Question

A TV tower is 120m high. How much more height is to be added to it, if its coverage range is to become double?
A. 120m
B. 240m
C. 360
D. 480m

Answer 1

Hint: Antennas are the devices used for the perception of signals. Radiofrequency waves from the transmitter are converted into electromagnetic waves from the antenna which are then fed to TVs and telephone systems.

 Complete step by step answer:
Given: The height of the TV tower is ${h_1} = 120\;{\rm{m}}$.
Let the initial coverage range of the antenna be ${d_1}$.
Express the relation for coverage range of a TV tower:
$d = \sqrt {2Rh} $
Here, d is the coverage range, R is the radius of the earth and h is the height of the tower.
From the above relation, since R is constant then.
$d \propto \sqrt h $
Hence it can be further simplified as,
$\dfrac{{{d_1}}}{{{d_2}}} = \sqrt {\dfrac{{{h_1}}}{{{h_2}}}} \,......\,\left( {\rm{I}} \right)$.
Here ${h_2}$ is the new height of the tower corresponding to new coverage ${d_2} = 2{d_1}$.
Substitute ${d_2} = 2{d_1}$, ${h_1} = 120\;{\rm{m}}$ in equation (I) to find the value of ${h_2}$.
$\begin{array}{l}
\dfrac{{{d_1}}}{{2{d_1}}} = \sqrt {\dfrac{{120\;{\rm{m}}}}{{{h_2}}}} \\
{h_2} = 480\;{\rm{m}}
\end{array}$
Let the extra height added be H, then,
$H = {h_2} - {h_1}$
Substitute ${h_2} = 480\;{\rm{m}}$, ${h_1} = 120\;{\rm{m}}$ to find the value of H.
$\begin{array}{l}
H = 480\;{\rm{m}} - 120\;{\rm{m}}\\
 = 360\;{\rm{m}}
\end{array}$

So, the correct answer is “Option C”.

Note:
There is a bit of a difference between antenna and transducer. Because electric energy is converted back to electrical energy from the transducer but the antenna converts the input energy into free radiation of electromagnetic waves.