1Two things to notice first
A wave has a speed it can't beat, and a shake has a rhythm
You only need two ideas. Watch each one:
A wave travels at a fixed speed
Make one bump and watch it crawl down the rope. Its travel speed is set by the rope itself — how tight and how heavy it is. Your hand can't make that one bump go any faster.
How often you shake
Every down-and-up of your hand makes one new wave. Shake quickly and you launch lots of waves a second. Shake slowly and you launch only a few.
2Two ways to shake
Lazy rolls vs crowded ripples
The same rope can carry two very different-looking waves, just from how fast your hand moves:
Long lazy rolls
Few waves on the rope, but each one is a long, spread-out hump.
Short crowded ripples
Lots of waves on the rope, but each one is a tiny, squished ripple.
3Your turn — be the shaking hand
Drag the speed and watch one rope wiggle
Slide your shake from slow to fast and watch the rope. The little number tells you how many whole waves fit on the rope right now. You can even hear the shake as a note.
4Now race them
A new race: the ropes have different lengths
Both ropes have the same tension and mass per metre. The slow-shaken top rope is 1 metre long; the fast-shaken bottom rope is 2 metres long. The drawings use the same length scale. Guess before racing one marked crest on each.
Guess before you race
Both crests leave together. Which reaches its own finish line first — the one on the fast-shaken rope, the one on the slow-shaken rope, or do they tie?