A T V transmission tower 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
Answer:
hi buddy...
hope my answer helps u
Explanation:
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
GIVEN :
A Transmission tower antenna of height , 20 m.
TO FIND :
◆ Service area can if receiving antenna is
(i) at ground level,
(ii) at a height of 25 m
◆The percentage increase in area covered in case (ii) relative to case (i).
SOLUTION :
(i) Range of the antenna ,
d = √(2Rh)
= √(2×20×6.4×10^6)
= 1.6 × 10^4 m
Where, h = height of antenna
R - radius of earth = 6.4× 10^6m
◆Area covered, A = π(d)^2
= 3.14×16×16 = 803.84 sq km
(ii) At a height of H = 25 m from ground level,
◆Total height = h + H
◆Distance d= √[2R(h + H)]
= √[2 × 6.4 × 10^6 × (20+ 25)]
= 17.8×10^3 m
◆Area covered = π(d)2
= 3.14 × 17.8 ×17.8
= 3608.52sq km
◆Percentage increases in area,
=[( Area (ii) - Area (i) ) / Area (i) ] ×100
= (3608.5 - 803.8 )×100/ 803.8
= 348.9%