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

Hint: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.