📚 C Wave Behaviour | 波的行为
Wave behaviour is a cornerstone of IB Physics, describing how waves interact with boundaries, obstacles, and each other. Understanding reflection, refraction, diffraction, interference, standing waves, polarization, and the Doppler effect provides insight into sound, light, water waves, and many technological applications. This article covers the essential concepts, equations, and real-world connections you need for the IB Physics syllabus.
波的行为是 IB 物理的核心内容，描述了波如何与边界、障碍物以及彼此相互作用。理解反射、折射、衍射、干涉、驻波、偏振和多普勒效应，有助于深入了解声波、光波、水波以及众多技术应用。本文涵盖 IB 物理大纲所要求的基本概念、方程式和现实联系。
1. Introduction to Wave Behaviour | 波行为概述
Wave behaviour refers to the phenomena that occur when a wave encounters a change in medium, a boundary, or another wave. Key behaviours include reflection, refraction, diffraction, interference, polarization, and the Doppler effect. Waves can transfer energy without transferring matter, and their behaviour is governed by wave properties such as wavelength, frequency, amplitude, and speed.
波的行为是指波在遇到介质变化、边界或另一列波时所发生的现象。主要行为包括反射、折射、衍射、干涉、偏振和多普勒效应。波可以传输能量而不传输物质，其行为受波长、频率、振幅和速度等波的性质支配。
2. Reflection of Waves | 波的反射
ᵣ), measured relative to the normal. Reflection can be observed with light, sound (echo), and water waves. Fixed-end reflection inverts the wave, while free-end reflection does not.
反射发生在波撞击边界并返回原介质时。反射定律指出入射角等于反射角（θᵢ = θᵣ），均相对于法线测量。反射可以在光、声（回声）和水波中观察到。固定端反射会使波发生反转，而自由端反射则不会。
3. Refraction of Waves | 波的折射
t, while wavelength and speed change. The refractive index n of a medium is defined as n = c / v, where c is the speed of light in vacuum and v is the speed in the medium.
折射是波从一种介质进入另一种介质时由于速度变化而发生的方向改变。当波进入速度较慢（光密）的介质时，它朝法线方向弯曲；当进入速度较快的介质时，则偏离法线。波的频率保持不变，而波长和速度发生变化。介质的折射率 n 定义为 n = c / v，其中 c 为真空中光速，v 为介质中光速。
4. Snell's Law and Total Internal Reflection | 斯涅耳定律与全内反射
Snell's law quantitatively relates the angles of incidence and refraction to the refractive indices of the two media:
n₁ sin θ₁ = n₂ sin θ₂
flected and none refracted. The critical angle is given by sin θc = n₂ / n₁ (for n₁ > n₂).
斯涅耳定律定量地将入射角和折射角与两种介质的折射率联系起来：n₁ sin θ₁ = n₂ sin θ₂。当光从光密介质射向光疏介质且入射角大于临界角 θc 时，会发生全内反射，此时所有光被反射，无折射发生。临界角满足 sin θc = n₂ / n₁（n₁ > n₂）。
Typical refractive indices for common materials illustrate how much light slows down:
| Medium | Refractive index n |
| Vacuum | 1 |
| Air | ~1.0003 |
| Water | 1.33 |
| Glass | 1.5 – 1.9 |
| Diamond | 2.42 |
这些常见物质的典型折射率显示了光速减缓的程度。
5. Diffraction | 衍射
Diffraction is the spreading of a wave as it passes through an opening or around an obstacle. The amount of diffraction depends on the wavelength λ and the size of the aperture or obstacle d. Significant diffraction occurs when λ is comparable to or larger than d. If d >> λ, the wave passes with minimal spreading. Diffraction explains why sound can be heard around corners and why light creates fringe patterns in single-slit experiments.
衍射是波通过缝隙或绕过障碍物时发生的扩展现象。衍射的程度取决于波长 λ 以及缝隙或障碍物的尺寸 d。当 λ 与 d 可相比拟或更大时，会发生显著的衍射。若 d >> λ，波几乎无扩展地通过。衍射解释了为什么声音可以绕过墙角传播，以及为什么光在单缝实验中会产生条纹图案。
6. Superposition and Interference | 叠加与干涉
er amplitude when waves are in phase (path difference = nλ), while destructive interference reduces or cancels amplitude when waves are out of phase (path difference = (n + ½)λ). Interference is fundamental to double-slit experiments and thin-film effects.
叠加原理指出，当两列或多列波相遇时，合位移是各列波位移的矢量和。当相干波（频率相同、相位差恒定）重叠时会发生干涉现象。相长干涉在波同相时（波程差 = nλ）产生更大的振幅，而相消干涉在波反相时（波程差 = (n + ½)λ）削弱或抵消振幅。干涉是双缝实验和薄膜效应的基础。
7. Young's Double-Slit Experiment | 杨氏双缝干涉实验
Young's double-slit experiment demonstrated the wave nature of light through the production of an interference pattern. Coherent light passing through two narrow slits produces alternating bright and dark fringes on a screen. The condition for bright fringes is:
d sin θ = nλ
, 1, 2, ... For small angles, the fringe spacing Δx on a screen at distance D is given by:
Δx = λD / d
杨氏双缝实验通过产生干涉图样证明了光的波动性。相干光通过两条窄缝后在屏幕上形成明暗相间的条纹。亮纹的条件为 d sin θ = nλ，其中 d 为缝间距，θ 为相对于中央极大的角度，n = 0, 1, 2, ...。对于小角度，在距离为 D 的屏幕上，条纹间距 Δx 满足 Δx = λD/d。
8. Standing Waves | 驻波
A standing wave is formed by the interference of two identical waves traveling in opposite directions, such as a wave and its reflection. The waveform appears stationary, with nodes (points of zero displacement) and antinodes (points of maximum displacement). The distance between adjacent nodes is half a wavelength. Standing waves can be produced on strings, in air columns, and on membranes. For a string fixed at both ends, the resonant frequencies are:
fₙ = n v / (2L)
where n =
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