Interactive standing waves
Standing Wave Explorer
Drive the line, match a natural frequency, and it locks into still nodes and swinging antinodes.
Fundamentals near mode 1 give the slowest, widest swing. Higher modes chop the line into more segments with more still nodes between them.
What locks it
A wave reflects at the boundary and stacks onto itself. When the round trip matches the drive, some spots always add (antinodes, big swing) and some always cancel (nodes, dead still).
Where it scales
A 2D plate does the same trick in two axes and draws the Chladni ridge lines. A bridge deck picks a slow torsional version. A dune face picks a longitudinal one. Same math, different shape.
For ultrasound
Transducer crystals ring at their own natural standing wave. Damping trims the pulse so echoes come back clean.