Waves: Motion Without Transport
A stadium wave circles the ground while every fan stays in their seat. That trick — energy travelling through stuff that doesn't — runs half of physics.
Builds on: 2.1 Energy: The Quantity That Only Changes Costume
Same idea, other course:⚡ Spark: Filters — circuits that sort signals by this same frequency idea
What actually travels
Drop a pebble in a pond and rings race outward — but a floating cork only bobs in place. The water does not travel; the disturbance does, handed from neighbour to neighbour, carrying energy without carrying material. That is a wave, and it is why you can be knocked over by surf that stayed offshore all day and hear a voice whose air never left the speaker’s lungs.
Two body plans:
- Transverse — the medium moves across the travel direction: a shaken rope, water ripples, light.
- Longitudinal — the medium moves along it, as squeezes and stretches: a pushed slinky, and — the important one — sound, which is pressure ripples in air.
Three numbers, one law
Wavelength λ — metres from crest to crest. Frequency f — crests per second, in hertz. Speed v — how fast a crest travels. They are locked together:
The catch that makes this law useful: speed belongs to the medium, not the wave. Sound does ~343 m/s in room air whether you whisper or shout, squeak or rumble. So when a source raises its frequency, the wavelength must shrink to compensate — f and λ trade off on a fixed budget. Concert A (440 Hz) rides on 78 cm waves; a bass drum’s 60 Hz spans nearly six metres.
One vocabulary, everything wavy
The same three numbers describe ocean swell (λ ≈ 100 m, leisurely), audible sound (17 mm–17 m), and radio — your Wi-Fi router works at 2.4 GHz, λ ≈ 12 cm. Learn the grammar once and every wavy phenomenon in the rest of this course — sound, light, even the quantum world — is a new accent, not a new language.
Light reaches you almost instantly; thunder plods along at 343 m/s — roughly a kilometre every three seconds. Flash, count, divide by three: kilometres to the strike. You have been doing wave physics since childhood.
⚗️ Lab — The Wave Machine
A driven rope with dials for frequency and medium — and a marked bead that tells the truth.
- Raise the frequency and watch the crests crowd together: v is fixed, so λ must shrink.
- Switch to a faster medium at the same f — the wavelength stretches instantly.
- Watch the red bead: it only bobs. The wave travels; the rope does not.
Work it by hand — 0 / 2
No multiple choice here: compute the value and type it. Suffixes like 2.5k or 20m are understood; answers within ±2% count.