...when displayed on an oscilloscope.Claude Bile said:These figures allow one to compare amplitudes, frequencies and phase between two oscillatory signals for one.
For example, if you had two sinusoidal signals of equal amplitude and frequency, you could determine the phase difference by looking at the shape of the trace. If the waves are in phase, you would see a straight line, if the waves are pi/2 out of phase, you would see a circle instead...
Gokul43201 said:...when displayed on an oscilloscope.
I don't know any other place. I just wanted to include it (for completeness) in case the OP wasn't aware of where these things are seen.Integral said:Where else?
Lissajous figures are complex mathematical curves that are created by plotting the relationship between two oscillating variables, such as sine and cosine functions, against each other.
Lissajous figures have various practical applications, including in physics (such as in the study of pendulums and waveforms), engineering (such as in designing electronic circuits and tuning musical instruments), and astronomy (such as in detecting exoplanets and analyzing their orbits).
Lissajous figures are created by using a device called a harmonograph, which consists of two pendulums connected to a pen that draws on a surface. As the pendulums oscillate, the pen creates the Lissajous figure by tracing the relationship between their movements.
The different patterns of Lissajous figures represent the relationship between the frequencies and phases of the two oscillating variables. The more complex the pattern, the more varied the relationship between the two variables.
Lissajous figures are used in music to tune instruments and create visual representations of sound waves. They can also be used to create unique visual effects during live performances and music videos.