AS Physics: Waves Essentials & Key Points | AS 物理：波考点精讲

📚 AS Physics: Waves Essentials & Key Points | AS 物理：波考点精讲

Waves are fundamental to many areas of physics, from sound and light to quantum mechanics. In AS Physics, you must master wave properties, terminology, the wave equation, superposition, interference, stationary waves, and diffraction. This revision guide distills the key concepts with clear explanations, equipping you for exam success.

波是物理学许多领域的基础，从声音、光到量子力学。在 AS 物理中，你必须掌握波的性质、术语、波动方程、叠加、干涉、驻波和衍射。这份复习指南用清晰的解释提炼了关键概念，助你考试成功。

1. What is a Wave? – Basic Concepts | 什么是波？基础概念

A wave is a disturbance that transfers energy from one place to another without transferring matter. All waves carry energy, and most require a medium to travel through, except electromagnetic waves which can propagate in a vacuum. The particles of the medium oscillate about fixed positions, passing energy to neighbouring particles.

波是一种扰动，它将能量从一个地方传递到另一个地方而不传递物质。所有波都携带能量，大多数波需要介质才能传播，除了能在真空中传播的电磁波。介质的粒子在固定位置附近振动，将能量传递给相邻粒子。

There are two main types of mechanical waves: progressive (travelling) waves and stationary (standing) waves. Progressive waves move energy from a source, while stationary waves store energy in a confined space.

机械波有两种主要类型：行波（前进波）和驻波（定波）。行波将能量从波源传出，而驻波将能量储存在有限空间内。

2. Transverse and Longitudinal Waves | 横波与纵波

In transverse waves, the particle oscillations are perpendicular to the direction of wave propagation (energy transfer). Examples include light, water ripples, and waves on a string. Transverse waves can be polarised.

在横波中，粒子的振动方向与波的传播方向（能量传递方向）垂直。例子包括光、水波涟漪和绳子上的波。横波可以发生偏振。

In longitudinal waves, the particle oscillations are parallel to the direction of propagation. Sound waves and ultrasound are longitudinal. They consist of compressions (regions of high pressure) and rarefactions (regions of low pressure). Longitudinal waves cannot be polarised.

在纵波中，粒子的振动方向与传播方向平行。声波和超声波是纵波。它们由压缩区（高压区域）和稀疏区（低压区域）组成。纵波不能发生偏振。

3. Wave Terminology | 波的术语

You must be precise with definitions:

你必须对这些定义精确掌握：

Displacement (x): distance a particle has moved from its equilibrium position in a particular direction. / 位移 (x)：粒子在特定方向上离开平衡位置的距离。
Amplitude (A): maximum displacement from equilibrium. / 振幅 (A)：离开平衡位置的最大位移。
Wavelength (λ): distance between two consecutive points in phase, e.g., crest to crest or compression to compression. / 波长 (λ)：两个相邻同相点之间的距离，例如波峰到波峰或压缩区到压缩区。
Period (T): time taken for one complete oscillation or for a wave to advance by one wavelength. / 周期 (T)：完成一次完整振动或波前进一个波长所需的时间。
Frequency (f): number of complete oscillations per unit time; measured in hertz (Hz), equal to s⁻¹. / 频率 (f)：单位时间内完整振动的次数，单位是赫兹 (Hz)，即 s⁻¹。
Wave speed (v): speed at which energy is transferred by the wave; v = fλ. / 波速 (v)：波传递能量的速度；v = fλ。

Phase difference describes how much one wave lags behind another, measured in radians or degrees. Two points one wavelength apart have a phase difference of 2π rad (or 360°).

相位差描述了一个波相对于另一个波的滞后程度，以弧度或度为单位。相距一个波长的两点相位差为 2π 弧度（或 360°）。

4. The Wave Equation | 波动方程

The relationship between wave speed, frequency and wavelength is fundamental:

波速、频率和波长之间的关系是基础性的：

v = f λ

where v is wave speed in m s⁻¹, f is frequency in Hz, and λ is wavelength in metres. The period T is the reciprocal of frequency: T = 1/f. Thus you can also write v = λ / T. This equation applies to all waves.

