Physics
Wave Equation
A drum skin where every point accelerates toward the average of its four neighbours. Put a probe anywhere and watch that pull live: down on a crest, up in a trough, nothing on a straight slope. Swap in the heat equation and the same pull only slides the point into place.
above restbelow restprobe height uneighbour average ūacceleration a
Click the skin to drop a pulse; hold and drag to pull a finger through it. Drag the yellow probe (or pick Move the probe) to inspect any point. Drag off the skin (or right-drag) to orbit, scroll to zoom.
Neighbours’ pull on the probe, ū − u—
—
Clicking the skin
Drum
Edge
slowfast
noneheavy
Numbers
Probe height u—
Neighbour average ū—
Acceleration a—
Energy left—
Kinetic—
Potential—
Time since reset—
Grid—
What to observe
- Watch the probe as a ring passes. On the crest its neighbours sit lower, so ū is below u and the arrow points down; in the trough behind, it points up.
- Put the probe on the flank of a wide bump. The skin is steep there, but what the uphill neighbours add the downhill ones take away: their average lands on the probe and there is no pull. Only curvature counts.
- Switch to the heat equation: the same gap now sets the velocity, not the acceleration. The probe on a bump slides toward its neighbours and never dips below rest, so the bump sags in place. Untick it and the point shoots straight past rest.
- Drop two pulses with the probe between them. The pulls just add, so the rings cross and come out the other side as if the other had never been there.
Shortcuts:space run/pause · s step · r reset · f fullscreen