Question

what percentage will the Transmission range of a tv tower be affected when the height of the tower is increased by 21 %​

Answer 1

The transmission range of a TV Tower is given by (LOS):

$r_{t} = \sqrt{2R_{e}h}$

If the height is increased by 21%, it becomes:

$h' = h + \frac{21}{100}h = \frac{121}{100}h$

Now, the new range becomes:

$r_{t}' = \sqrt{2R_{e}h'} = \sqrt{2R_{e}\frac{121}{100}h} = \frac{11}{10}\sqrt{2R_{e}h} = \frac{11}{10}r_{t}$

Or, $r_{t}' = \frac{11}{10}r_{t}$

The increase in range is: $\Deltar_{t} = r_{t}' - r_{t} = \frac{r_{t}}{10}$

And so, the percentage increase is: $\frac{\Deltar_{t}}{r_{t}} * 100%$

Substituting, increase % = 10%.