📚 Wave Revision for IB & Edexcel Physics | IB 与 Edexcel 物理波考点精讲
Waves are a cornerstone topic in both IB and Edexcel Physics, underpinning phenomena from sound and light to quantum mechanics. This revision guide distils the essential definitions, equations and applications, balancing conceptual depth with exam-ready precision to maximise your performance.
波是 IB 和 Edexcel 物理中的基石性课题，支撑着从声、光到量子力学的各种现象。本复习指南提炼了核心定义、公式与应用，兼顾概念深度与考试所需精准度，助你发挥最佳水平。
1. Wave Basics: Types and Definitions | 波的基础：类型与定义
A wave is a disturbance that transfers energy through space or a medium without permanent net displacement of particles. Waves are broadly classified as transverse or longitudinal based on the oscillation direction relative to energy propagation.
波是一种在空间或介质中传播能量而粒子不发生永久净位移的扰动。根据振动方向与能量传播方向的关系，波主要分为横波和纵波。
In transverse waves, such as light, water ripples and seismic S-waves, particles oscillate perpendicular to the direction of energy transfer. In longitudinal waves, for instance sound and seismic P-waves, particles oscillate parallel to the direction of energy transfer, producing compressions and rarefactions.
在横波（如光波、水波和地震S波）中，粒子振动方向垂直于能量传播方向。在纵波（例如声波和地震P波）中，粒子振动方向平行于能量传播方向，形成压缩区和稀疏区。
A quick comparison helps in problem solving:
以下对比有助于解题：
| Property | Transverse | Longitudinal |
|---|---|---|
| Particle motion | Perpendicular to wave direction | Parallel to wave direction |
| Examples | Light, water, S-waves | Sound, P-waves |
| Polarisation | Possible | Not possible |
| Medium requirement | Electromagnetic waves travel in vacuum | Requires material medium |
2. Fundamental Wave Quantities | 基本波动量
The period T is the time for one complete oscillation (unit: s). Frequency f is the number of oscillations per second (unit: Hz, where 1 Hz = 1 s⁻¹). Wavelength λ is the distance between two consecutive points in phase, like crest to crest or compression to compression. Amplitude A is the maximum displacement from equilibrium, and wave speed v is the speed at which the wave energy or phase travels.
周期 T 是一次完整振动所需的时间（单位：s）。频率 f 是每秒振动的次数（单位：Hz，1 Hz = 1 s⁻¹）。波长 λ 是两个相邻同相点（例如波峰到波峰或密部到密部）之间的距离。振幅 A 是偏离平衡位置的最大位移，波速 v 是波能量或相位传播的速度。
These quantities are interlinked: T = 1/f . The intensity I of a wave is proportional to the square of its amplitude – I ∝ A² – and this explains the brightness variation in interference patterns. In a given medium, wave speed depends only on the medium properties, not on frequency or amplitude.
这些量相互关联：T = 1/f。波的强度 I 与振幅的平方成正比——I ∝ A²，这解释了干涉图样中亮度的变化。在给定介质中，波速仅取决于介质本身的性质，与频率或振幅无关。
3. The Wave Equation v = fλ | 波速方程
The fundamental relationship linking wave speed, frequency and wavelength is the wave equation. It holds for all wave types, from water waves to X-rays.
将波速、频率和波长联系起来的基本关系式是波速方程，对所有类型的波都成立，从水波到X射线。
v = f × λ
When a wave passes from one medium to another, its frequency stays fixed (it is determined by the source) while speed and wavelength change. For instance, light entering water slows down, so its wavelength decreases, causing refraction. This principle is essential when drawing wavefronts in IB and Edexcel ray-diagram questions.
当波从一种介质进入另一种介质时，其频率保持不变（由波源决定），而速度和波长改变。例如，光进入水中速度减慢，波长减小，从而产生折射。在做 IB 和 Edexcel 的光线图题时，这一原理对绘制波前至关重要。
4. Phase and Path Difference | 相位与路径差
Phase describes the stage of an oscillation cycle, measured in radians or degrees. Two points on a wave are in phase if their phase difference is a multiple of 2π (360°); they are in antiphase if the difference is an odd multiple of π (180°). Phase difference is often linked to path difference, the extra distance travelled by one wave relative to another.
相位描述振动循环的阶段，用弧度或度表示。如果两点的相位差是 2π（360°）的整数倍，则它们同相；如果相差 π（180°）的奇数倍，则反相。相位差通常与路径差相关，路径差是一列波相对于另一列波多传播的距离。
Constructive interference occurs when the path difference equals a whole number of wavelengths, nλ, giving a phase difference of 2πn. Destructive interference occurs when the path difference equals an odd half-wavelength, (n+½)λ, corresponding to a phase difference of (2n+1)π. This concept is central to understanding Young’s slits and diffraction gratings.
当路径差等于波长的整数倍 nλ 时，相位差为 2πn，发生相长干涉；当路径差等于半波长的奇数倍 (n+½)λ 时，相位差为 (2n+1)π，发生相消干涉。这一概念是理解杨氏双缝和衍射光栅的核心。
5. Reflection, Refraction and Diffraction | 反射、折射与衍射
All waves obey the law of reflection: the angle of incidence equals the angle of reflection, measured from the normal. Refraction is the bending of a wave due to a change in speed at a boundary. Snell’s law quantifies refraction: n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index.
所有波都遵循反射定律：入射角等于反射角，均从法线测量。折射是波在边界处因速度改变而发生弯曲的现象。斯涅尔定律量化了折射：n₁ sin θ₁ = n₂ sin θ₂，其中 n 为折射率。
Diffraction is the spreading of waves around obstacles or through gaps. Noticeable diffraction occurs when the gap width or obstacle size is comparable to the wavelength. A wide gap (much larger than λ) produces little spreading, whereas a narrow gap acts like a point source. Both IB and Edexcel require clear wavefront diagrams for these three processes.
衍射是波绕障碍物或穿过间隙时发生的展宽现象。当间隙宽度或障碍物尺寸与波长相近时，衍射显著。宽间隙（远大于 λ）几乎不会引起展宽，而窄间隙则类似点波源。IB 和 Edexcel 都要求能清晰画出这三种过程的波前图。
6. Superposition and Interference | 波的叠加与干涉
The principle
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