This demonstration creates and projects large Lissajous figures on the overhead screen. The apparatus consists of a laser and mirrors mounted on two speakers. The frequencies and amplitudes of the mirrors’ oscillations are adjusted on two separate function generators that power the speakers.
- Clear plexiglass box with two speakers and attached mirrors
- He-Ne Laser (5 mW)
- 2 function generators
- Aline the laser so that it goes through the plexiglass box and reflects off of both mirrors and onto the screen.
- Turn on both speakers using the function generators
- 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.
These figures are created through the superposition of two perpendicular sinusoidal waves. One mirror oscillates in the x direction while the other one oscillates in the y direction. The laser reflected from the mirrors traces patterns which depend on the relative frequencies of the sounds. These Lissajous figures can be represented by the two equations below:
Where a and b represent the amplitude of the wave, ω represents the angular frequencies, φ’s represent the phase and t is time.
Written by: Nick McCabe