What should be the length of  transmitting Antenna for radiating radio waves of 900 MHz

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 900 MHz are transmitted, i.e.,

f = 900 × 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 frequency of the wave

∴ \(L=\frac{{3 \times {{10}^8}}}{{4 \times 900 \times {{10}^6}}} = 0.083\;m\)

L = 8.3 cm