📚 GCSE AQA Physics: Waves Revision Guide | GCSE AQA 物理：波 考点精讲
Waves are a fundamental topic in AQA GCSE Physics, and they appear in both Paper 1 and Paper 2 questions on combined and triple science. This guide breaks down everything you need to master: wave types, wave properties, the wave equation, wave behaviour, sound, seismic waves and the electromagnetic spectrum. Use it to consolidate your knowledge, check your definitions and prepare for exam-style questions.
波是 AQA GCSE 物理中的基础主题，在组合科学和三科科学的 Paper 1 与 Paper 2 中都会出现。本指南系统梳理你需要掌握的全部内容：波的种类、波的特性、波速方程、波的行为、声波、地震波以及电磁波谱。用它来巩固知识、检查定义表述，并备考考试题型。
1. Introduction to Waves | 波的基础
A wave is a disturbance that transfers energy from one place to another without transferring matter. This is the single most important sentence in the topic, and it is worth learning word-for-word. When a wave travels through a material, the particles of that material vibrate about a fixed point, but they do not travel along with the wave.
波是一种扰动，它把能量从一个地方传递到另一个地方，而不传递物质。这是本主题最重要的一句话，值得逐字背下来。当波在某种物质中传播时，该物质的粒子只围绕固定位置振动，并不会跟着波一起前进。
The material a wave travels through is called the medium. Mechanical waves, such as sound and water waves, need a medium - they cannot travel through a vacuum. Electromagnetic waves are different: they can travel through a vacuum, which is why we receive light and radio signals from the Sun and from satellites.
波传播所经过的物质叫做介质。机械波（例如声波和水波）需要介质，无法在真空中传播。电磁波则不同：它们可以在真空中传播，这正是我们能接收到来自太阳和卫星的光与无线电信号的原因。
Waves are also used to transfer information. Radio waves carry broadcasts, microwaves carry mobile phone signals, and light in optical fibres carries internet data. Recognising this link between energy transfer and information transfer is a common feature of higher-mark exam questions.
波也被用来传递信息。无线电波传输广播，微波传输手机信号，光纤中的光传输互联网数据。认识到能量传递与信息传递之间的联系，是高分题目的常见考点。
2. Transverse and Longitudinal Waves | 横波与纵波
In transverse waves, the oscillations are perpendicular to the direction of energy transfer. If the wave travels left to right, the particles vibrate up and down. Examples include water waves, waves on a string or rope, and all electromagnetic waves.
在横波中，振动方向与能量传递方向垂直。如果波从左向右传播，粒子就上下振动。例如水波、绳波以及所有电磁波。
In longitudinal waves, the oscillations are parallel to the direction of energy transfer. If the wave travels left to right, the particles vibrate left and right. These waves contain regions of compression (where particles are close together) and rarefaction (where particles are spread out). Examples include sound waves in air and P-waves from earthquakes.
在纵波中，振动方向与能量传递方向平行。如果波从左向右传播，粒子也左右振动。这类波包含密部（粒子彼此靠近的区域）与疏部（粒子彼此远离的区域）。例如空气中的声波和地震产生的 P 波。
A common demonstration uses a slinky spring: pushing and pulling the spring coils produces a longitudinal wave, while shaking one end side-to-side produces a transverse wave. This is a favourite practical question because it shows both wave types with the same piece of equipment.
常见的演示使用弹簧（slinky）：前后推拉弹簧线圈产生纵波；左右摇动一端产生横波。这是很受欢迎的实验题素材，因为同一件器材同时展示了两种波。
When drawing waves, remember to label the direction of energy transfer, the direction of vibration, and - for longitudinal waves - the compressions and rarefactions. A clear diagram with correct labels is often worth a mark on its own.
画波的时候，记得标注能量传递方向、振动方向，以及（对纵波而言）密部和疏部。一张标注正确的清晰示意图本身常常就能得分。
3. Wave Properties: Amplitude, Wavelength, Frequency and Period | 波的特性：振幅、波长、频率与周期
Amplitude is the maximum displacement of a point on the wave from its undisturbed position. Amplitude is measured in metres, and it tells you how much energy the wave carries: a larger amplitude means a louder sound, a brighter light, or a bigger water wave.
