Sum of two complex exponentials

Oscillation A
Oscillation B ( )


Explore how two complex waves/oscillations interfere de- or constructively. Use the controls above to set the frequency, amplitude and phase of the waves. Enable either both or only one of the waves and show or hide the sum.

If the one wave has the opposite(negative) frequency of the other wave their sum oscialates in only one direction because the other direction is cancelled by destructive interference. The difference of their two phases determines the direction in which the interference occurrs. Changing the phase of only one of the summed waves results in the sum to be rotated.

If neither frequency nor amplitude of the two waves match then their sum may look pretty wild. You may enable only the sum and hide the two individual waves for a better view.