Antenna theory states that one full, half wavelength, no more, no less, is the optimum length for an Antenna to receive Radio Waves.
Antenna's are tunned for a specific Frequency, the calculation is as follows: l = 1/2 * c/f * v/c
Where:
- l is the Length of the Antenna.
- c is the speed of light in free space
- f is the frequency
- v is the speed of the electric wave in the wire
Sometimes you may see this simply written as 1/λ is the free-space wavelength. @50Hz 1/λ = 6,000,000 meters. Wavelength is equal to λ = v/f
Where:
- f is the frequency
- v is the speed of the electric wave in the wire
For 1/4 wavelength antennas, a Ground must be used:
The Ground, completes the other half of the wavelength, effectively making up the other 1/4 wavelength like so:
Note: We have evidence, to point to more than just Wave Theory applying.to these Coils and Circuits. Some say EM Wave Theory is incomplete. We have evidence to suggest that v is the Wave itself, and not the speed at which the Wave travels in the particular medium. So, if Speed of the Wave = Wavelength x Frequency, then Speed of the Wave = 50, and the wavelength is λ =50/50 = 1. which is the length of the Wire the wavelength is applied across. This means in our situation, 1/4 wavelength is 1/4 of λ.
I posted some picture some time back:

More Soon!
Chris