振幅是波上一个点偏离其平衡位置的最大位移。振幅的单位是米，它反映波所携带的能量大小：振幅越大，声音越响、光越亮、水波越大。
Wavelength (λ) is the distance between two corresponding points on the wave, such as crest to crest, trough to trough, or compression to compression. It is measured in metres. The Greek letter λ (lambda) is used in the wave equation, so make sure you can write and recognise it.
波长（λ）是波上两个对应点之间的距离，例如波峰到波峰、波谷到波谷，或密部到密部。它用米作单位。波速方程中使用希腊字母 λ（lambda），要确保能写出并认出它。
Frequency (f) is the number of complete waves passing a point each second. It is measured in hertz (Hz), where 1 Hz means one complete wave per second. Frequency is related to the source of the wave: a faster source produces a higher frequency.
频率（f）是每秒通过某点的完整波的个数。它的单位是赫兹（Hz），1 Hz 表示每秒一个完整波。频率与波的波源有关：波源振动越快，产生的频率越高。
Period (T) is the time taken for one complete wave to pass a point, measured in seconds. Period and frequency are reciprocals of each other, which gives the relationship:
周期（T）是一个完整波通过某一点所需的时间，单位是秒。周期与频率互为倒数，因此有关系式：
T = 1 ÷ f and f = 1 ÷ T
unit with your answer - missing units is one of the most common causes of lost marks in calculations.
例如，如果波的频率为 50 Hz，其周期为 1 ÷ 50 = 0.02 s。如果波的周期为 0.25 s，其频率为 1 ÷ 0.25 = 4 Hz。答案务必带上单位——漏写单位是计算题丢分最常见的原因之一。
4. The Wave Equation | 波速方程
Wave speed (v) is the speed at which energy is transferred by the wave, or the speed at which the wave moves forward. It depends on the medium the wave is travelling through. As a wave enters a denser medium, its speed usually decreases.
波速（v）是波传递能量的速度，也就是波向前推进的速度。它取决于波所经过的介质。当波进入更稠密的介质时，波速通常会降低。
The key equation that links speed, frequency and wavelength is:
联系波速、频率和波长的关键方程是：
v = f × λ
In this equation, v is wave speed in metres per second (m/s), f is frequency in hertz (Hz), and λ is wavelength in metres (m). Because frequency is set by the source and does not change when a wave enters a new medium, any change in wave speed must be caused by a change in wavelength.
在这个方程中，v 是波速，单位米每秒（m/s）；f 是频率，单位赫兹（Hz）；λ 是波长，单位米（m）。由于频率由波源决定，当波进入新介质时频率不变，因此波速的任何变化必然由波长的变化引起。
another example, a radio wave travelling at 3 × 10⁸ m/s with a frequency of 100 × 10⁶ Hz has a wavelength of λ = v ÷ f = 3 × 10⁸ ÷ 1 × 10⁸ = 3 m.
例题：某声波频率为 250 Hz，波长为 1.36 m，则波速 v = 250 × 1.36 = 340 m/s，即声音在空气中的典型速度。再如，某无线电波以 3 × 10⁸ m/s 传播，频率为 100 × 10⁶ Hz，则波长 λ = v ÷ f = 3 × 10⁸ ÷ 1 × 10⁸ = 3 m。
ou whether to multiply or divide. Remember that 1 kHz = 1000 Hz and 1 MHz = 1 000 000 Hz, since exam questions often mix these units.
变形时可以用三角形法：v 放在顶端，f 和 λ 在底部。遮住要求的量，另外两个量的位置就告诉你该乘还是该除。记住 1 kHz = 1000 Hz，1 MHz = 1 000 000 Hz，因为考题经常混用这些单位。
5. Measuring Wave Speed | 波速的测量
Wave speed can be measured directly by timing a wave over a known distance, or calculated from frequency and wavelength. In the school laboratory, a ripple tank is used to study water waves: a vibrating bar creates regular waves, a lamp projects them onto a screen, and you measure the distance across several wavelengths before dividing by the number of waves.
波速可以通过计时波在已知距离上传播来直接测量，也可以由频率和波长计算得出。在学校实验室中，用水波槽（ripple tank）研究水波：振动杆产生规则的水波，灯光把波形投射到屏幕上，先测量若干个波长的总距离，再除以波的个数。
For waves on a string or a stretched spring, you can measure the length of several whole waves with a ruler and time how long one wave takes to travel a measured distance. Repeating the timing several times and taking a mean improves reliability and reduces the effect of random error.
