A-Level Edexcel Physics: Waves Key Points | A-Level Edexcel 物理：波考点精讲

📚 A-Level Edexcel Physics: Waves Key Points | A-Level Edexcel 物理：波考点精讲

In the Edexcel A-Level Physics specification, waves form a central topic that links mechanics, optics, and modern physics. Understanding wave behaviour is crucial for tackling questions on interference, diffraction, standing waves, polarisation, and the Doppler effect. This article distils the key concepts you need to master, presenting definitions, equations, and experimental details in a clear, bilingual format to support your revision.

在 Edexcel A-Level 物理考纲中，波动是连接力学、光学和近代物理的核心主题。理解波的行为对于解决干涉、衍射、驻波、偏振和多普勒效应等问题至关重要。本文提炼了必须掌握的关键概念，以清晰的中英双语格式呈现定义、公式和实验细节，助力你的复习。

1. Longitudinal vs Transverse Waves | 纵波与横波

A wave is a disturbance that transfers energy without transferring matter. In transverse waves, the particle oscillations are perpendicular to the direction of energy propagation. Examples include electromagnetic waves, water ripples, and waves on a string. In longitudinal waves, particle oscillations are parallel to the energy transfer direction. Sound waves in air and primary seismic P-waves are longitudinal.

波是一种传递能量但不传递物质的扰动。在横波中，质点振动方向与能量传播方向垂直，例如电磁波、水波和弦上的波。在纵波中，质点振动方向与能量传递方向平行，例如空气中的声波和地震纵波 P 波。

Transverse waves can be polarised, proving that their oscillations are in a single plane perpendicular to the direction of travel. Longitudinal waves cannot be polarised because their oscillations already lie along the direction of propagation.

横波可以发生偏振，这证明其振动方向在垂直于传播方向的单一平面内。纵波不能偏振，因为其振动沿传播方向。

2. Key Wave Parameters | 关键波动参数

The displacement of a point on a wave is its distance from the equilibrium position. The amplitude (A) is the maximum displacement from equilibrium. The wavelength (λ) is the distance between two consecutive points in phase, e.g., crest to crest. The period (T) is the time for one complete oscillation, and frequency (f) is the number of oscillations per second, with f = 1/T.

质点的位移是它离开平衡位置的距离。振幅(A)是离平衡位置的最大位移。波长(λ)是两个相邻同相点之间的距离，例如波峰到波峰。周期(T)是一次完整振动所需的时间，频率(f)是每秒振动的次数，且 f = 1/T。

The wave speed v is the distance travelled by the wave profile per unit time. For all progressive waves, the relationship between speed, frequency, and wavelength is fundamental.

波速 v 是波形在单位时间内传播的距离。对所有行波而言，波速、频率和波长之间的关系至关重要。

3. The Wave Equation v = fλ | 波动方程 v = fλ

The wave equation links speed v, frequency f, and wavelength λ:

v = f λ

. This equation applies to all types of progressive waves. If any two quantities are known, the third can be calculated. Remember that frequency is determined by the source and does not change when a wave enters a different medium, whereas speed and wavelength may change.

波动方程将波速 v、频率 f 和波长 λ 联系起来：

v = f λ

。该方程适用于所有类型的行波。已知任意两个量即可计算第三个。注意，频率由波源决定，当波进入不同介质时频率不变，而波速和波长可能改变。

Practice using the equation in contexts such as water waves moving from deep to shallow water, where speed and wavelength decrease but frequency remains constant. On an oscilloscope, knowing the time base and the number of cycles displayed allows you to determine period and hence frequency.

请通过情景练习应用该方程，例如水波从深水区进入浅水区时，波速和波长减小，但频率恒定。在示波器上，已知时基和显示周期数，可以求出周期进而得到频率。

4. Phase and Phase Difference | 相位与相位差

Phase describes the stage in a wave cycle that a point has reached, often measured in radians or degrees. Two points are in phase if their displacements vary identically with time (phase difference of 0, 2π, 4π, … radians). They are antiphase if they are half a cycle apart (phase difference of π, 3π, … radians).

相位描述一个点在波形周期中所处的阶段，通常以弧度或度来度量。如果两个点的位移随时间的变化完全相同，则它们同相（相位差为 0、2π、4π……弧度）。如果它们相差半个周期，则反相（相位差为 π、3π……弧度）。

Phase difference is crucial in superposition. When two identical waves meet, constructive interference occurs if they are in phase; destructive interference occurs if they are antiphase. Path difference Δx and phase difference φ are related by φ = (2π/λ) × Δx.

