Question

by what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 10%

Answer 1

by 10% as the height is increased

Answer 2

Transmission and range are related as:

$d = \sqrt{2Rh}$

$\frac{d}{d'} = \frac{\sqrt h}{\sqrt {h'}}$

New height of the tower, h' = 1.1 h (as there is 10% increase}

$\frac{d}{d'} = \frac{\sqrt h}{\sqrt {1.1h}}$

$d' = \sqrt{1.1}d=1.048 d$

percentage increase in the transmission range =

$\frac{d'-d}{d} \times 100 \%= \frac{1.048-1}{1}\times 100\% = 4.8%$