A You can credit the name to French physicist Jules Antoine Lissajous. He originally used sounds at differing frequencies to vibrate a mirror and trace patterns with a beam of reflected light.
In electronic applications we can generate Lissajous patterns by applying different signals to the horizontal and vertical inputs of an oscilloscope. In fact, this technique was often used to measure frequencies in the days before frequency meters. A signal of a known frequency was applied to the horizontal input and the signal to be measured was applied to the vertical input. The resulting pattern was a function of the ratio of the two frequencies. For example, if you put a 1-Hz 1-V signal on the vertical input and the same on the horizontal, a circle will appear on the screen. If you change the horizontal input to 2 Hz, you will get a horizontal figure 8—showing that the horizontal to vertical ratio is 2:1. By observing the patterns you can interpret the ratio, which tells you the frequency of the signal you’re attempting to measure.
If you have a Web browser that supports Java, check out the “Lissajous Lab” at http://ovpserv4.rug.ac.be/toegepfysica/Applets/Lissajous4/index.htm. You can plug in the frequencies of your choice and view the resulting Lissajous patterns (see Figure 1).
Figure 1— Check out the “Lissajous Lab” on the Web at http://ovpserv4.rug.ac.be/toegepfysica/Applets/Lissajous4/index.htm.
From QST September 1999
