General properties of waves · 波的一般性质
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| wave/weɪv/ | 波 | bō |
| wavelength/ˈweɪvleŋθ/ | 波长 | bō cháng |
| amplitude/ˈæmplɪtjuːd/ | 振幅 | zhèn fú |
| frequency/ˈfriːkwənsi/ | 频率 | pín lǜ |
| wave speed/weɪv spiːd/ | 波速 | bō sù |
| transverse/trænsˈvɜːs/ | 横波 | héng bō |
| longitudinal/ˌlɒŋɡɪˈtjuːdɪnl/ | 纵波 | zòng bō |
| reflection/rɪˈflekʃn/ | 反射 | fǎn shè |
| refraction/rɪˈfrækʃn/ | 折射 | zhé shè |
| diffraction/dɪˈfrækʃn/ | 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.
移动中的能量
- 把一块石头丢进一个池塘:涟漪扩散出去,但一个漂浮的软木塞只是上下浮动——它不沿着前进。
- 一个波(wave)把能量从一处带到另一处,而不携带物质。
- 所有波——水、光、声——共享同一套想法。
A wave carries matter along with it from place to place. · 一个波把物质随它从一处带到另一处。
A wave carries energy, not matter. A floating cork bobs up and down but does not travel with the wave. · 一个波携带能量,不是物质。一个漂浮的软木塞上下浮动但不随波前进。
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
描述一个波
- 波长(wavelength,$\lambda$):一个完整波的距离(例如波峰到波峰)。
- 振幅(amplitude):一个点从它的静止位置移动的最大距离。
- 频率(frequency,$f$):每秒经过一个点的波的数量,以赫兹(Hz)计。
- 波速(wave speed,$v$):一个波前传播得多快。这些由波动方程(wave equation)联系:
一个横波的各部分
Properties of waves · 波的性质
y = a sin(bx + c)
A wave: a is amplitude, b sets the wavelength. · 一个波:a 是振幅,b 设定波长。
Transverse & longitudinal waves · 横波与纵波
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. · 在一个横波(粒子上下浮动,像水和光)和一个纵波(粒子来回滑动,聚集成压缩,像声)之间切换。波移动;粒子留在原处。
A wave has frequency $5.0\ \text{Hz}$ and wavelength $2.0\ \text{m}$. What is its speed, in m/s? · 一个波有频率 $5.0\ \text{Hz}$ 和波长 $2.0\ \text{m}$。它的速度是多少,以 m/s 计?
$v = f\lambda = 5.0 \times 2.0 = 10\ \text{m/s}$. · $v = f\lambda = 5.0 \times 2.0 = 10\ \text{m/s}$。
A sound wave travels at $330\ \text{m/s}$ with a frequency of $110\ \text{Hz}$. What is its wavelength, in m? · 一个声波以 $330\ \text{m/s}$ 传播,频率 $110\ \text{Hz}$。它的波长是多少,以 m 计?
Rearrange $v = f\lambda$: $\lambda = \dfrac{v}{f} = \dfrac{330}{110} = 3.0\ \text{m}$. · 重排 $v = f\lambda$:$\lambda = \dfrac{v}{f} = \dfrac{330}{110} = 3.0\ \text{m}$。
The amplitude of a wave is: · 一个波的振幅是:
Amplitude is the maximum displacement from rest. The crest-to-crest distance is the wavelength. · 振幅是从静止的最大位移。波峰到波峰的距离是波长。
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.
两种类型的波
- 横波(transverse)——粒子在与波的前进成直角($90°$)处振动。光和水波是横波。
- 纵波(longitudinal)——粒子沿前进方向振动,产生压缩(compressions)和稀疏(rarefactions)。声是纵波。
Sound is which type of wave? · 声是哪种类型的波?
In sound, the particles vibrate along the direction of travel, making compressions and rarefactions — a longitudinal wave. · 在声中,粒子沿前进方向振动,产生压缩和稀疏——一个纵波。
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
波如何表现
- 所有波都能做三件事(在一个水波槽(ripple tank)中容易看到):
- 反射(reflection)——波从一个表面弹回。
- 折射(refraction)——波在进入一种新材料或深度时改变速度(且通常方向)。
- 衍射(diffraction)——波穿过一个缝隙或绕过一个边缘扩散;当缝隙 ≈ 波长时扩散最大。
平面波穿过一个窄缝后扩散成弯曲的波——当缝隙约为一个波长宽时衍射最强
一个水波槽中的两个起波器产生重叠的圆形水波
A wave spreads out after passing through a narrow gap. This is: · 一个波穿过一个窄缝隙后扩散。这是:
Spreading out through a gap or around an edge is diffraction — greatest when the gap is about one wavelength wide. · 穿过一个缝隙或绕过一个边缘扩散是衍射——当缝隙约一个波长宽时最大。
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
你掌握了
- 一个波携带能量,不是物质
- 波动方程:$v = f\lambda$(速度 = 频率 × 波长)
- 横波(垂直于前进振动)对纵波(沿前进振动;声)
- 波能反射、折射和衍射