对于绳波或拉伸弹簧上的波，可以用尺测量若干个完整波的长度，并计时一个波通过某段已知距离所需的时间。多次重复计时并取平均值可以提高可靠性，减小随机误差的影响。
echo to return. The sound has travelled 2d, so the speed of sound is v = 2d ÷ t. Another approach uses a signal generator with a loudspeaker and an oscilloscope to find frequency, combined with a microphone to measure wavelength.
对于声波，一种简单的方法是回声法。站在距离大而平整的墙面为 d 的位置，拍手或发出响声，测量回声返回的时间 t。声音传播了 2d 的距离，因此声速 v = 2d ÷ t。另一种方法是用信号发生器连接扬声器，用示波器测频率，再配合麦克风测量波长。
In method questions, always state what you measure, how you measure it, and how you process the results. Describing the repetition and averaging step is usually worth an extra mark, and you should also mention any safety or practical precautions, such as keeping the ripple tank on a level bench.
在实验方法题中，一定要说明测量什么、如何测量、以及如何处理数据。写出"重复实验并取平均"这一步通常能多得一分，同时还应提及安全或操作注意事项，例如把水波槽放在水平台面上。
6. Reflection, Refraction and Diffraction | 反射、折射与衍射
Reflection occurs when a wave bounces off a boundary between two different media. For a smooth surface, the angle of incidence equals the angle of reflection, both measured from the normal, which is an imaginary line perpendicular to the surface. Sound reflects to produce echoes, light reflects in mirrors, and radio waves reflect off the ionosphere to travel long distances.
反射发生在波遇到两种不同介质的分界面并弹回时。对于光滑表面，入射角等于反射角，两者都从法线量起；法线是垂直于表面的假想线。声波反射产生回声，光在镜子中反射，无线电波被电离层反射从而能远距离传播。
Refraction occurs when a wave changes speed as it crosses a boundary, causing it to change direction. When light passes from air into glass it slows down and bends towards the normal; when it leaves glass back into air it speeds up and bends away from the normal. The frequency stays the same, but the wavelength changes along with the speed.
折射发生在波穿过界面时因波速改变而改变方向。当光从空气进入玻璃时，速度降低并向法线偏折；当光从玻璃回到空气时，速度增大并偏离法线。频率保持不变，但波长随波速一起改变。
Diffraction is the spreading of waves when they pass through a gap or around an obstacle. The effect is most noticeable when the wavelength is similar in size to the gap or obstacle. This explains why sound passes easily through doorways and can be heard around corners, while light, with its much shorter wavelength, spreads much less.
衍射是波通过狭缝或绕过障碍物时向外扩散的现象。当波长与狭缝或障碍物的尺寸相当时，衍射效果最明显。这就解释了为什么声音容易穿过门道、并能绕过墙角被听到，而波长小得多的光则扩散得不明显。
Diffraction is important in real technology: radio waves with long wavelengths can diffract around hills and buildings to reach receivers, which is why long-wave radio reception is possible in valleys where television signals, using much shorter wavelengths, are poor.
衍射在实际技术中很重要：波长较长的无线电波能绕过山丘和建筑物到达接收器，这就是为什么在电视信号（波长更短）很差的峡谷中，长波无线电仍能正常接收。
7. Sound Waves | 声波
Sound waves are longitudinal waves that travel through a medium by making its particles vibrate. They cannot travel through a vacuum because there are no particles to vibrate. This is why space is silent, and it is a common exam question worth an easy mark.
声波是纵波，通过使介质中的粒子振动来传播。它们无法穿过真空，因为真空里没有可振动的粒子。这就是太空是寂静的原因，也是考试中常见的易得分题。
Sound travels faster in solids than in liquids, and faster in liquids than in gases, because the particles are closer together and can pass on vibrations more quickly. The typical speed of sound in air at room temperature is about 340 m/s, in water about 1500 m/s, and in steel about 5000 m/s.
声音在固体中比在液体中传播得快，在液体中比在气体中传播得快，因为粒子之间距离更近，能更快地传递振动。室温下空气中的声速约为 340 m/s，水中约为 1500 m/s，钢中约为 5000 m/s。
The human ear can detect frequencies from about 20 Hz to 20 000 Hz. Sound above this range is called ultrasound, and sound below it is called infrasound. Ultrasound has many uses, including medical scanning, cleaning delicate items, and measuring the depth of the sea by reflecting pulses off the seabed.
