Sine Wave 4 - Lissajous Figures

A Lissajous figure is what you get when you plot a graph of one sine wave against another. The shape of the Lissajous figure depends on the frequency of each sine wave and the relative phase of one sine wave against the other.

The phase of a sine wave is the angle at its starting point. For example, if you look carefully at the left hand end of the above sine wave and change its phase from 0 to 30 degrees you will see that its starting point will change from 0 to 30 degrees. You will also see that the Lissajous figure will "open up" slightly.

If you progressively increase the phase the Lissajous figure will appear to rotate.

The Australian Broadcasting Corporation (A.B.C.) logo is based on a Lissajous figure. Can you work out which one? Non Australian visitors to this web site may need to visit the Australian Broadcasting Corporation web site at to see what the logo looks like.