Lissajous figures simulation
Feed two sine waves into the X and Y inputs of an oscilloscope and the dot traces a Lissajous figure. Simple frequency ratios give stable closed shapes, which is also why those musical intervals sound consonant.
Interactive, free and runs in your browser. Part of the Acoustic Physics simulations.
What you will see
A glowing beam traces the figure on an oscilloscope screen while the two input waves scroll out along its edges, so you can see how they combine. Choose an interval from unison to a minor sixth, play both tones, and change the phase to morph the shape.
Try this
- Pick unison (1:1) and change the phase: line, ellipse, circle.
- Pick the octave (1:2) and look for the figure of eight.
- Compare a fifth (2:3) with a minor sixth (5:8): simpler ratios give simpler figures.
Common misconception
A Lissajous figure does not show the waves’ shapes directly. It plots one signal against the other, so it reveals their frequency ratio and phase difference rather than either wave on its own.
Exam-style question
What shape does x = sin(t), y = sin(t + δ) trace for δ = 0, π/2 and π?
δ = 0: a straight line at 45°. δ = π/2: a circle (an ellipse if the amplitudes differ). δ = π: a straight line at −45°. In between it is an ellipse.
Key equations
x = sin(at)y = sin(bt + δ)
Curriculum
AQA A-level physics 3.3.1, IB Physics C.4.