其中 v 是波速（m s⁻¹），f 是频率（Hz），λ 是波长（m）。周期 T 是频率的倒数：T = 1/f。因此你也可以写成 v = λ / T。这个方程适用于所有波。

5. Electromagnetic Spectrum | 电磁波谱

Electromagnetic (EM) waves are transverse, travel at 3.00 × 10⁸ m s⁻¹ in a vacuum, and do not require a medium. The spectrum, in order of increasing frequency (decreasing wavelength), is: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.

电磁波是横波，在真空中以 3.00 × 10⁸ m s⁻¹ 的速度传播，并且不需要介质。电磁波谱按频率递增（波长递减）的顺序依次为：无线电波、微波、红外线、可见光、紫外线、X 射线、伽马射线。

All EM waves share the same speed c in free space, so c = fλ. Visible light occupies a narrow band from about 400 nm (violet) to 700 nm (red). Remember the dangers and uses of each region, as these are common exam contexts.

所有电磁波在自由空间中都有相同的速度 c，因此 c = fλ。可见光占据一个狭窄的波段，大约从 400 nm（紫光）到 700 nm（红光）。记住每个波段的危害和用途，因为这些是常见的考试背景。

6. Polarisation | 偏振

Polarisation is a phenomenon exclusive to transverse waves. A wave is plane-polarised if the oscillations occur in only one plane. Unpolarised light has oscillations in many planes perpendicular to the direction of travel. A Polaroid filter transmits only the component of oscillation parallel to its transmission axis.

偏振是横波独有的现象。如果振动只发生在一个平面内，那么波就是平面偏振的。非偏振光在与传播方向垂直的许多平面内都有振动。偏振片只允许平行于其透射轴的振动分量通过。

According to Malus’s law, the transmitted intensity I after a perfect polariser is I = I₀ cos²θ, where I₀ is the incident intensity and θ is the angle between the incident polarisation direction and the filter’s axis. Polarisation provides evidence that light is a transverse wave.

根据马吕斯定律，通过理想偏振片后的透射强度 I 为 I = I₀ cos²θ，其中 I₀ 是入射强度，θ 是入射偏振方向与偏振片轴之间的夹角。偏振证明了光是一种横波。

7. Superposition and Interference | 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 effects.

叠加原理指出，当两个或更多的波在一点相遇时，合成位移是各个位移的矢量和。这导致了干涉效应。

Constructive interference occurs when waves are in phase (phase difference 0, 2π…), producing a resultant amplitude greater than the individual amplitudes. Destructive interference occurs when waves are in antiphase (phase difference π, 3π…), resulting in a smaller or zero amplitude. For sustained interference, the sources must be coherent (constant phase difference and same frequency).

当波同相时（相位差为 0, 2π……），发生相长干涉，合成振幅大于单个波的振幅。当波反相时（相位差为 π, 3π……），发生相消干涉，导致振幅变小或为零。要产生稳定的干涉图样，波源必须是相干的（相位差恒定且频率相同）。

8. Young’s Double-Slit Experiment | 杨氏双缝实验

Young’s experiment demonstrates the wave nature of light by producing an interference pattern of bright and dark fringes. Monochromatic light passes through two narrow slits close together (separation a) and illuminates a screen at distance D. Bright fringes form where the path difference = nλ (constructive interference), and dark fringes where the path difference = (n + ½)λ.

杨氏实验通过产生亮暗相间的干涉条纹证明了光的波动性。单色光通过两条距离很近的狭缝（间距为 a），照亮距双缝 D 远处的屏幕。光程差等于 nλ 处形成亮纹（相长干涉），光程差等于 (n + ½)λ 处形成暗纹。

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

条纹间距（相邻亮纹间的距离）由下式给出：

Δx = λ D / a

This formula shows that increasing wavelength or screen distance increases fringe spacing, while increasing slit separation decreases it. The experiment requires coherent light; lasers are ideal sources.

