IGCSE OCR Physics: Waves Revision Guide | IGCSE OCR 物理：波考点精讲

📚 IGCSE OCR Physics: Waves Revision Guide | IGCSE OCR 物理：波考点精讲

Waves are one of the most fundamental ways in which energy and information are transferred without the bulk movement of matter. In the OCR IGCSE Physics specification, waves appear in contexts ranging from ripples on a pond to seismic tremors that probe the Earth’s interior. This guide consolidates every key concept you need to master: the distinction between transverse and longitudinal motion, the meaning of amplitude, wavelength and frequency, the wave equation, and the behaviours of reflection, refraction and diffraction. It also covers sound, the electromagnetic spectrum and seismic waves, all with clear explanations and practical applications.

波是能量和信息传递的最基本方式之一，无需物质的整体移动即可实现。在 OCR IGCSE 物理考纲中，波的相关内容遍布于从池塘涟漪到探测地球内部的地震颤动等各种情境。本篇指南整合了你必须掌握的每个核心概念：横波与纵波运动的区别，振幅、波长和频率的含义，波速方程，以及反射、折射和衍射的行为。文章同时涵盖声波、电磁波谱和地震波，均配有清晰的解释和实际应用。

1. Types of Waves | 波的类型

All waves fall into two main categories: transverse and longitudinal. In a transverse wave, the oscillations are perpendicular to the direction of energy transfer. Ripples on a water surface and all electromagnetic waves, such as light and radio waves, are transverse. You can visualise this by imagining a rope shaken up and down: the wave travels horizontally, but the rope particles vibrate vertically.

所有波可分为两大类：横波和纵波。在横波中，振动方向与能量传递方向垂直。水面涟漪以及所有电磁波（例如光和无线电波）都是横波。你可以想象一根上下抖动的绳子：波沿水平方向传播，但绳子上的质点垂直振动。

In a longitudinal wave, the oscillations are parallel to the direction of energy transfer. Sound waves in air and the primary (P) waves from an earthquake are longitudinal. They consist of compressions, where particles are crowded together, and rarefactions, where they are spread apart. A slinky spring pushed and pulled along its length demonstrates a longitudinal pulse clearly.

在纵波中，振动方向与能量传递方向平行。空气中的声波和地震产生的纵波（P 波）都是纵波。它们由密部（质点挤压在一起）和疏部（质点分散开来）组成。沿长度方向推拉一个弹簧玩具，可以清晰地演示纵波脉冲。

Features	Transverse waves	Longitudinal waves
Vibration direction	Perpendicular to energy travel	Parallel to energy travel
Examples	Water waves, EM waves, S-waves	Sound, P-waves
Can travel through	Solids, liquids, vacuum (EM)	Solids, liquids, gases

2. Describing Waves | 描述波的物理量

The amplitude of a wave is the maximum displacement of a point from its undisturbed position. In a transverse wave, it is the height of a crest or the depth of a trough measured from the equilibrium line. Amplitude is linked to the energy of the wave: a louder sound has a larger amplitude, and a brighter light has a higher amplitude of its electric field oscillation.

振幅是波上某点离开其静止位置的最大位移。在横波中，它是从平衡线测得的波峰高度或波谷深度。振幅与波的能量相关：声音越响，振幅越大；光线越亮，其电场振荡的振幅越高。

The wavelength (λ) is the distance between two consecutive points that are in phase, such as crest to crest or compression to compression. It is measured in metres (m). Frequency (f) is the number of complete waves passing a fixed point per second, measured in hertz (Hz). One hertz means one complete oscillation per second.

波长 (λ) 是相邻两个同相位点之间的距离，例如波峰到波峰或密部到密部，单位为米 (m)。频率 (f) 是每秒通过某固定点的完整波数目，单位为赫兹 (Hz)。一赫兹表示每秒一次完整振动。

The time period (T) is the time taken for one complete wave to pass a point, and it is the reciprocal of frequency:

周期 (T) 是一个完整波通过某点所需的时间，它是频率的倒数：

T = 1 / f

For example, a wave with a frequency of 50 Hz has a period of 0.02 s. When a wave source moves up and down, the wave profile is a snapshot of the wave pattern at an instant; the distance from crest to crest on this profile is the wavelength.

