📚 IGCSE CIE Science: Waves – Key Points Review | IGCSE CIE 科学：波 考点精讲
Waves are a fundamental topic in the IGCSE CIE Science syllabus, appearing in both the Physics and Co-ordinated Sciences papers. Understanding wave behaviour, from basic properties to light and sound, is essential for exam success. This article breaks down every key point you need to know.
波是 IGCSE CIE 科学课程大纲中的基础主题，同时出现在物理和协调科学试卷中。理解波的行为，从基本特性到光和声，对考试成功至关重要。本文分解了你需要知道的每一个关键点。
1. Types of Waves | 波的种类
Waves can be classified into two main types: transverse and longitudinal. In transverse waves, vibrations are perpendicular to the direction of energy transfer. Examples include light waves and water waves. Transverse waves have crests (peaks) and troughs.
波可以分为两种主要类型：横波和纵波。在横波中，振动方向与能量传递方向垂直。例子包括光波和水波。横波有波峰和波谷。
In longitudinal waves, vibrations are parallel to the direction of energy transfer, such as sound waves. These waves consist of compressions (regions of high pressure) and rarefactions (regions of low pressure).
在纵波中，振动方向与能量传递方向平行，例如声波。这类波由压缩区（高压区）和稀疏区（低压区）组成。
2. Describing Waves | 描述波的关键术语
ts or compressions. Frequency (f) is the number of complete waves passing a point per second, measured in hertz (Hz). The period (T) is the time for one complete wave, and T = 1/f.
你必须知道的关键术语：振幅是偏离平衡位置的最大位移。波长（λ）是两个相邻波峰或压缩区之间的距离。频率（f）是每秒通过某点的完整波的数量，单位为赫兹（Hz）。周期（T）是一个完整波所需的时间，且 T = 1/f。
Wave speed is the distance a wave travels per unit time. When reading a waveform displayed on an oscilloscope, the horizontal axis represents time and the vertical axis represents displacement.
波速是波每秒传播的距离。当读取示波器上显示的波形时，横轴代表时间，纵轴代表位移。
3. The Wave Equation | 波动方程
v = f × λ
hip applies to all waves. You must be able to rearrange it to find f = v ÷ λ or λ = v ÷ f.
通用波动方程指出波速（v）等于频率（f）与波长（λ）的乘积。此关系适用于所有波。你必须能够进行公式变形，得出 f = v ÷ λ 或 λ = v ÷ f。
wave has a frequency of 50 Hz and a wavelength of 0.4 m. The speed v = 50 × 0.4 = 20 m/s.
计算示例：一列波的频率为 50 Hz，波长为 0.4 m，则波速 v = 50 × 0.4 = 20 m/s。
4. Reflection of Waves | 波的反射
All waves can be reflected. The law of reflection states that the angle of incidence (i) equals the angle of reflection (r). Both angles are measured from the imaginary line called the normal. This law holds for light, sound, and water waves.
所有波都能发生反射。反射定律指出，入射角（i）等于反射角（r）。两个角均从名为法线的假想线量起。该定律适用于光波、声波和水波。
In a ripple tank, a straight barrier reflects plane waves, creating clear incident and reflected wavefronts. The reflected waves appear to originate from a point behind the barrier.
在波纹水箱中，直线障碍物反射平面波，产生清晰的入射波前和反射波前。反射波看起来像是从障碍物后方某点发出的。
5. Refraction of Waves | 波的折射
Refraction occurs when a wave passes from one medium to another and changes speed. This causes a change in direction unless the wave enters along the normal. Crucially, the frequency of the wave never changes during refraction; only the wavelength and speed alter.
折射发生在波从一种介质进入另一种介质并改变速度时。除非沿法线入射，否则传播方向会改变。关键的是，折射时波的频率从不改变，只有波长和速度发生变化。
For light waves, when moving from a less dense medium (air) to a denser medium (glass), the ray bends towards the normal as it slows down. The refractive index n is given by:
对于光波，当从光疏介质（空气）进入光密介质（玻璃）时，由于速度减慢，光线向法线偏折。折射率 n 由下式给出：
n = sin i ÷ sin r
Water waves entering shallower regions slow down, causing a reduction in wavelength and a change in direction towards the normal of the boundary.
水波进入较浅区域时速度减慢，导致波长减小，传播方向向边界法线偏折。
6. 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 extent of diffraction depends on the size of the gap relative to the wavelength. When the gap width is approximately equal to or smaller than the wavelength, maximum diffraction occurs.
衍射是波通过缝隙或绕过障碍物时发生的扩散现象。衍射的程度取决于缝隙尺寸与波长的关系。当缝隙宽度约等于或小于波长时，衍射现象最明显。
This explains why long radio waves (large λ) diffract around hills and buildings more effectively than microwaves (small λ). Ripple tank experiments show that circular waves spread out uniformly after a narrow gap.
这就解释了为何长波无线电波（波长较大）比微波（波长较小）更容易绕山或建筑物传播。波纹水箱实验显示，经过窄缝后，圆形波均匀地扩散开来。
7. Electromagnetic Spectrum | 电磁波谱
ffer in frequency and wavelength. In order of decreasing wavelength (increasing frequency), the spectrum is: Radio, Microwaves, Infrared, Visible Light, Ultraviolet, X-rays, Gamma rays.