人耳能听到的频率范围大约是 20 Hz 到 20 000 Hz。高于这一范围的声音叫超声波，低于这一范围的声音叫次声波。超声波有许多用途，包括医学成像、清洗精密物品，以及通过发射脉冲并接收海底反射来测量海洋深度。
The loudness of a sound depends on the amplitude of the wave, and the pitch depends on the frequency. On an oscilloscope trace, a louder sound shows a taller wave, and a higher pitch shows a wave with more waves packed into the same horizontal distance.
声音的响度取决于波的振幅，音调取决于频率。在示波器波形上，声音更响表现为波形更高；音调更高表现为同样水平距离内波数更多。
8. Seismic Waves | 地震波
Earthquakes produce seismic waves that travel through the Earth and can be detected by seismometers around the world. There are two main types of body wave: P-waves and S-waves. P-waves are longitudinal and travel faster, so they are detected first. S-waves are transverse and travel more slowly.
地震会产生地震波，穿过地球并被世界各地的地震仪探测到。主要的两类体波是 P 波和 S 波。P 波是纵波，传播更快，因此最先被探测到；S 波是横波，传播较慢。
Both P-waves and S-waves can pass through solids, but S-waves cannot travel through liquids and gases. S-waves therefore cannot pass through the liquid outer core of the Earth, which creates a shadow zone on the opposite side of the planet where no S-waves are detected. This observation is direct evidence that the outer core is liquid.
P 波和 S 波都能穿过固体，但 S 波不能穿过液体和气体。因此 S 波无法穿过地球的液态外核，从而在地球另一侧形成探测不到 S 波的"影区"。这一观测结果是外核为液态的直接证据。
P-waves also refract as they pass through the Earth because the properties of the layers change with depth. By analysing the arrival times and paths of seismic waves, scientists built up a picture of the Earth's internal structure: a solid inner core, a liquid outer core, a mantle and a thin crust.
P 波在地球内部传播时也会发生折射，因为各圈层的性质随深度而变化。通过分析地震波的到达时间和传播路径，科学家建立起地球内部结构的图像：固态内核、液态外核、地幔和很薄的地壳。
Comparing seismic waves with other waves is a favourite exam task. Remember: P-waves are longitudinal and can travel through solids and liquids; S-waves are transverse and only travel through solids; both are mechanical waves that transfer energy through the Earth.
把地震波与其他波进行比较是常见考题。记住：P 波是纵波，能穿过固体和液体；S 波是横波，只能穿过固体；两者都是通过地球传递能量的机械波。
9. The Electromagnetic Spectrum | 电磁波谱
ium, which is why light from distant stars and signals from spacecraft can reach us through space.
电磁波谱是一个连续的横波谱段，它们在真空中的传播速度都相同：3 × 10⁸ m/s。电磁波不需要介质，这正是遥远恒星的光和航天器的信号能穿过太空到达地球的原因。
The seven regions, in order of increasing wavelength and decreasing frequency, are: gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves and radio waves. Visible light itself is a narrow band from red (longest wavelength) to violet (shortest wavelength).
按波长递增、频率递减的顺序，这七个波段是：伽马射线、X 射线、紫外线、可见光、红外线、微波和无线电波。可见光本身只是一个很窄的波段，从红光（波长最长）到紫光（波长最短）。
| Region | 波段 | Wavelength trend | 波长趋势 | Typical use | 典型用途 |
| Radio waves 无线电波 | Longest 最长 | Broadcasting, TV 广播、电视 |
| Microwaves 微波 | Long 较长 | Mobile phones, satellite, cooking 手机、卫星、加热 |
| Infrared 红外线 | Medium 中等 | Heaters, thermal cameras 取暖器、热成像 |
| Visible 可见光 | Narrow band 窄波段 | Sight, photography, fibre optics 视觉、摄影、光纤 |
| Ultraviolet 紫外线 | Short 较短 | Sun tanning, sterilising 晒黑、杀菌 |
| X-rays X 射线 | Shorter 更短 | Medical imaging 医学成像 |
| Gamma rays 伽马射线 | Shortest 最短 | Cancer treatment 癌症治疗 |
a vacuum, a shorter wavelength must mean a higher frequency, and therefore a higher energy photon. This is why gamma rays are the most penetrating and the most ionising part of the spectrum.