例如，频率为 50 Hz 的波周期为 0.02 s。当波源上下运动时，波形图是某一瞬间波形的快照；图上波峰到波峰的距离就是波长。

3. The Wave Equation | 波速方程

All waves obey the relationship between speed, frequency and wavelength. This is expressed by the wave equation:

所有波都遵循波速、频率与波长之间的关系，可用波速方程表示：

v = f × λ

where v is the wave speed in metres per second (m/s), f is the frequency in hertz (Hz), and λ is the wavelength in metres (m). This equation tells you that if the frequency increases while the speed stays constant, the wavelength must decrease. For electromagnetic waves in a vacuum, the speed v is always 3.0 × 10⁸ m/s, so high-frequency gamma rays have extremely short wavelengths.

其中 v 是波速，单位为米每秒 (m/s)，f 是频率 (Hz)，λ 是波长 (m)。该方程表明，若波速保持不变而频率升高，波长必然减小。对于真空中的电磁波，波速 v 恒为 3.0 × 10⁸ m/s，因此高频伽马射线波长极短。

You must be able to rearrange the equation. For instance, to find the frequency of a water wave travelling at 2 m/s with a wavelength of 0.5 m, use f = v / λ = 2 / 0.5 = 4 Hz. The wave equation is equally valid for sound, light and even seismic waves.

你必须能够变换该方程。例如，求一个波速为 2 m/s、波长为 0.5 m 的水波的频率，用 f = v / λ = 2 / 0.5 = 4 Hz。波速方程同样适用于声波、光波乃至地震波。

When waves travel from one medium to another, their speed and wavelength change, but the frequency remains the same because it is determined by the source. This is the key to understanding refraction.

当波从一种介质进入另一种介质时，波速和波长会改变，但频率保持不变，因为它由波源决定。这是理解折射的关键。

4. Reflection of Waves | 波的反射

Reflection occurs when waves bounce off a surface or boundary. The law of reflection states that the angle of incidence equals the angle of reflection, where both angles are measured from the normal – an imaginary line perpendicular to the surface at the point of incidence. A plane mirror produces a virtual image that is upright, laterally inverted and the same size as the object.

当波从表面或边界反弹时发生反射。反射定律指出，入射角等于反射角，两个角度均从法线（入射点处垂直于表面的假想线）测量。平面镜产生一个正立、左右颠倒且与物体等大的虚像。

In ripple tank experiments, straight water waves are reflected by a solid barrier, and the reflected wavefronts emerge at the same angle as the incident ones. Echoes are sound wave reflections; a smooth, large surface like a cliff will reflect an audible echo if the distance is large enough for the sound to travel and return after 0.1 s.

在波纹水槽实验中，直水波被固体障碍物反射，反射波前以与入射波前相同的角度出现。回声是声波的反射；若距离足够远，声音经过 0.1 秒后往返，一面光滑的大表面（如悬崖）就会反射出可听的回声。

For a curved mirror, a concave mirror can focus parallel light rays to a focal point, while a convex mirror spreads them out, giving a wider field of view. Reflections are also used in optical fibres where total internal reflection keeps light inside the core.

对于曲面镜，凹面镜可将平行光线汇聚到焦点，凸面镜则将其发散，提供更宽的视野。反射也用于光纤中，全内反射使光保持在纤芯内部。

5. Refraction of Waves | 波的折射

Refraction is the change in direction of a wave when it enters a new medium at an angle, due to a change in its speed. When a wave slows down, it bends towards the normal; when it speeds up, it bends away from the normal. This is why a straw appears bent in a glass of water: light travels slower in water than in air.

折射是波在斜向进入新介质时，因波速改变而发生的方向变化。波减速时，向法线方向弯折；波加速时，偏离法线。这就是吸管在水中看起来弯折的原因：光在水中的传播速度比在空气中慢。

Using a ripple tank, water waves can be seen to refract when they enter a shallower region. The water depth changes the wave speed, causing the wavelength to shorten and the wavefronts to bend. Crucially, the frequency of the wave does not alter when crossing the boundary.

利用波纹水槽，可以观察到水波进入较浅区域时发生折射。水深改变波速，导致波长缩短、波前弯折。关键在于波穿过边界时频率不变。

Sound waves refract too. On a warm day, sound bends upward because the air near the ground is warmer and sound travels faster in warmer air. At night, the cooling ground can cause sound to bend downward, making distant noises more audible.