该公式表明，增加波长或屏幕距离会增大条纹间距，而增加缝间距则会减小条纹间距。实验需要相干光；激光是理想的光源。

9. Diffraction Gratings | 衍射光栅

A diffraction grating consists of many equally spaced parallel slits (lines). The grating spacing d is the reciprocal of the number of lines per metre. When monochromatic light passes through a grating, sharp interference maxima are observed at angles θ satisfying the grating equation:

衍射光栅由许多等间距的平行狭缝（刻线）组成。光栅常数 d 是每米刻线数的倒数。当单色光通过光栅时，在满足光栅方程的 θ 角处可观察到锐利的干涉极大：

d sinθ = nλ, n = 0, 1, 2, …

where n is the order of the maximum. The zeroth order (n=0) is the central bright line. Higher orders are symmetric. Gratings produce sharper, brighter fringes than double slits, allowing more precise measurement of wavelength. If white light is used, each order (except n=0) displays a spectrum with violet closest to the centre and red farthest.

其中 n 是亮纹的级数。零级 (n=0) 是中央亮线。更高级对称分布。光栅产生的条纹比双缝更锐利、更明亮，可用于更精确地测量波长。如果使用白光，除零级外每一级都会显示出光谱，紫光最靠近中心，红光最远。

10. Stationary Waves | 驻波

A stationary wave is formed by the superposition of two progressive waves of equal frequency and amplitude travelling in opposite directions. Unlike progressive waves, no net energy is transported. The wave pattern has nodes (points of zero displacement) and antinodes (points of maximum displacement).

驻波由两个频率和振幅相同、传播方向相反的行波叠加形成。与行波不同，驻波没有净能量的传递。波形中有波节（位移为零的点）和波腹（位移最大的点）。

Common examples include vibrating strings (both ends fixed) and air columns in pipes. For a string of length L fixed at both ends, the standing wave condition is L = nλ/2, with n = 1, 2, 3… The fundamental frequency (first harmonic, n=1) has one antinode at the centre. For a pipe closed at one end, the resonant lengths are L = nλ/4, where n is an odd integer (1, 3, 5…).

常见的例子包括振动的弦（两端固定）和管中的空气柱。对于长度为 L 且两端固定的弦，驻波条件为 L = nλ/2，n = 1, 2, 3……。基频（第一谐波，n=1）在中心有一个波腹。对于一端封闭的管，共振长度为 L = nλ/4，其中 n 为奇数（1, 3, 5……）。

11. Wave Intensity and Amplitude | 波的强度与振幅

Intensity I is the power per unit area incident on a surface, measured in W m⁻². For any wave, intensity is proportional to the square of the amplitude:

强度 I 是入射到表面上的单位面积的功率，单位为 W m⁻²。对于任何波，强度与振幅的平方成正比：

I ∝ A²

This means doubling the amplitude quadruples the intensity. For a point source radiating uniformly in three dimensions, intensity obeys the inverse square law: I = P / (4πr²), so as distance r increases, intensity decreases with 1/r². This relationship helps explain why light and sound get fainter with distance.

这意味着振幅加倍会使强度变为四倍。对于在三维空间中均匀辐射的点源，强度服从平方反比定律：I = P / (4πr²)，因此随着距离 r 增大，强度以 1/r² 的比例减小。这一关系有助于解释为什么光和声音随距离变远而减弱。

12. Diffraction of Waves | 波的衍射

Diffraction is the spreading of waves when they pass through an aperture or around an obstacle. The amount of diffraction depends on the wavelength relative to the size of the gap: noticeable diffraction occurs when the gap width is comparable to or smaller than the wavelength.

衍射是波通过缝隙或绕过障碍物时发生扩展的现象。衍射的程度取决于波长与缝隙尺寸的相对大小：当缝隙宽度与波长相当或更小时，衍射现象显著。

For a single slit, a central bright maximum is flanked by dimmer, narrower fringes. The condition for the first minimum in single-slit diffraction is a sinθ = λ, where a is the slit width. Diffraction explains why we can hear sound around corners but light does not bend noticeably through a doorway, because sound wavelengths are much larger.

对于单缝，中央亮纹两侧是较暗、较窄的条纹。单缝衍射第一极小的条件为 a sinθ = λ，其中 a 是缝宽。衍射解释了为什么我们能够听到拐角处传来的声音，而光通过门口时不会明显弯曲——这是因为声波的波长大得多。

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AS Physics: Waves Essentials & Key Points | AS 物理：波 考点精讲