I take a wireless antenna and I run a current through it 3 times per second.
I have now created a 3 Hz ELF frequency.
According to Wikipedia this radiation has a wavelength of 100000 km.
Needless to say that I highly doubt that. I also know that to create ELF radiation, you need a very big antenna.
What am I missing here?
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$\begingroup$ It's the other way around. Frequency is strictly controlled by the source. For radio waves, that means that the wavelength depends on the frequency. $\endgroup$– David WhiteCommented Mar 19, 2020 at 18:18
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Traveling Waves have a relationship that the frequency multiplied by the wavelength equals the propagation speed.
$$ v = f\lambda$$
For electromagnetic waves in air, the speed is fixed at nearly the speed of light. When you select the frequency, that means only one wavelength fits.
$$ \lambda = \frac{c}{f} = \frac{3\times 10^8 \text{m/s}}{3 \text{Hz}} = 1 \times 10^5 \text{km}$$
While an antenna may radiate most efficiently at wavelengths similar to its size, it is possible for it to radiate at other wavelengths/frequencies as well (at least a little bit).
answered Mar 19, 2020 at 17:32
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$\begingroup$ To expand on the last sentence, what this says is that the wireless antenna you have is very efficient on keeping energy from 3Hz signals inside itself. It does not radiate much of it at all. For an ELF antenna, you want to radiate as much of the ELF energy as possible $\endgroup$ Commented Mar 19, 2020 at 18:11