声波也会折射。在温暖的日子里，声音向上弯折，因为地面附近空气较暖，声音在暖空气中传播更快。夜间，地面冷却会使声音向下弯折，使远处的声响更清晰可闻。

6. Diffraction of Waves | 波的衍射

Diffraction is the spreading out of waves when they pass through a gap or move past an obstacle. The extent of diffraction increases when the wavelength is comparable to the size of the gap or obstacle. If the gap is much wider than the wavelength, the wave passes through with little spreading; if the gap is similar in width to the wavelength, the wave spreads out almost semicircularly.

衍射是波穿过缝隙或绕过障碍物时发生的扩展现象。当波长与缝隙或障碍物的尺寸相近时，衍射程度增大。若缝隙远宽于波长，波几乎不扩散地通过；若缝隙宽度与波长相近，波则几乎呈半圆形展开。

Sound waves have wavelengths from about 2 cm to 20 m, which overlap with the dimensions of everyday openings such as doors. This is why you can hear sound from around a corner even when the source is not in your direct line of sight. Light, with wavelengths around 400–700 nm, diffracts only through extremely narrow slits, which is why shadows are typically sharp.

声波波长约为 2 cm 至 20 m，与门等日常开口的尺寸范围重叠。因此即使声源不在你视线内，你也能听到从转角处传来的声音。光的波长约为 400–700 nm，只能通过极窄的狭缝衍射，所以影子通常很清晰。

In practical contexts, diffraction sets a limit on the resolution of microscopes and telescopes. Radio telescopes use large dishes partly to minimise diffraction and produce sharper images of astronomical sources.

在实际应用中，衍射限制了显微镜和望远镜的分辨率。射电望远镜使用大型碟面，部分原因就是要减小衍射，产生更清晰的天文源图像。

7. Sound Waves | 声波

Sound waves are longitudinal waves consisting of alternating compressions and rarefactions that travel through solids, liquids and gases. In air at room temperature, sound travels at approximately 340 m/s. Sound cannot propagate through a vacuum because there are no particles to vibrate.

声波是纵波，由交替的密部和疏部组成，可在固体、液体和气体中传播。在室温空气中，声速约为 340 m/s。声音无法在真空中传播，因为没有振动的粒子。

Human hearing typically ranges from 20 Hz to 20,000 Hz. Frequencies above 20,000 Hz are called ultrasound. The amplitude of a sound wave determines its loudness, while its frequency determines the pitch. An oscilloscope can display a sound wave as a voltage-time graph, where a taller trace indicates greater amplitude (louder) and a tighter repeated pattern indicates higher frequency (higher pitch).

人类听觉范围通常为 20 Hz 至 20,000 Hz。超过 20,000 Hz 的频率称为超声波。声波的振幅决定响度，频率决定音调。示波器可将声波显示为电压-时间图像，其中较高的轨迹表示更大的振幅（更响），更密集的重复波形表示更高的频率（音调更高）。

Ultrasound has many applications. In medical imaging, ultrasound pulses reflect off boundaries between tissues to build up a picture of an unborn baby. In industry, it is used to detect flaws inside metal castings. Because ultrasound waves are partially reflected by cracks, a pulse-echo technique reveals internal defects.

超声波有许多应用。在医学成像中，超声波脉冲在组织边界反射，构建出胎儿的图像。在工业中，它用于检测金属铸件内部的瑕疵。由于超声波会被裂缝部分反射，脉冲回波技术能揭示内部缺陷。

8. The Electromagnetic Spectrum | 电磁波谱

The electromagnetic (EM) spectrum is a continuous family of transverse waves that all travel at the speed of light in a vacuum and do not require a medium. From longest wavelength to shortest, the main regions are: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Their frequencies and photon energies increase in the opposite direction.

电磁波谱是一系列连续的横波，它们在真空中均以光速传播，不需要介质。从长波长到短波长，主要区域为：无线电波、微波、红外线、可见光、紫外线、X 射线和伽马射线。其频率和光子能量沿相反方向递增。

Region	Wavelength range	Key uses and properties
Radio waves	> 0.1 m	Broadcasting, communications
Microwaves	0.1 m to 1 mm	Satellite signals, cooking, radar
Infrared	1 mm to 700 nm	Thermal imaging, remote controls, heating
Visible light	700 nm to 400 nm	Seeing, photography, fibre optics
Ultraviolet	400 nm to 10 nm	Sunbeds, security marking, fluorescent lamps
X-rays	10 nm to 0.01 nm	Medical imaging, security scanners
Gamma rays	< 0.01 nm	Cancer treatment, sterilisation

Higher-frequency EM waves tend to carry more energy and are more ionising. X-rays and gamma rays can damage living tissue, so their use requires shielding and careful exposure management. Microwaves are absorbed by water molecules, which is why they heat food, while infrared is emitted by all warm objects.

