transmission tower,
dT is also called the radio horizon of the transmitting antenna .
In this problem, height of antenna hT = 20m
(i) Distance or Range dT = √(2hT) = √(2×20×6.4×106)
= 16000 m = 16 km
Area covered A = π(d)2
= 3.14×16×16 = 803.84 km2
(ii) At a height of hR = 25 m gfrom ground level
Distance or range dM = √(2hT) + √(2hR)
= √(2×20×6.4×106) + √(2×25×6.4×106)
= 16×103 + 17.9×103
= 33.9×103 m
= 33.9 km
Area covered = π(d)2
= 3.14 × 33.9 × 33.9
= 3608.52 km2
Therefore, percentage increases in area
answered Dec 16, 2018 by udit giria Basic (24 points)
D = √2htR + √2hRR
= √2*20*6.4*106 + √2*25*6.4*106
= 16 * 103 + 17.9 * 103
= 33.9 * 103m
= 33.9 *KM
hope this will help you.
thank you