注意波长与频率的反比关系：由于在真空中所有电磁波的 v = f × λ 都相同，波长越短就必然频率越高，因而光子能量越大。这就是伽马射线在电磁波谱中穿透力最强、电离能力最强的原因。
10. Uses and Hazards of Electromagnetic Waves | 电磁波的用途与危害
Each region of the electromagnetic spectrum has properties that make it useful, and each also carries risks. Radio waves are used for communication because they diffract around obstacles and pass through walls. Microwaves are used for satellite communication and for heating food, because water molecules absorb them strongly.
电磁波谱的每个波段都有使其有用的特性，同时也各自带有风险。无线电波用于通信，因为它们能绕过障碍物并穿透墙壁。微波用于卫星通信和加热食物，因为水分子能强烈吸收微波。
Infrared is used in heaters, thermal imaging and remote controls, since all warm objects emit infrared radiation. Visible light is used for sight and in optical fibres, where total internal reflection keeps signals inside the fibre over long distances. Ultraviolet is used in sun beds and sterilising equipment, but it can damage skin cells and cause sunburn and skin cancer.
红外线用于取暖器、热成像和遥控器，因为所有温暖物体都会发出红外辐射。可见光用于视觉和光纤，在光纤中全反射使信号能在长距离内保持在纤芯中传播。紫外线用于日光浴床和消毒设备，但它会损伤皮肤细胞，引起晒伤甚至皮肤癌。
X-rays pass through soft tissue but are absorbed by denser material such as bone, which is why they are used for medical imaging. However, X-rays are ionising and can damage living cells, so radiographers stand behind lead screens and exposure times are kept as short as possible. Gamma rays are used to sterilise medical equipment and to treat cancer, but they are highly ionising and require thick lead or concrete shielding.
X 射线能穿过软组织，但会被骨骼等较致密的物质吸收，因此被用于医学成像。然而 X 射线具有电离性，会损伤活细胞，所以放射技师会站在铅屏后，并尽量缩短曝光时间。伽马射线用于医疗器械灭菌和癌症治疗，但电离能力很强，需要厚厚的铅或混凝土屏蔽。
In exam answers about hazards, always name the specific wave and the specific danger: "ultraviolet can ionise skin cells and cause skin cancer" scores higher than a vague statement such as "it is dangerous". Linking each hazard to increased exposure is another way to gain marks.
在回答危害类题目时，一定要写出具体波段和具体危害："紫外线会电离皮肤细胞并引发皮肤癌"比"它很危险"这类笼统表述得分更高。把每种危害与"过量暴露"联系起来，也是得分要点。
11. Key Formulae and Wave Comparison | 核心公式与波的对比
The two formulae you must know by heart are the period-frequency relationship and the wave equation. Together they solve almost every wave calculation in the AQA specification.
必须熟记的两个公式是周期—频率关系式和波速方程。它们合起来几乎能解决 AQA 考纲中所有的波的运算题。
T = 1 ÷ f v = f × λ speed of EM waves in a vacuum = 3 × 10⁸ m/s
Use this comparison table to check you can distinguish the two main wave types at a glance. Exam questions frequently ask you to state two differences between transverse and longitudinal waves, or to classify a given wave correctly.
用下面的对比表检查你是否能一眼区分两种主要波型。考题常要求你说出横波与纵波的两点区别，或正确判断某一给定波的类别。
| Feature | 特征 | Transverse 横波 | Longitudinal 纵波 |
| Oscillation direction 振动方向 | Perpendicular to energy transfer 垂直于能量传递方向 | Parallel to energy transfer 平行于能量传递方向 |
| Structure 结构 | Crests and troughs 波峰与波谷 | Compressions and rarefactions 密部与疏部 |
| Examples 实例 | Light, water waves, S-waves 光、水波、S 波 | Sound, ultrasound, P-waves 声波、超声波、P 波 |
| Vacuum 真空 | EM waves can travel 电磁波可传播 | Cannot travel 不能传播 |
12. Exam Tips and Common Mistakes | 考试技巧与常见错误
First, learn the definitions precisely. "A wave transfers energy without transferring matter" and "amplitude is the maximum displacement from the undisturbed position" are standard mark-scheme sentences. Vague paraphrases often score zero even when the physics is understood.
第一，精确掌握定义。"波传递能量而不传递物质"以及"振幅是偏离平衡位置的最大位移
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