Question

Television signals reach us only through the ground waves. The range $R$ related to the transmitter height $h$ is in proportion to

• A. $h$
• B. $h^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
• C. $h^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
• D. $h^{-1}$

Answer 1

The correct option is B

$h^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

Step 1: Given data

Range of television signal =$R$

Transmitter height = $h$

Step 2: Find the relation between $h$ and $R$

The relation between the height $\left(h\right)$ and the covering range$\left(R\right)$ of the TV antenna is given by the formula,

Covering range $R=\sqrt{2hr}$ Where, $r$ is the radius of the earth.

So, from the formula, it is clear that, $R\propto \sqrt{h}$.

Thus, the range$\left(R\right)$ is directly proportional to the square root of the height $\left(h\right)$.

Hence, option B is the correct answer.