Question

A 25 m long antenna is mounted on an antenna tower. The height of the antenna tower is 75 m. The wavelength (in meter) of the signal transmitted by this antenna would be:
a. 200
b. 400
c. 100
d. 300

Answer 1

Hint: Wavelengths depend only on the length of the antenna, not on the height of the tower. Therefore, the length of the antenna can be determined according to the frequency or wavelength of the transmitted and received signals.So, from the length of the antenna we can easily calculate the wavelength of the signal transmitted.

Complete answer:
Antennas are guided transmission lines which usually radiate energy in terms of EM waves.They are used to transmit and receive radio signals in all directions. They are mostly used in radio engineering to propagate radio waves through electric current moving in metal conductorsThere is a sine wave travelling from the antenna. Now at the end of the antenna there must be an antinode for maximum power transmission.

By sine wave curve you can see that peaks occur at two points where we can get an antinode.

When the length of the antenna is $\dfrac{1}{4}$ of the wavelength, the transmission efficiency of the antenna is the highest.
$\dfrac{{{\lambda _{\max }}}}{4} = H$
Where
H = length of antenna

Given that length of antenna H = 25m and length of antenna tower L = 75m
$ \Rightarrow \dfrac{{{\lambda _{\max }}}}{4} = 25$
$ \Rightarrow {\lambda _{\max }} = 25 \times 4$
$ \Rightarrow {\lambda _{\max }} = 100m$

Hence, option (c) is correct.

Note: The length of the antenna is directly proportional to the wavelength. The shorter the wavelength, the shorter the antenna can be made..An antenna resonates at an odd multiple of 1/4 wavelength. It is most efficient at 1/4 wavelength, working against ground. Care must be taken while taking maximum length, we can also take ¾ wavelength but it doesn’t give maximum height.