A T.V. tower has a height 200 m

• Communication Systems

A T.V. tower has a height 200 m. By how much the height of tower be increased to triple its coverage range?

1. 1800 m
2. 1600 m
3. 800 m
4. 600 m

Answer

Covering range, R ∝ √h

R² ∝ h

If range is to be tripled,

R′ = 3R

(R/3R)² = h/h′

1/9 = h/h′

h′ = 9h

Height of the tower initially, h = 200 m

h′ = 9×200 = 1800 m

∴ The height of the tower has to be increased by

h′ − h = 1800 − 200 = 1600 m

The correct option is B.