Monday, May 23, 2011

At the Speed of Radio

It is usually said that radio waves travel at the speed of light. This is not exactly true, the speed of radio waves is actually variable. [Wikipedia has this wrong] In 1865 James Clerk Maxwell first made the first observations on the similar properties of light and radio waves. He proposed equations that described light waves and radio waves as "waves." This critical early observation was correct. Light and radio waves are both electromagnetic radiation and they propagate the same way. (Even if we aren't exactly sure how that is.)

The speed of light is usually represented as "C" because the speed of light is a very long number.  It is 299,792,458 m/s (meters per second) or 983,571,056 ft/s (feet per second) or about 300,000 kilometers per second. Radio waves certainly are able to travel at this speed, but can only do so in a vacuum. When propagating through any medium they are slowed down according to the permeability and permittivity of the substance.  We calculate this as C = 1÷  √(Permeability * Permittivity). The permittivity ε and permeability of a medium determine the phase velocity C of electromagnetic radiation through that medium. These are important enough to define here and not send you off to links you're probably not going to read.
  • Permeability: This is is ability of a material to support the formation of a magnetic field within itself. All matter is thus divided into four categories, depending on their level of permeability. Diamagnetic, Non-magnetic, Paramagnetic and Ferromagnetic. Air for example falls into the category of Nonmagnetic, copper would obviously be paramagnetic but so are many metals. Aluminum is an exception, it is Paramagnetic, only carrying a magnetic field when one is externally applied. Iron is also an exception as it is Ferromagnetic. In other words it can be permanently magnetized. It's not alone in that category, lithium gas is ferromagnetic at about 1 degrees kelvin.
  • Permittivity: This is the measure of the resistance encountered when forming an electric field in a medium. It is determined by the ability of a material to polarize in response to the field. It's expressed as the ratio of its electric displacement to the applied field strength. In some application is is also called the dielectric constant.
NOTE: In a circuit, permittivity is defined as a measure of the capacitance and dimensions of a capacitor, and permittivity is reduced to the a constant as defined by amperes law. 
Photons travel at the speed of light until they hit an atom. Then they are interact with the electromagnetic fields created by the arrangements structure of those atoms. It is in an excited state while interacting with these fields. it returns to the speed of light on the other side. These infinitesimal pauses accumulate and are what produces the variance between any medium and it's travel through a vacuum. Empedocles, a Greek philosopher born in 430 BCE, was the first to claim that the light has a finite speed. [image above] He maintained that light was something in motion, and therefore must take some time to travel. Around 1270 Erazmus Witelo a Polish mathematician, first suggested that light traveled at an infinite speed in vacuum, but slowed down in denser matter. The first decent estimate of the speed of light was made in 1676 by Ole Rømer and he was still off by over than 25%. In 1729, James Bradley estimated C to within 5 seconds and that's close enough for me. You can read about that here.

Water, air, and copper all transmit radio waves at below the speed of light. Actually they travel through copper at around 10% the speed of light. It's something we rarely think about because even at that speed you can connect to anywhere in the world in a few seconds. But the exact speed it travels is directly proportional to the capacity of the mass of copper. The longer the wire, the more electricity is needed to "fill it." This is a situation that John Steele Gordon once compared to filling a garden hose with water. Attenuation does not slow down the signal, it merely reduces the amplitude. Even as the wave is being attenuated to nothing it is still traveling at a fraction of C as determined by permeability and permittivity. What speeds it up is much more complicated.