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Wave Studio

Learning goal

See superposition do its three famous tricks: traveling waves adding, opposite travelers freezing into standing waves (with visible nodes), and nearby frequencies breathing as beats.

Things to try

  1. Opposite mode, equal frequencies: the sum stops traveling. Count the node dots — spaced half a wavelength; raise the frequency and watch them crowd.
  2. Same direction, φ₂ = 180°: perfect cancellation — noise-cancelling headphones in one picture. Slide the phase and watch the amplitude revive.
  3. Beats mode: set \(f_1 = 1.0\), \(f_2 = 1.2\) Hz and watch the envelope throb at 0.2 Hz. Narrow the gap — the throb slows, exactly how instruments are tuned.

Traveling waves · Superposition & standing waves · Beats · Sound