📚 Waves Revision Notes | 波 考点精讲
Waves are fundamental phenomena that transfer energy without transferring matter. Understanding waves helps you explain everything from sound and light to earthquakes and mobile phone signals. In CCEA GCSE Physics, you need to know how waves behave, how to use the wave equation, and the properties of different types of waves including sound, light, and the electromagnetic spectrum.
波是一种传递能量而不传递物质的基本现象。理解波可以帮助你解释从声音和光到地震和手机信号的一切现象。在 CCEA GCSE 物理中，你需要掌握波的行为、如何使用波动方程，以及包括声波、光波和电磁波谱在内的不同类型波的性质。
1. What is a Wave? | 什么是波？
A wave is a disturbance that travels through a medium or space, transferring energy from one point to another. The particles of the medium only oscillate about fixed positions; they do not travel with the wave. For example, when you produce a wave in a rope by moving your hand up and down, the rope itself does not move forward – only the energy travels along the rope.
波是一种通过介质或空间传播的扰动，将能量从一点传递到另一点。介质的粒子仅在其平衡位置附近振动，并不随波一同移动。例如，当你上下移动手在绳子上产生波时，绳子本身并不向前移动——只有能量沿着绳子传播。
2. Types of Waves: Transverse and Longitudinal | 波的种类：横波与纵波
There are two main types of waves. In a transverse wave, particle vibrations are perpendicular to the direction of energy transfer. Light and water waves are transverse. In a longitudinal wave, vibrations are parallel to the direction of energy transfer. Sound is a longitudinal wave, and it travels as a series of compressions and rarefactions.
波主要有两种类型。在横波中，粒子的振动方向与能量传递方向垂直。光波和水波是横波。在纵波中，振动方向与能量传递方向平行。声音是一种纵波，以一系列疏密相间的形式传播。
3. Key Wave Terms | 波的关键术语
You must be confident with these definitions:
- Amplitude (A): The maximum displacement of a point on the wave from its equilibrium position. It determines the energy carried by the wave.
- Wavelength (λ): The distance between two successive identical points on a wave, e.g., crest to crest.
- Frequency (f): The number of complete wave cycles per second, measured in hertz (Hz).
- Period (T): The time taken for one complete oscillation, T = 1 / f.
- Wave speed (v): The speed at which the wave energy travels, measured in m/s.
你需要熟悉以下定义：
- 振幅 (A)：波上某点偏离平衡位置的最大位移，决定波携带的能量。
- 波长 (λ)：波上两个连续相同点之间的距离，例如波峰到波峰。
- 频率 (f)：每秒完整波动循环的次数，单位是赫兹 (Hz)。
- 周期 (T)：完成一次全振动所需的时间，T = 1 / f。
- 波速 (v)：波能量传播的速度，单位是 m/s。
4. The Wave Equation | 波动方程
The relationship between wave speed, frequency and wavelength is given by the wave equation:
v = f × λ
velength (m). You can rearrange the equation to find any unknown: f = v ÷ λ, or λ = v ÷ f.
波速、频率和波长之间的关系由波动方程给出：
v = f × λ
其中 v 是波速 (m/s)，f 是频率 (Hz)，λ 是波长 (m)。你可以变换公式来求任意未知量：f = v ÷ λ，或 λ = v ÷ f。
ts speed is v = 5 × 3 = 15 m/s. Using this equation is essential in all wave calculations.
例如，若一水波的频率为 5 Hz，波长为 3 m，则其波速为 v = 5 × 3 = 15 m/s。掌握该方程对所有波动计算至关重要。
5. Wave Graphs | 波动图像
Two types of graphs are used to describe waves: displacement–distance graphs show the position of all particles at one instant in time – you can read the wavelength directly from the horizontal axis. Displacement–time graphs show how the displacement of one particle varies over time – you can read the period and hence calculate the frequency.
描述波动常使用两类图像：位移–距离图显示某一瞬间所有粒子的位置，可直接从横轴读取波长。位移–时间图显示单个粒子位移随时间的变化，可读出周期，进而计算频率。
Exam questions often ask you to measure wavelength, amplitude and period from such graphs, so practise drawing and interpreting them.
考试题目常要求你从这些图像中测量波长、振幅和周期，因此要练习绘制和解读它们。
6. Reflection of Waves | 波的反射
When waves hit a boundary, they can bounce back – this is reflection. The law of reflection states that the angle of incidence equals the angle of reflection (both measured from the normal). Reflection explains echoes in sound, and how we see objects in mirrors.
当波遇到界面时，它们会反弹回来——这就是反射。反射定律指出入射角等于反射角（两者均从法线测量）。反射解释了声音中的回声，以及我们如何从镜子中看到物体。
For light, a smooth surface gives a clear reflection; a rough surface scatters the light in all directions (diffuse reflection), but each ray still obeys the law of reflection.
对于光而言，光滑表面产生清晰的反射；粗糙表面将光散射到各个方向（漫反射），但每条光线仍遵守反射定律。
7. Refraction of Waves | 波的折射
Refraction occurs when a wave passes from one medium to another and changes speed, causing it to change direction unless it hits the boundary along the normal. If the wave slows down, it bends towards the normal; if it speeds up, it bends away from the normal. This is why a pencil appears bent in a glass of water.
当波从一种介质进入另一种介质时，速度发生变化，导致其改变方向，除非它沿法线方向射入界面。若波速减慢，波会向法线偏折；若波速加快，则偏离法线。这就是铅笔在水中看起来弯曲的原因。
= fλ, a change in speed while frequency remains constant means the wavelength must change.
