Beside the pond
What happens when
two ripples meet?
Make two sources ripple together. Change their timing and look for places where the surface barely moves.
The height map is unavailable. The model controls and numerical probe still work.
A and B are continuous ripple sources. P is the equal-path midpoint. Color shows signed height, not brightness or energy.
Starts paused. Animation runs only when you choose Play. Time and distances belong to this model.
Distance between successive crests. Wave speed stays fixed; wavelength also changes the oscillation rate.
At midpoint P
- A’s height
- 0.00 u
- B’s height
- 0.00 u
- A + B
- 0.00 u
Local peak amplitude 1.26 u
Add the heights, point by point
A crest and another crest reinforce. An equal trough cancels a crest at that instant. Each ripple continues through the other.
At P, the two paths are equal. With opposite phases, A and B cancel there throughout the cycle. Other points have different path lengths, so the whole surface need not be flat.
The model, its limits, and sources
For each source we draw height = w(r) cos(2πr/λ − 2πft + phase), then add the two heights. Here w(r) = 1/√(1 + r), and f = 2/λ. The envelope is an illustrative choice that keeps the source finite. Peak amplitude is the maximum size of the local oscillation, not its current height.
This is an established, idealized linear field with continuous sources. It does not simulate a stone splash, a moving switch-on front, reflected waves, dispersion, currents, or wave breaking. Source changes update the field immediately. Heights and distances are model units, not measurements of this park pond.