What is the length of the antenna needed to a signal of 500 KHz frequency?

Question

Question

This question was previously asked in

ALP CBT 2 Electronic Mechanic Previous Paper: Held on 21 Jan 2019 Shift 2

Answer 1

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,

Electromagnetic waves of frequency 500 kHz is transmitted, i.e.,

f = 500 kHz

Hence the minimum length of antenna = \(\frac{\lambda }{4} = \frac{c}{{4f}}\;\left( {\because c = f\lambda } \right)\)

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

∴ length of antenna = \(\frac{{3 \times {{10}^8}}}{{4 \times 5 \times {{10}^5}}} = 150\;m\)