Basic Principles of Electromagnetic Energy, Part 2: Wave Definitions

Whether in the form of radio waves or visible light, all electromagnetic energy is inherently similar. The behaviour of electromagnetic energy is governed by basic wave theory, which is described by Maxwell's equations. These equations describe electromagnetic radiation as traveling at a velocity [c] equal to 3 x 108 m/s, in a sinusoidal, harmonic fashion. The electromagnetic wave is propegated in a direction perpendicular to the electric and magnetic fields. According to this, electromagnetic waves are characterized by amplitude, wavelength, period, frequency, and velocity.

Some Basic Definitions:
  • Amplitude is the distance from a wave's midpoint to its crest or trough.
  • Wavelength (lambda)is the distance between crests
  • Period (T) is the time elapsed between two consecutive crests passing a given point
  • Frequency (f) is the number of crests passing a given point in one second. Frequency is the inverse of period (f=1/T). For example, if T = 0.1 seconds, f= 10 per second.
  • Velocity (v) is the distance traveled in a given period of time (v=distance/time).

Remember that wavelength of an electromagnetic wave is the distance between crests and the period of an electromagnetic wave is the time between crests. The velocity of an electromagnetic wave is the wavelength (distance) divided by the period (time). This is not an especially useful description of velocity, however, because many applications of remote sensing make reference to wavelength and frequency, not wavelength and period. However, since the definitions above tell us frequency is the inverse of the period, it is not too difficult to express velocity in terms of freqency and wavelength:

A very important point to make at this time is that this relationship holds for all waves. Velocity always equals frequency times wavelength. Beyond this, electromagnetic waves are a special case, because the velocity of electromagnetic waves is essentially constant. Electromagnetic energy travels at the speed of light (indeed, light is electromagnetic energy), and that is always 3 x 108 meters/second (186,000 miles/second) in a vacuum.

Because the speed of light is constant, you can see a simple inverse relationship between the frequency and wavelength of electromagnetic waves. As the frequency increases, the wavelength decreases, and the opposite is true as well. Notice how the diagram on the left has a very short wavelength (but high frequency) compared with the diagram on the right.

If you are working on a JavaScript-enabled browser (Netscape 2.0 or Internet Explorer 3.0 or newer), you can use this calculator to get a quick idea of how changing either the wavelength or frequency of an electromagnetic wave effects the other. Enter a value for either wavelength or frequency and click on the "calculate" buttons to solve for the value of the missing variable. This should give you an idea of the way the relationship between wavelength and frequency is governed by the speed of light. If your browser is not JavaScript-capable, this chart also indicates the relationship between wavelength and frequency.
Speed of light: 3 X108 m/sec
Wavelength (micrometers):
Frequency (Hz):


Although most of the characteristics of electromagnetic waves are described sufficiently by classical wave theory, at very short wavelengths electromagnetic radiation interacts with matter in ways that wave theory (and Maxwell's equations) cannot account for. In this case, a particle description of electromagnetic radiation is more appropriate than a wave description. In such a description, electromagnetic energy travels in discrete units, or quanta, of energy. The energy of a quantum is given as Q=hf, where h = Plank's constant (6.26 X 10-34 Jsec), f = frequency, and Q is the energy of a quantum is Joules. The basic difference between the wave description and quantum (particle) description is that the quantum description predicts energy will be delivered to a target on a probabilistic basis, not as if it is spread evenly over the wave. However, even though light has this "particle nature", the overall average effect in nature follows Maxwell's equations.

You can relate the wave and quantum models of electromagnetic radiation by:

1. solving for f yielding
2. substituting into Q=hf yielding

You should be able to see from this equation that the shorter the wavelength, the higher its energy content (the inverse is also true). For this reason, shorter wavelengths are easier to sense than very long ones such as passive terrestrial microwave emissions.