相位差在叠加中至关重要。当两列相同的波相遇时，若同相则发生相长干涉，若反相则发生相消干涉。路程差 Δx 与相位差 φ 的关系为 φ = (2π/λ) × Δx。

5. Superposition and Interference | 波的叠加与干涉

The principle of superposition states that when two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements. This leads to interference patterns. Constructive interference yields a maximum amplitude when waves are in phase; destructive interference yields a minimum when they are in antiphase.

叠加原理指出，当两列或更多的波在一点相遇时，合位移等于各个位移的矢量和。这产生了干涉图样。当波同相时发生相长干涉，振幅最大；当波反相时发生相消干涉，振幅最小。

For two coherent sources (same frequency, constant phase difference), a stable interference pattern is observed. Coherence is essential for clear fringes. In A-Level experiments, this is often achieved using a double slit or dividing a single laser beam.

对于两个相干波源（频率相同且相位差恒定），可观察到稳定的干涉图样。相干性是获得清晰条纹的关键。在 A-Level 实验中，通常通过双缝或将单束激光分光来实现相干。

6. Young’s Double-Slit Experiment | 杨氏双缝干涉实验

When monochromatic coherent light passes through two narrow slits separated by a distance a, overlapping diffracted beams produce an interference pattern of bright and dark fringes on a screen at distance D. For bright fringes (constructive), path difference = nλ; for dark fringes (destructive), path difference = (n + ½)λ, where n = 0, 1, 2, …

单色相干光通过间距为 a 的两条狭缝，衍射光束叠加后在距离为 D 的屏幕上产生明暗相间的干涉条纹。亮条纹（相长）满足路程差 = nλ；暗条纹（相消）满足路程差 = (n + ½)λ，其中 n = 0, 1, 2, …

The fringe spacing Δy (distance between adjacent bright fringes) is given by

Δy = λD / a

. This formula is used to determine the wavelength of light. The experiment also demonstrates the wave nature of light and is a classic example of two-source interference.

条纹间距 Δy（相邻亮纹中心距离）由下式给出：

Δy = λD / a

。该公式用于测量光的波长。杨氏实验还证明了光的波动性，是双源干涉的经典实例。

Safety note: never look directly into a laser beam. Use a screen or indirect viewing methods.

安全提示：切勿直视激光束，应使用屏幕或间接观察。

7. Diffraction and the Single Slit | 衍射与单缝衍射

Diffraction is the spreading of waves when they pass through a gap or around an obstacle. Significant diffraction occurs when the size of the gap is comparable to the wavelength. For a single slit of width a, a central bright fringe is flanked by dark and dimmer bright fringes. The first minimum (dark fringe) satisfies

a sin θ = λ

, where θ is the angle from the centre to the first minimum.

衍射是波穿过缝隙或绕过障碍物时发生的扩散现象。当缝隙尺寸与波长可比拟时，衍射显著。对于宽度为 a 的单缝，中央亮纹两侧分布着暗纹和次亮纹。第一级暗纹满足

a sin θ = λ

，其中 θ 为中心到第一级暗纹的角位置。

Diffraction gratings, consisting of many equally spaced slits, produce sharp, well-separated maxima. The grating equation is d sin θ = nλ, where d is the slit spacing and n the order. Gratings are used for precise wavelength measurements.

衍射光栅由许多等间距的狭缝构成，可产生锐利且分得很开的最大值。光栅方程为 d sin θ = nλ，其中 d 为缝间距，n 为级数。光栅用于精密波长测量。

8. Standing Waves | 驻波

A standing wave is formed by the superposition of two identical progressive waves travelling in opposite directions. On a stretched string fixed at both ends, standing waves exhibit nodes (zero displacement) and antinodes (maximum displacement). The fundamental frequency f₀ corresponds to a pattern with one antinode between two nodes (half a wavelength). Harmonics follow: fₙ = n f₀ where n = 1, 2, 3, …

驻波由两列相同且相向传播的行波叠加形成。在两端固定的弦上，驻波显示出波节（位移恒为零）和波腹（振幅最大）。基频 f₀ 对应两端节点之间有一个波腹（半个波长）的模式。谐频满足 fₙ = n f₀，n = 1, 2, 3, …

In air columns, standing waves are used in musical instruments. For a pipe open at both ends, antinodes exist at the ends; for a closed-at-one-end pipe, there is a node at the closed end and an antinode at the open end. The wavelength of the fundamental and overtones differs accordingly.

