Question

If the frequency of the signal is 1 MHz, the minimum height of the transmitting antenna should be:
1. 70 m
2. 75 m
3. 50 m
4. 72.5 m

Answer 1

Correct Answer - Option 2 : 75 m

Concept:

• For transmitting a signal, we need an antenna or an aerial.
• This antenna should have a size comparable to the wavelength of the signal (at least 1/4 in dimension) so that the antenna properly senses the time variation of the signal.
• For example, if we have an electromagnetic wave of frequency (f) 20 kHz, the wavelength (λ) is 15 km

Calculation:

Given that,

Radio waves of frequency 1 MHz are transmitted, i.e.,

f = 1 × 106 Hz

Hence the minimum length of the antenna is given as:

\(L=\frac{\lambda }{4} = \frac{c}{{4f}}\;\left( {\because c = n\lambda } \right)\)

Here c is the velocity of light, λ is wavelength and f are the frequency of the wave

\(L=\frac{{3 \times {{10}^8}}}{{4 \times 1 \times {{10}^6}}} = 75 \ m\)