General properties of waves
| English | Chinese | Pinyin |
|---|---|---|
| wave | 波 | bō |
| wavelength | 波长 | bō cháng |
| amplitude | 振幅 | zhèn fú |
| frequency | 频率 | pín lǜ |
| wave speed | 波速 | bō sù |
| transverse | 横波 | héng bō |
| longitudinal | 纵波 | zòng bō |
| reflection | 反射 | fǎn shè |
| refraction | 折射 | zhé shè |
| diffraction | 衍射 | yǎn shè |
Energy on the move
- Drop a stone in a pond: ripples spread out, but a floating cork just bobs up and down — it does not travel along.
- A wave 波 carries energy from place to place without carrying matter.
- All waves — water, light, sound — share the same set of ideas.
A wave carries matter along with it from place to place.
A wave carries energy, not matter. A floating cork bobs up and down but does not travel with the wave.
Describing a wave
- wavelength 波长 ($\lambda$): the distance for one full wave (e.g. crest to crest).
- amplitude 振幅: the largest distance a point moves from its rest position.
- frequency 频率 ($f$): the number of waves passing a point each second, in hertz (Hz).
- wave speed 波速 ($v$): how fast a wavefront travels. These link by the wave equation:
The parts of a transverse 横波 wave
Properties of waves
y = a sin(bx + c)
A wave: a is amplitude, b sets the wavelength.
Transverse & longitudinal waves
Flip between a transverse wave (particles bob up and down, like water and light) and a longitudinal one (particles slide back and forth, bunching into compressions, like sound). The wave moves; the particles stay put.
A wave has frequency $5.0\ \text{Hz}$ and wavelength $2.0\ \text{m}$. What is its speed, in m/s?
$v = f\lambda = 5.0 \times 2.0 = 10\ \text{m/s}$.
A sound wave travels at $330\ \text{m/s}$ with a frequency of $110\ \text{Hz}$. What is its wavelength, in m?
Rearrange $v = f\lambda$: $\lambda = \dfrac{v}{f} = \dfrac{330}{110} = 3.0\ \text{m}$.
The amplitude of a wave is:
Amplitude is the maximum displacement from rest. The crest-to-crest distance is the wavelength.
Two types of wave
- Transverse — the particles vibrate at right angles ($90°$) to the wave's travel. Light and water waves are transverse.
- Longitudinal 纵波 — the particles vibrate along the travel direction, making compressions and rarefactions. Sound is longitudinal.
Sound is which type of wave?
In sound, the particles vibrate along the direction of travel, making compressions and rarefactions — a longitudinal wave.
How waves behave
- All waves can do three things (easy to see in a ripple tank):
- Reflection 反射 — the wave bounces off a surface.
- Refraction 折射 — the wave changes speed (and usually direction) entering a new material or depth.
- Diffraction 衍射 — the wave spreads out through a gap or around an edge; spreading is greatest when the gap ≈ the wavelength.
Plane waves passing through a narrow gap spread out into curved waves — diffraction is strongest when the gap is about one wavelength wide
Two dippers in a ripple tank make overlapping circular water waves
A wave spreads out after passing through a narrow gap. This is:
Spreading out through a gap or around an edge is diffraction — greatest when the gap is about one wavelength wide.
You've got it
- a wave carries energy, not matter
- wave equation: $v = f\lambda$ (speed = frequency × wavelength)
- transverse (vibrate across travel) vs longitudinal (vibrate along travel; sound)
- waves can reflect, refract and diffract