📚 Waves | 波
Waves are a fundamental concept in physics, transferring energy from one point to another without the transfer of matter. The CIE A-Level Physics syllabus requires a thorough understanding of wave types, properties, and behaviours, including interference, diffraction, polarisation, and the Doppler effect. This bilingual article covers all key concepts, with paired English and Chinese explanations to support your revision.
波是物理学中的基本概念，它将能量从一个点传递到另一个点而不传递物质。CIE A-Level 物理大纲要求透彻理解波的种类、性质及行为，包括干涉、衍射、偏振和多普勒效应。这篇双语文章涵盖所有关键概念，提供英中对照讲解，帮助你高效复习。
1. What is a Wave? | 什么是波？
A wave is a disturbance that propagates through a medium or space, transferring energy without any net movement of matter. In a mechanical wave, particles of the medium oscillate about their equilibrium positions, but do not travel with the wave.
波是一种在介质或空间中传播的扰动，它传递能量而不发生物质的净移动。在机械波中，介质的粒子在其平衡位置附近振动，但并不随波前进。
Waves can be classified as mechanical waves, such as sound and water waves, which require a material medium, or electromagnetic waves, which can travel through a vacuum. All waves share common parameters like wavelength, frequency, and amplitude.
波可分为需要物质介质的机械波（如声波、水波），以及能在真空中传播的电磁波。所有波都具有波长、频率和振幅等共同参数。
2. Transverse vs Longitudinal Waves | 横波与纵波
In transverse waves, the oscillations of particles are perpendicular to the direction of energy transfer. Examples include all electromagnetic waves, waves on a stretched string, and seismic S-waves. A key feature is that transverse waves can be polarised.
在横波中，粒子的振动方向与能量传递方向垂直。例子包括所有电磁波、弦上的波以及地震S波。一个关键特征是横波能够被偏振。
In longitudinal waves, the oscillations are parallel to the direction of energy transfer. Sound waves in air, ultrasound, and seismic P-waves are longitudinal. They consist of compressions (regions of high pressure) and rarefactions (regions of low pressure).
在纵波中，振动方向与能量传递方向平行。空气中的声波、超声波和地震P波都是纵波。它们由压缩区（高压区）和稀疏区（低压区）构成。
Distinguishing between these two types and knowing that polarisation is only possible for transverse waves is essential for CIE exam questions.
区分这两种波并理解只有横波才能偏振，对CIE考试至关重要。
3. Wave Equation and Parameters | 波动方程与参数
The fundamental parameters describing a wave are wavelength (λ), frequency (f), period (T), amplitude (A), and wave speed (v). The relationship between speed, frequency, and wavelength is given by the wave equation:
描述波的基本参数有波长（λ）、频率（f）、周期（T）、振幅（A）和波速（v）。波速、频率和波长之间的关系由波动方程给出：
v = f × λ
ath difference (Δx) by Δφ = (2π/λ) × Δx. A phase difference of 2π corresponds to one full wavelength.
周期T是一次完整振动所需的时间，T = 1/f。波上两点之间的相位差（Δφ）与它们的间隔或路径差（Δx）有关，Δφ = (2π/λ) × Δx。相位差2π对应一个完整波长。
Wave intensity (I) is the power per unit area. For a wave, intensity is directly proportional to the square of the amplitude: I ∝ A². This relationship is vital when studying wave energy and in polarisation problems (Malus's law).
波的强度（I）是单位面积上的功率。波的强度与振幅的平方成正比：I ∝ A²。这个关系在研究波能以及偏振问题（马吕斯定律）时非常重要。
4. Electromagnetic Waves and Spectrum | 电磁波与波谱
rection of propagation. They all travel at the speed of light in a vacuum, c = 3.00 × 10⁸ m s⁻¹.
电磁波是由相互垂直的振荡电场和磁场组成的横波，且两者均与传播方向垂直。它们在真空中均以光速 c = 3.00 × 10⁸ m s⁻¹ 传播。
The electromagnetic spectrum, in order of increasing frequency (decreasing wavelength), is: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Visible light ranges from roughly 400 nm (violet) to 700 nm (red).
电磁波谱按频率递增（波长递减）的顺序为：无线电波、微波、红外线、可见光、紫外线、X射线和伽马射线。可见光波长范围大约从400 nm（紫色）到700 nm（红色）。
Recall that all EM waves can be reflected, refracted, diffracted, and can undergo interference. Their differing wavelengths lead to their specific uses and dangers, a common topic in the syllabus.
所有电磁波都能发生反射、折射、衍射以及干涉。它们的不同波长决定了各自的用途和危害，这是大纲中的常见考点。
5. Polarisation | 偏振
Polarisation is the confinement of oscillations of a transverse wave to a single plane. Unpolarised light has electric field oscillations in all possible planes perpendicular to the direction of travel.