在气柱中，驻波用于乐器。两端开口管的管口处为波腹；一端封闭的管在封闭端为波节，开口端为波腹。基频和谐波的波长相应不同。

9. Refraction and Snell’s Law | 折射与斯涅尔定律

When a wave passes from one medium to another, its speed changes, causing a change in direction if it hits the boundary at an angle. The refractive index n of a material is the ratio of the speed of light in a vacuum c to that in the material v:

n = c / v

. Snell’s law states

n₁ sin θ₁ = n₂ sin θ₂

, where angles are measured from the normal.

当波从一种介质进入另一种介质时，波速改变，若入射角不为零，方向也会改变。材料的折射率 n 是光在真空中速度 c 与在介质中速度 v 之比：

n = c / v

。斯涅尔定律为

n₁ sin θ₁ = n₂ sin θ₂

，角度均从法线量起。

Optical density and refractive index are linked. Light travels slower in optically denser media. When light enters a denser medium (n₂ > n₁), it bends toward the normal.

光密介质与折射率相关。光在光密介质中传播更慢。当光进入光密介质（n₂ > n₁）时，会向法线偏折。

10. Total Internal Reflection and Critical Angle | 全内反射与临界角

Total internal reflection (TIR) occurs when light travelling from a denser medium to a less dense one strikes the boundary at an angle of incidence greater than the critical angle θc. At the critical angle, the angle of refraction is 90°. Using Snell’s law, sin θc = n₂ / n₁ (where n₁ > n₂). For light leaving glass (n ≈ 1.5) to air, θc ≈ 42°.

当光从光密介质射向光疏介质，且入射角大于临界角 θc 时，发生全内反射（TIR）。在临界角时，折射角为 90°。由斯涅尔定律可得 sin θc = n₂ / n₁（其中 n₁ > n₂）。光从玻璃（n ≈ 1.5）射向空气时，θc ≈ 42°。

Applications include optical fibres (endoscopes, telecommunications), where light is guided by repeated TIR along the core–cladding interface. The core must have a higher refractive index than the cladding.

应用包括光纤（内窥镜、通信），纤芯与包层界面的反复 TIR 使光在其中传播。纤芯的折射率必须高于包层。

11. Polarisation | 偏振

Polarisation provides evidence for the transverse nature of electromagnetic waves. Unpolarised light has oscillations in all planes perpendicular to the direction of propagation. After passing through a polarising filter, oscillations are confined to a single plane. If two polarisers are crossed (axes perpendicular), no light is transmitted.

偏振为电磁波是横波提供了证据。非偏振光在所有垂直于传播方向的平面内振动。通过偏振片后，振动被限制在单一平面内。若两个偏振片垂直放置（透振轴正交），则无光透过。

Polarisation by reflection: when light reflects off a non-metallic surface, it becomes partially polarised parallel to the surface. Brewster’s angle is the angle of incidence at which the reflected light is fully polarised, but this is usually beyond the scope of Edexcel A-Level except for qualitative understanding. Polaroid sunglasses reduce glare by blocking horizontally polarised light reflected from roads or water.

反射偏振：光从非金属表面反射时，会部分偏振化，偏振方向平行于表面。布儒斯特角是反射光全偏振时的入射角，但 Edexcel A-Level 通常只需定性了解。偏光太阳镜通过滤除从路面或水面反射的水平偏振光来减少眩光。

12. The Doppler Effect | 多普勒效应

The Doppler effect is the change in observed frequency when a wave source and observer move relative to each other. For sound, a source moving toward an observer gives a higher frequency (higher pitch); moving away gives a lower frequency. The observed frequency f’ for a source moving with speed vₛ relative to stationary observer is

f’ = f (c / (c ± vₛ))

, where c is the wave speed and the sign depends on direction (minus for moving towards, plus for moving away).

多普勒效应是指波源与观察者相对运动时，观察到的频率发生变化的现象。对于声波，波源朝向观察者运动时频率升高（音调变高），远离时频率降低。波源以速度 vₛ 相对于静止观察者运动时，观察频率 f’ 为

f’ = f (c / (c ± vₛ))

，其中 c 为波速，符号取决于方向（朝向取减号，远离取加号）。

For electromagnetic waves, the relativistic Doppler effect applies, but at A-Level a simplified formula Δf/f ≈ v/c is often used when v << c. The effect is used in radar speed guns, sonar, and red/blue shift in astronomy to determine radial velocities of stars and galaxies.

对于电磁波，需用相对论多普勒效应，但在 A-Level 中当 v << c 时常使用近似式 Δf/f ≈ v/c。该效应应用于雷达测速、声呐，以及天文学中通过红移/蓝移测定恒星和星系的径向速度。

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A-Level Edexcel Physics: Waves Key Points | A-Level Edexcel 物理：波 考点精讲