Idea
In one medium, the total displacement is the algebraic sum of the displacements of each wave (the superposition principle). In one dimension, a phase difference changes how the waveforms add. For two waves of the same frequency traveling in opposite directions, the difference in initial phase shifts all the stationary-wave nodes together. For two sources, a phase difference shifts the bright and dark fringes in space. Chladni figures extend the same way of reading a picture, “places where the amplitude is close to zero form nodal lines”, and their shape comes from the eigenmodes of the vibrating plate.
Interaction
- Guide: use a single to compare displacement superposition, the shift of stationary-wave nodes, and the shift of two-source fringes
- Superposition: show wave A, wave B, and their sum separately. Change frequency, amplitude, and phase, and watch constructive and destructive interference
- Beats: add two waves with nearby frequencies and watch the sum and its envelope. The angular frequency difference is ; in ordinary frequency it is
Suggested order: first use Guide to see how phase becomes visible structure → move to Superposition and adjust the two waves → finish with Beats and watch the envelope of nearby frequencies.
What to notice
- The same phase difference becomes reinforcement or cancellation in displacement, a shift of nodes in a stationary wave, and a shift of fringes for two sources.
- Nodes, dark fringes, and nodal lines are all “places where the amplitude is close to zero”. In a different medium, the geometry of that reading changes with it.
- What nearby frequencies add is an envelope. The phase relation still decides how the waves add; the frequency difference just makes the reinforcement itself drift slowly over time.
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