Source code: sinusSum01    Built with Processing

Doctor Matt >> Graphics

This applet illustrates the fact that the sum of sinusoidal functions with the same frequency but different phases results in a sinusoidal function with that same frequency. The summand functions can also have varying amplitudes, though in this applet they are all equal.

Here, the lengths of five rectangles are changing sinusoidally. Each has its own phase shift, controlled by the sliders at the bottom. Initially these are set randomly, so you can reload to get a different set of values.

Note that the amplitude of the resulting sinusoidal function is quite variable.