偏振是将横波的振动限制在单一平面内的现象。非偏振光的电场在垂直于传播方向的所有可能平面内振动。
A polarising filter transmits only the component of the wave oscillating parallel to its transmission axis. When polarised light of intensity I₀ passes through a second polariser (analyser), the transmitted intensity obeys Malus's law:
偏振片只允许平行于其透射轴振动的分量通过。当强度为I₀的偏振光通过第二个偏振片（检偏器）时，透射强度遵循马吕斯定律：
I = I₀ cos²θ
where θ is the angle between the transmission axes of the two polarisers. This law provides evidence of the transverse nature of light and is frequently tested.
其中θ是两个偏振片透射轴之间的夹角。该定律为光的横波特性提供了证据，也是常考内容。
6. Superposition and Interference | 叠加与干涉
The principle of superposition states that when two or more waves of the same type meet at a point, the resultant displacement is the vector sum of the individual displacements.
叠加原理指出，当两列或多列同类波在同一点相遇时，合位移等于各个位移的矢量和。
Constructive interference occurs when waves are in phase (phase difference 0, 2π, ...), producing a maximum amplitude. Destructive interference occurs when waves are in antiphase (phase difference π, 3π, ...), leading to a minimum amplitude.
当波同相（相位差0, 2π…）时发生相长干涉，产生最大振幅；当波反相（相位差π, 3π…）时发生相消干涉，产生最小振幅。
ence Δx = nλ, and destructive interference occurs at Δx = (n + ½)λ, where n is an integer.
对于两个相干波源（恒定相位差且频率相同），相长干涉发生在路径差Δx = nλ处，相消干涉发生在Δx = (n + ½)λ处，其中n为整数。
7. Stationary Waves | 驻波
Stationary (standing) waves are formed when two identical progressive waves travelling in opposite directions superpose. They do not transfer energy; instead, energy is stored. The pattern consists of nodes (zero amplitude) and antinodes (maximum amplitude).
驻波由两列相同且相向传播的行波叠加形成。它们不传递能量，而是储存能量。波形由波节（振幅为零）和波腹（振幅最大）组成。
1,2,3... and L is the string length. The fundamental frequency (1st harmonic) is when n=1.
在两端固定的弦线上，可能的振动模式是频率为 fₙ = n × (v/2L) 的谐波，其中 n = 1,2,3…，L 是弦长。基频（一次谐波）就是 n=1 的情况。
n = 1,3,5... The fundamental frequency corresponds to a quarter-wavelength standing wave.
对于一端封闭（另一端开口）的管，只存在奇次谐波：fₙ = n × (v/4L)，n = 1,3,5…。基频对应四分之一波长驻波。
8. Diffraction | 衍射
Diffraction is the spreading of waves when they pass through an aperture or around an obstacle. The amount of diffraction increases as the size of the gap (or obstacle) becomes comparable to the wavelength.
衍射是波穿过缝隙或绕过障碍物时发生的扩散现象。缝隙（或障碍物）的尺寸与波长越接近，衍射效应越显著。
When monochromatic light passes through a single slit, a central bright maximum is formed, flanked by alternating dark and bright fringes. The minima occur at angles satisfying:
当单色光穿过单缝时，会形成一个中央亮纹，两侧交替出现暗纹和亮纹。极小值出现的角度满足：
a sinθ = nλ
t width and n = ±1, ±2, ... The central maximum is twice as wide as the subsidiary maxima.
其中 a 是缝宽，n = ±1, ±2, …。中央亮纹的宽度是次级亮纹的两倍。
9. Double-Slit Interference | 双缝干涉
Young's double-slit experiment demonstrates light's wave nature by producing an interference pattern of bright and dark fringes. Two narrow slits act as coherent sources when illuminated by the same monochromatic light.
杨氏双缝实验通过产生明暗相间的干涉条纹证明了光的波动性。当同一单色光源照亮两条窄缝时，它们充当相干波源。
n = 0, ±1, ±2,... For small angles, the fringe separation y on a screen at distance D is:
亮纹（极大值）满足条件 d sinθ = nλ，其中 d 是双缝间距，n = 0, ±1, ±2…。对于小角度，距离为D的屏幕上条纹间距y为：
y = (λ × D) / d
rating equation d sinθ = nλ applies, where d = 1 / N (N is the number of lines per metre).
使用衍射光栅（多条狭缝）可获得更尖锐、更亮的极大值，非常适合光谱分析。同样的光栅方程 d sinθ = nλ 适用，其中 d =
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