Question

What is the wavelength of a half wave dipole antenna at$30MHz$?

\left( A \right)10m \\\ \left( B \right)5m \\\ \left( C \right)2.5m \\\ \left( D \right)20m \\\

Answer 1

In order to solve this question, we are going to firstly consider the frequency of the dipole antenna as given in the question and using the frequency- wavelength relation, the wavelength of the half wave dipole antenna is calculated. Then, the height of the antenna is found from the wavelength.

Formula used: The relation between the frequency and the wavelength is given as
$\lambda = \dfrac{c}{f}$
Where, $c$is the speed of light and $f$is the frequency
The length of a half wave dipole antenna is given as
${l_{\dfrac{1}{2}}} = \dfrac{\lambda }{2}$
Where $\lambda$is the wavelength of the half wave dipole antenna.

Complete step-by-step solution:
It is given that the frequency of the half wave dipole antenna is equal to
$f = 30MHz$
Converting this frequency into hertz, we get
$f = 30 \times {10^6}Hz$
Now, we know that the frequency and the wavelength are inversely proportional to each other. Hence, the relation between the frequency and the wavelength is given as
$\lambda = \dfrac{c}{f}$
Where, $c$is the speed of light and $f$is the frequency
Now putting the values of the speed and frequency, we get
$\lambda = \dfrac{{3 \times {{10}^8}}}{{30 \times {{10}^6}}} = 10m$
Now, as we know that the length of a half wave dipole antenna is given as
${l_{\dfrac{1}{2}}} = \dfrac{\lambda }{2}$
Thus, putting the value of the general wavelength as obtained above, we get
${l_{\dfrac{1}{2}}} = \dfrac{{10}}{2} = 5m$
Hence, the correct answer is$\left( B \right)5m$

Note: It is important to note that the dipole antenna is cut and bent for effective radiation. The length of the total wire, which is being used as a dipole, equals half of the wavelength
i.e. $l = \dfrac{\lambda }{2}$
Such an antenna is called a half-wave dipole antenna. This is the most widely used antenna because of its advantages.