电磁波谱是一系列连续的横波，它们在真空中的传播速度均为 c = 3.0 × 10⁸ m/s。各成员的区别在于频率和波长。按波长递减（频率递增）的顺序，光谱依次为：无线电波、微波、红外线、可见光、紫外线、X 射线、伽马射线。
Energy increases with frequency, so gamma rays have the highest energy and are the most penetrating. Visible light is just a small part that we can detect with our eyes.
能量随频率增大而增大，因此伽马射线能量最高、穿透力最强。可见光只是我们可以用眼睛探测到的一小部分。
Uses to remember: Radio – broadcasting and communications; Microwaves – cooking and satellite transmissions; Infrared – heaters and thermal imaging; Visible light – sight; Ultraviolet – sunbeds and sterilisation; X-rays – medical imaging and security; Gamma rays – cancer treatment and sterilising equipment.
需记忆的用途：无线电波——广播与通信；微波——烹饪和卫星传输；红外线——加热器和热成像；可见光——视觉；紫外线——日光浴和消毒；X 射线——医学成像与安检；伽马射线——癌症治疗和器材灭菌。
8. Sound Waves | 声波
Sound waves are longitudinal mechanical waves. They need a medium (solid, liquid or gas) to travel and cannot propagate through a vacuum. The approximate speed of sound in air is 330–340 m/s.
声波是纵波，属于机械波。它们需要介质（固体、液体或气体）才能传播，不能在真空中传播。声音在空气中的速度约为 330–340 m/s。
On an oscilloscope, a sound is displayed as a waveform. Pitch depends on frequency: a higher frequency produces a higher-pitched sound. Loudness depends on amplitude: a larger amplitude gives a louder sound.
在示波器上，声音显示为波形。音调取决于频率：频率越高，音调越高。响度取决于振幅：振幅越大，声音越响。
Echoes are caused by the reflection of sound. Ultrasound refers to sound with a frequency above 20,000 Hz, which has medical applications such as foetal scanning and industrial uses like sonar.
回声由声音的反射引起。超声波指频率高于 20,000 Hz 的声音，在医学上用于胎儿扫描，在工业上用于声纳等。
9. Light Waves – Reflection and Refraction | 光波 – 反射与折射
Light travels in straight lines in a uniform medium. The law of reflection for a plane mirror produces an image that is virtual, upright, laterally inverted, and the same size as the object. The image distance behind the mirror equals the object distance in front.
光在均匀介质中沿直线传播。平面镜的反射定律所成的像为虚像、正立、左右颠倒、与物体等大，且像在镜后的距离等于物在镜前的距离。
When light enters a denser medium at an angle, it slows down and bends towards the normal. When it exits back into a less dense medium, it speeds up and bends away from the normal. The frequency of light remains unchanged throughout.
当光以一定角度进入光密介质时，速度减慢并向法线偏折。当光重新进入光疏介质时，速度加快并偏离法线。在整个过程中，光的频率保持不变。
Dispersion of white light occurs in a prism because different colours travel at slightly different speeds in glass. Violet light is refracted the most, red light the least, producing a continuous spectrum.
白光在棱镜中发生色散，这是因为不同颜色的光在玻璃中的传播速度略有不同。紫光偏折最多，红光偏折最少，从而产生连续光谱。
10. Total Internal Reflection | 全内反射
Total internal reflection (TIR) can occur when light travels from a denser medium to a less dense medium, such as from glass to air. If the angle of incidence is greater than the critical angle (c) for the two media, all the light is reflected back into the denser medium; no refraction occurs.
当光从光密介质射向光疏介质（例如从玻璃到空气）时，可能发生全内反射（TIR）。若入射角大于两种介质间的临界角（c），则所有光线反射回光密介质，不会发生折射。
n = 1 ÷ sin c
For glass-air boundary, the critical angle is about 42°. TIR is used in optical fibres for high-speed data transmission and in medical endoscopes for internal examination, as well as in reflecting prisms in periscopes.
对于玻璃-空气界面，临界角约为 42°。全内反射用于光纤的高速数据传输、医用内窥镜进行体内检查，以及潜望镜中的反射棱镜。
11. Wave Phenomena in Ripple Tanks | 波纹水箱中的波现象
A ripple tank is an excellent tool for visualising wave behaviour. A straight dipper generates plane waves, while a point dipper produces circular waves. By placing barriers and differently shaped blocks, you can investigate reflection, refraction, and diffraction of water waves.
波纹水箱是观察波的行为的绝佳工具。直线振动源产生平面波，点振动源产生圆形波。通过放置障碍物和不同形状的块，可以探究水波的反射、折射和衍射。
When plane waves enter shallower water (slow speed), the wavelength shortens and the wavefronts bend towards the boundary normal. After passing through a narrow opening, waves become more curved, demonstrating diffraction clearly.
当平面波进入浅水区（速度较慢）时，波长变短，波前向边界法线偏折。在通过狭窄的开口后，波变得更弯曲，清晰地展示了衍射现象。
12. Exam Tips and Common Mistakes | 考试技巧与常见错误
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