The speed of light in free space (a vacuum; dielectric constant of 1, therefore, the Velocity Factor (VF) in a vacuum is 1 [100%]) is roughly the speed at which electromagnetic waves propagate (The dielectric constant of pure dry air is ~1.00059 at 1 atmosphere, so the VF in this example is 0.99971. In regards to dry air, in practice, it's all going to depend on the air pressure, altitude, humidity, pollutant content, and other factors.) It is just easy to say they are equal (by rounding up .99971 to 1; it makes the math a bit easier!
To get started in Antennas 101 for amateur radio, it would make sense to discuss what an antenna actually is. An antenna is defined as a device that is an interface between radio waves propagating through free-space and electric currents moving and voltages on metal conductors, which are used with a transmitter, receiver and/or a transceiver.
There are many variables that affect the resonant frequency of a half-wavelength dipole; of the top of my head, the two primary factors being the length-to-diameter ratio of the antenna conductor and most strongly, the antenna’s height above ground.
A radio wave’s wavelength is the distance traveled during one complete cycle of a wave. Since
one complete cycle takes 1/f the velocity of a wave is the speed of light, c, the wavelength, "λ" in where λ = c / f
1. Therefore: A Radio frequency "f" in where f = c / λ
On paper, the speed of light "c" = 299,792,458 m/s (When rounding the speed of light to 300,000,000 m/s you get the frequency 1 MHz (1,000,000Hz = 10^6Hz) or just 300m for one full wavelength.
2. The Earth has a circumference of ~24,901 Miles, and radio waves propagate ~186,000 mi/sec , it would take a radio wave roughly ~1/7th of a second to travel around the earth.
3. In regards to feet, 300 meters * 3.28 = 984 feet for 1 full wave length.
4. In regards to feet, 300 meters * 3.28 = 984 /2 = 492 for 1 half wave length
5. In regards to feet, 300 meters * 3.28 = 984 /4 = 246 for 1 quarter of a wave length
Antennas work so much better in a vacuum; with that being said, the ratio between the wave’s velocity in a specific medium (Air, Water, etc.) and that of free space is called the medium’s velocity factor (VF) and is a value between 0 and 1.
power is voltage times current: P = E I. Also from Ohm's Law voltage is current times resistance: E = I R. Therefore, we can calculate the needed voltage and current from power and resistance using I = SQRT(P / R) and V = SQRT(P R).√