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.

Materials:

• Clear plexiglass box with two speakers and attached mirrors
• He-Ne Laser (5 mW)
• 2 function generators

Demo:

1. Aline the laser so that it goes through the plexiglass box and reflects off of both mirrors and onto the screen.
2. Turn on both speakers using the function generators
3. 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.

Explanation:

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:

$X=acos(\omega&space;_{x}t+\phi&space;_{x})$       $Y=bcos(\omega&space;_{y}t+\phi&space;_{y})$

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

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