Question

The height of transmitting antenna if the TV telecast is to cover a radius of 128km is:
A) 1560m
B) 1280m
C) 1050m
D) 79m

Answer 1

Hint: Height of the transmitting antenna (basic element of radio technology must to transmit and receive signals) is directly proportional to the radius of the area which the television telecast is to cover:
${d_{\max }} = \sqrt {2R{H_T}} $ (R is the radius of the earth, HT is the height of the antenna and dmax is the radius of the TV telecast).

Complete step by step solution:
Let’s discuss some points about antenna and then we will proceed for the problem for calculation:
A transmitting antenna is the basic element of Radio technology. Antenna for transmission purposes are composed of a conductor that carries an electric current whose intensity fluctuates over time and converts it into radio frequency radiation that propagates in space.

TV and radio broadcasting station, use transmission antennas to transmit specific types of signals that propagate through the air. These signals are detected by receiving antennas which convert them into signals and then received by an appropriate device.

Now let’s come to the calculation of height.
$
   \Rightarrow {d_{\max }} = \sqrt {2R{H_T}} \\
   \Rightarrow {H_T} = \dfrac{{{d^2}_{\max }}}{{2R}} \\
 $(We have rewritten the formula to find height)
Now we will substitute the numerical values in the above formula.
$ \Rightarrow {H_T} = \dfrac{{{{\left( {128} \right)}^2}}}{{2 \times 6400}}$ (R value is taken as 6400Km which is radius of the earth)
$
   \Rightarrow {H_T} = \dfrac{{128 \times 128}}{{2 \times 6400}} \\
   \Rightarrow {H_T} = 1.28Km \\
 $(We will convert km into m as the option are in metre)
$ \Rightarrow {H_T} = 1.28 \times 1000 = 1280m$

Therefore, option (B) is correct.

Note: We have different types of antennas for indoor and outdoor. Generally we use a dipole and laser antenna and for outdoor antennas are the yagi and log periodic. For ultra high frequency channels multilayer reflective array antennas are used. Nowadays HD antennas have come into the picture for better signal reception.