较高频率的电磁波往往携带更多能量，更具电离性。X 射线和伽马射线会损害活体组织，因此使用时需要屏蔽和谨慎的照射管理。微波被水分子吸收，因此可加热食物；而红外线由所有温热物体发射。

9. Seismic Waves and Earth Structure | 地震波与地球结构

When earthquakes occur, they produce seismic waves that travel through the Earth. There are two main types: P-waves (primary) and S-waves (secondary). P-waves are longitudinal and travel through both solids and liquids. S-waves are transverse and can only travel through solids; they are slower than P-waves.

地震发生时，会产生穿过地球的地震波。主要有两种类型：P 波（纵波）和 S 波（横波）。P 波是纵波，可穿过固体和液体。S 波是横波，只能穿过固体，且速度比 P 波慢。

By studying the arrival times of P-waves and S-waves at seismograph stations around the world, scientists have discovered that the Earth has a layered structure. P-waves travel through the mantle, the liquid outer core and the solid inner core, but S-waves are blocked by the liquid outer core. This absence of detected S-waves beyond a certain angular distance creates the S-wave shadow zone, providing strong evidence that the outer core is liquid.

通过研究 P 波和 S 波到达全球地震台站的时间，科学家发现地球具有层状结构。P 波可穿行地幔、液态外核和固态内核，而 S 波被液态外核阻挡。在某一角距离之外探测不到 S 波，形成了 S 波影区，这为外核是液态提供了有力证据。

P-waves refract at the boundary between the mantle and the core, creating a P-wave shadow zone between about 103° and 142° from the earthquake focus. These observations are a crucial piece of evidence for the internal structure of the Earth and are directly referenced in OCR IGCSE Physics.

P 波在地幔与地核边界发生折射，在距震源约 103° 至 142° 之间形成 P 波影区。这些观察结果是地球内部结构的关键证据，在 OCR IGCSE 物理中直接涉及。

10. Applications and Safety of Waves | 波的应用与安全

Waves are not just abstract concepts; they enable much of modern technology. Radio waves and microwaves carry TV, radio and mobile phone signals. Infrared is used in thermal cameras and intruder alarms. X-rays image bones and teeth, while gamma rays target tumours in radiotherapy.

波并不只是抽象概念，它们支撑着大量现代科技。无线电波和微波传输电视、广播和手机信号。红外线用于热像仪和入侵报警器。X 射线可拍摄骨骼和牙齿图像，而伽马射线在放射治疗中靶向肿瘤。

However, the energy carried by waves can also pose risks. Ultraviolet radiation from the Sun can cause sunburn and skin cancer; sunscreens and clothing reduce this exposure. X-rays and gamma rays are ionising radiation – they can remove electrons from atoms and damage DNA. Medical and industrial use of ionising radiation is controlled by the principle of ALARA (As Low As Reasonably Achievable), using shielding, minimising exposure time and maximising distance from the source.

然而，波携带的能量也可能带来风险。太阳的紫外线辐射可导致晒伤和皮肤癌；防晒霜和衣物可减少此类暴露。X 射线和伽马射线是电离辐射——它们可使原子失去电子，损害 DNA。医疗和工业中使用电离辐射遵循 ALARA 原则（合理可达尽量低），即采用屏蔽、缩短暴露时间和最大化距离源。

Loud sounds can damage hearing, so ear protection is required in noisy environments. Even visible light from lasers demands caution because of its high intensity and collimation. By understanding wave properties, engineers design systems that harness wave energy safely and effectively.

响亮的声音可能损伤听力，因此在噪音环境中需要佩戴护耳装置。即便是来自激光的可见光，因其高强度和准直性，也需谨慎对待。通过理解波的性质，工程师能设计出安全且有效地利用波能的系统。

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IGCSE OCR Physics: Waves Revision Guide | IGCSE OCR 物理：波 考点精讲