Electromagnetic (EM) Waves
Fourier synthesis

When two EM waves occupy the same space, their effects combine to form a new wave of a different shape. For example, air pressure changes caused by two sound waves add together. The electrical and magnetic forces caused by two light waves or two radio waves are also added together.

Jean Baptiste Fourier is responsible for one of the great mathematical discoveries. He proved that a special sum of sine waves, of harmonically related frequencies, could be added together to create any wave pattern. Harmonically related frequencies are simply frequencies that are multiples of some basic frequency. Complex waves can be built out of simple waves. Another way of stating this is that any repeating wave is mathematically and physically equivalent to the result of adding just the right collection of sine waves together. This sum is known as a Fourier series.

Use the interactive activity to create multiple sine waves and a complex wave that is formed from the additive effects of the individual waves.

Finally, a square wave, or a square pulse, can be built by using the right combination of sine waves. The importance of this will be clarified when modulation is discussed.


Interactive Media Activity

Interactive Activity: Fourier Synthesis

In this activity, the student will draw sine waves by selecting the amplitude, frequency, and phase of each.