Correct Answer - Option 3 : 8.3 cm
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
