Where a and b represent the amplitude of the wave, ω represents the angular frequencies, φ’s represent the phase and t is time. These Lissajous figures can be represented by the two equations below: The laser reflected from the mirrors traces patterns which depend on the relative frequencies of the sounds. One mirror oscillates in the x direction while the other one oscillates in the y direction. These figures are created through the superposition of two perpendicular sinusoidal waves. Show different Lissajous patterns and sounds that are related frequencies with the ratio 1:1 (200Hz:200Hz), 1:2 (200Hz:400Hz), 1:3 (200Hz:600Hz), 2:3 (400Hz:600Hz), etc. In this paper, an innovative method based on an algorithm utilizing discrete convolutions of discrete-time functions is developed to obtain and represent discrete Lissajous.Lissajous figures or Lissajous curves are the curves in the x-y plane obtained by taking x and y to vary sinusoidally with respect to a parameter t, typically with different frequencies. Turn on both speakers using the function generators Nick Trefethen, October 2010 (Chebfun example geom/Lissajous.m).(Center the beam on both mirrors to ensure maximum possible amplitude) Align the laser so that it goes through the plexiglass box and reflects off of both mirrors and onto the screen.Clear plexiglass box with two speakers and attached mirrors.The frequencies and amplitudes of the mirrors’ oscillations are adjusted on two separate function generators that power the speakers. The apparatus consists of a laser and mirrors mounted on two speakers. This demonstration creates and projects large Lissajous figures on the overhead screen.

Lissajous figures equation