Waves
| English | Chinese | Pinyin |
|---|---|---|
| wave | 波 | bō |
| frequency | 频率 | pín lǜ |
| wavelength | 波长 | bō cháng |
| speed | 波速 | bō sù |
| transverse waves | 横波 | héng bō |
| longitudinal waves | 纵波 | zòng bō |
| electromagnetic spectrum | 电磁波谱 | diàn cí bō pǔ |
Energy without matter
- A wave 波 transfers energy without transferring matter.
- A cork on a rippling pond bobs up and down and stays where it is. The wave crosses the pond; the water does not.
- That distinction is the single most examined idea in the unit.
A cork bobs on a rippling pond. What has the wave transferred?
The medium oscillates about a fixed position and returns to it. Water travelling would be a current.
The wave equation
- Frequency 频率 is waves per second, wavelength 波长 is the distance between crests, and speed 波速 is how fast the wave travels.
- Two of the three always give the third, and most numerical questions in the unit are this equation with different words around it.
Two kinds of wave
- Transverse waves 横波 oscillate across the direction of travel — light, and a wave on a rope.
- Longitudinal waves 纵波 oscillate along it, as compressions and rarefactions — sound.
- The electromagnetic spectrum 电磁波谱 runs from radio to gamma, all travelling at the same speed in a vacuum and differing only in frequency and wavelength.
Match each wave type to an example.
Transverse oscillates across the direction of travel; longitudinal oscillates along it.
Radio waves and X-rays travel at the same speed in a vacuum.
The whole electromagnetic spectrum is one phenomenon, differing only in frequency and wavelength.
A wave has frequency 250 Hz and wavelength 1.4 m.
That is close to the speed of sound in air, which is a useful check: an answer of 350,000 m/s would tell you the units went wrong somewhere.
Knowing roughly what the answer should be is worth as much as the calculation, and it is what catches an arithmetic slip before it reaches the page.
A wave has frequency 250 Hz and wavelength 1.4 m. What is its speed in m/s?
v = fλ = 250 × 1.4 = 350 m/s, close to the speed of sound in air — a useful sanity check.
You calculate a sound wave's speed as 350000 m/s. What does that tell you, and what would you check?
Sound in air is about 340 m/s, so a value a thousand times larger points at a unit conversion, most often mm or cm read as m.
Every part of the electromagnetic spectrum is the same phenomenon. Radio, light, X-rays: identical speed in a vacuum, differing only in frequency — which is why one equation describes all of them.
Do not say a wave "carries the water along". The medium oscillates about a fixed position and returns to it. A description in which the water travels is describing a current, which is a different thing entirely.