Lalawave

ripple tank / wave interference / finite differences

Tank
click to drop a source drag to move it tap it to remove
0sources freq c · dt/dx fps

Arrangement

Parameters

What you are looking at

The surface is a grid of about a hundred thousand cells. Each one carries a single number — how far the water sits above or below rest. Warm amber marks a crest, cool teal a trough, and the flat ink between them is undisturbed water.

Nothing here is drawn by hand. Every ring, every dark nodal line, every fringe behind a barrier falls out of one equation applied over and over to neighbouring cells.

The equation

2u / ∂t2  =  c22u

Acceleration of the surface is proportional to its curvature. Where the water bends sharply it is pulled back hard; where it is flat, nothing happens. That single statement is the whole of it.

Replacing the derivatives with differences between adjacent cells gives an explicit update — the value at the next tick from the two ticks before it:

un+1 = 2unun−1 + C2(∑neighbours un − 4un)

The scheme stays stable only while C = c · dt/dx stays below 1/√2. Push the speed slider to its limit and you are standing on that edge.

Things worth trying

  • Two sources. Look for the still lines fanning outward. Along them the two waves arrive exactly out of step and cancel — destructive interference, drawn in water.
  • Double slit. A straight wave meets a wall with two gaps. Each gap becomes a fresh source, and the far side fills with fringes. This is Young's experiment, minus the optics bench.
  • Single slit. Narrow the opening and the wave spreads instead of passing straight through. The tighter the gap relative to the wavelength, the wider it fans out.
  • Damping to zero. Energy stops leaving. Reflections pile up until the tank fills with standing waves and the picture turns to noise.