在折射过程中，波的频率保持不变。由于 v = fλ，当速度改变而频率恒定时，波长必然改变。
8. Diffraction of Waves | 波的衍射
Diffraction is the spreading out of waves when they pass through a gap or around an obstacle. The amount of diffraction increases when the gap size is similar to the wavelength. If the gap is much larger than the wavelength, diffraction is barely noticeable. You need to be able to describe how changing the gap width or wavelength affects the pattern.
衍射是波穿过狭缝或绕过障碍物时的扩散现象。当狭缝尺寸与波长接近时，衍射效应最显著。如果狭缝远大于波长，衍射几乎不可见。你需要能描述改变狭缝宽度或波长如何影响衍射图样。
Diffraction explains why you can hear sounds around corners even though you cannot see the source; sound waves have long wavelengths (approx. 1 m) and easily diffract around everyday objects.
衍射解释了为什么你能在拐角处听到声音却看不见声源；声波具有较长的波长（约 1 m），很容易绕过日常物体。
9. Sound Waves | 声波
Sound is a longitudinal wave that travels through solids, liquids and gases. It cannot travel through a vacuum. The speed of sound in air is about 340 m/s. You can recall the experiment with a bell in a vacuum jar to demonstrate the need for a medium.
声音是一种纵波，能在固体、液体和气体中传播，但不能在真空中传播。声音在空气中的速度约为 340 m/s。你可以回忆真空罩中的电铃实验来证明传播需要介质。
The pitch of a sound depends on its frequency: higher frequency gives a higher pitch. Loudness depends on the amplitude of the wave: a larger amplitude means a louder sound. Ultrasound is sound with frequencies above 20 000 Hz (the upper limit of human hearing). It is used in medical scanning (e.g., pre-natal scans) and sonar because it can be reflected to form images.
声音的音调取决于其频率：频率越高，音调越高。响度取决于波的振幅：振幅越大，声音越响。超声波是频率超过 20 000 Hz（人类听觉上限）的声音，用于医学扫描（如产前检查）和声呐，因为它能被反射以形成图像。
10. The Electromagnetic Spectrum | 电磁波谱
ectromagnetic spectrum, in order of decreasing wavelength (or increasing frequency), is: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
电磁波是横波，在真空中均以相同的速度传播：c = 3.0 × 10⁸ m/s。按照波长递减（或频率递增）的顺序，电磁波谱依次为：无线电波、微波、红外线、可见光、紫外线、X 射线、伽马射线。
| Wave | Uses | Hazards |
|---|---|---|
| Radio waves | Broadcasting, communications | Very low risk |
| Microwaves | Satellite communication, cooking | Internal heating of body tissue |
| Infrared | Remote controls, thermal imaging | Skin burns |
| Visible light | Vision, photography | Eye damage at high intensity |
| Ultraviolet | Fluorescent lamps, detecting forged bank notes | Skin cancer, eye damage |
| X-rays | Medical imaging, security | Cancer, cell mutation |
| Gamma rays | Sterilising equipment, cancer treatment | Cancer, genetic damage |
The higher the frequency, the more dangerous the radiation: gamma rays and X-rays are ionising and can damage cells.
频率越高，辐射越危险：伽马射线和 X 射线具有电离能力，会损伤细胞。
11. Light – Reflection and Refraction in Detail | 光——反射与折射详述
Light waves follow the laws of reflection and refraction. For reflection, the image in a plane mirror is virtual, upright, laterally inverted and the same size as the object, located as far behind the mirror as the object is in front.
光波遵循反射和折射定律。对于反射，平面镜中的像是虚像、正立、左右颠倒，与物体等大，且位于镜后与物距相等的距离。
For refraction, when light travels from air into glass, it slows down and bends towards the normal. The refractive index (n) is not required for GCSE CCEA, but you should understand the qualitative relationship: the denser the medium, the more the light bends. The critical angle and total internal reflection occur when light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle. This principle is used in optical fibres and periscopes.
对于折射，当光从空气进入玻璃时，速度减慢并向法线偏折。折射率在 GCSE CCEA 中不作要求，但你需要理解定性关系：介质越密，光偏折越显著。当光从光密介质射向光疏介质，且入射角大于临界角时，会发生全内反射。此原理被用于光纤和潜望镜中。
12. Lenses and Image Formation | 透镜与成像
Convex (converging) lenses bring parallel light rays to a focus at the principal focus. They can form real, inverted images when the object is placed beyond the focal point, or magnified, upright virtual images when the object is inside the focal length (as in a magnifying glass). Concave (diverging) lenses cause parallel rays to spread out, and they always form virtual, upright, diminished images.
凸透镜（会聚透镜）将平行光线会聚于主焦点。当物体位于焦点之外时，成倒立实像；当物体在焦距之内时（如放大镜），成正立放大的虚像。凹透镜（发散透镜）使平行光线发散，始终成正立缩小的虚像。
You should be able to draw ray diagrams showing how images are formed by a single convex lens, using at least two of the three standard rays: a ray parallel to the axis that passes through the principal focus, a ray through the centre that continues straight, and a ray through the focus that emerges parallel.
你需要能画出利用单块凸透镜成像的光路图，至少使用三条标准光线中的两条：平行于主轴的光线折射后通过主焦点，通过光心的光线沿直线传播，以及通过焦点的光线折射后平行于主轴。
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