Calibrating the frequency of tuning forks by means of Lissajous figures

We produce Lissajous figures by modulating a laser beam along two perpendicular directions by means of two tuning forks. When the ratio of the resonant frequencies of the tuning forks is a small rational number, Lissajous figures are clearly resolved on a screen. Because the ratio of frequencies is never exactly a rational number, a phase drift of the Lissajous figures is observed as a function of time. If the period of this phase drift is measured, variations in the resonant frequencies as small as 0.01 Hz can be detected.