Properties of Waves | 波的特性

📚 Properties of Waves | 波的特性

Waves are fundamental to physics, governing everything from the sound we hear to the light we see. In the IGCSE Edexcel syllabus, understanding the properties of waves is essential for mastering topics such as reflection, refraction, diffraction, and the electromagnetic spectrum. This article provides a comprehensive, exam-focused guide to the key ideas you must know.

波是物理学的基石，从我们听到的声音到看见的光，无一不受波的支配。在 Edexcel IGCSE 课程大纲中，理解波的特性是掌握反射、折射、衍射以及电磁波谱等专题的关键。本文将提供一份系统、紧扣考点的学习指南。

1. What Are Waves? | 什么是波？

A wave is a disturbance that transfers energy from one point to another without transferring matter. When a wave travels through a medium, the particles of the medium oscillate about their fixed positions; they do not travel along with the wave. For example, when you drop a stone into a pond, circular ripples spread outward, yet the water itself does not travel across the pond — only the energy does.

波是一种将能量从一处传递到另一处的扰动，但不会传递物质。当波在介质中传播时，介质的粒子仅在固定位置附近振动，并不会随波前进。例如，向池塘投入石子后，圆形涟漪向外扩散，但水本身并不会横穿池塘移动——只有能量在传播。

All waves are produced by something that vibrates, such as a loudspeaker cone, a vibrating guitar string, or an oscillating electric charge. The vibration creates a disturbance that propagates outward through the surrounding medium or, in the case of electromagnetic waves, through empty space.

所有波都由某种振动物体产生，例如扬声器振膜、振动的吉他弦或振荡的电荷。振动产生扰动，并通过周围介质向外传播；对于电磁波而言，则可以在真空中传播。

2. Transverse and Longitudinal Waves | 横波与纵波

Waves are classified into two types according to the direction of particle oscillation relative to the direction of energy propagation. In a transverse wave, the particles oscillate perpendicularly to the direction of wave travel. Transverse waves display crests and troughs. Common examples are light waves, water ripples, and waves on a stretched string.

波根据粒子振动方向与传播方向的关系分为两类。在横波中，粒子垂直于波的传播方向振动，具有波峰和波谷。常见例子包括光波、水面波和绳波。

In a longitudinal wave, the particles oscillate parallel to the direction of wave travel. This creates alternating compressions (regions where particles are squeezed together) and rarefactions (regions where particles are spread apart). Sound waves in air are the most familiar example of longitudinal waves.

在纵波中，粒子平行于波的传播方向振动，形成交替的密部（粒子被挤压的区域）和疏部（粒子被拉开的区域）。空气中的声波是最常见的纵波例子。

Feature	Transverse Wave	Longitudinal Wave
Particle direction	Perpendicular to wave direction	Parallel to wave direction
Shape	Crests and troughs	Compressions and rarefactions
Examples	Light, water waves, S-waves	Sound waves, P-waves

You should be able to identify and sketch both types of waves, and describe one example of each. The ability to label a transverse wave diagram with amplitude, wavelength, crest, and trough is a common exam requirement.

你应该能识别并绘制这两种波，并分别举出一个例子。考试中常要求标注横波示意图中的振幅、波长、波峰和波谷。

3. Key Quantities of a Wave | 波的关键物理量

There are five essential quantities used to describe a wave, and you must know their definitions, symbols, and units.

描述波有五个关键物理量，你需要牢记它们的定义、符号和单位。

Amplitude (A) — the maximum displacement of a particle from its equilibrium position, measured in metres (m). Larger amplitude means more energy carried by the wave.

振幅 (A) — 粒子偏离平衡位置的最大位移，单位为米 (m)。振幅越大，波携带的能量越多。
Wavelength (λ) — the distance between two corresponding points on adjacent waves, such as crest to crest, measured in metres (m).

波长 (λ) — 相邻两个对应点（如波峰到波峰）之间的距离，单位为米 (m)。
Frequency (f) — the number of complete waves passing a fixed point per second, measured in hertz (Hz). 1 Hz = 1 wave per second.

频率 (f) — 每秒通过某固定点的完整波数，单位为赫兹 (Hz)。1 Hz = 每秒一个波。
Period (T) — the time taken for one complete wave to pass a point, measured in seconds (s). The period is related to frequency by T = 1 ÷ f.

周期 (T) — 一个完整波通过某点所需时间，单位为秒 (s)。周期与频率的关系为 T = 1 ÷ f。
Wave speed (v) — the distance a wave travels per unit time, measured in metres per second (m/s).

波速 (v) — 波在单位时间内传播的距离，单位为米每秒 (m/s)。

In an exam, you may be asked to read these values directly from a diagram. For example, the wavelength can be measured from crest to crest, and the amplitude from the equilibrium line to a crest.

考试中，你可能需要直接从图中读取这些数值。例如，波长可由波峰到波峰测量，振幅由平衡线到波峰测量。

4. The Wave Equation | 波动方程

The wave speed, frequency, and wavelength of a wave are related by the wave equation. This is one of the most important equations in the IGCSE course.

波速、频率和波长之间的关系由波动方程给出。这是 IGCSE 课程中最重要的公式之一。

v = f × λ

where v is the wave speed in m/s, f is the frequency in Hz, and λ is the wavelength in m.

其中 v 为波速（m/s），f 为频率（Hz），λ 为波长（m）。

This equation applies to all types of waves — mechanical and electromagnetic. For a given type of wave, if the frequency increases, the wavelength must decrease when the speed is constant.

该方程适用于所有类型的波——无论是机械波还是电磁波。对于特定波种，若速度不变，频率增大时波长必然减小。

Worked example: A sound wave in air has a frequency of 500 Hz and a wavelength of 0.68 m. Calculate the wave speed.

例题：空气中的声波频率为 500 Hz，波长为 0.68 m。计算波速。

v = f × λ = 500 × 0.68 = 340 m/s

Another common question involves rearranging the equation. For instance, λ = v ÷ f, or f = v ÷ λ. Always remember to check your units before substituting values.

另一类常见题目是公式变形，例如 λ = v ÷ f 或 f = v ÷ λ。代入数值前务必检查单位是否一致。

5. Reflection of Waves | 波的反射

Reflection occurs when a wave strikes a boundary between two media and bounces back into the original medium. The law of reflection states that the angle of incidence equals the angle of reflection, both measured from the normal — an imaginary line drawn perpendicular to the surface at the point of incidence.

反射发生在波遇到两种介质的边界时，波返回原介质中。反射定律指出：入射角等于反射角，两者均以法线——即入射点处垂直于界面的假想线——为基准来测量。

angle of incidence = angle of reflection

入射角 = 反射角

For plane waves reflecting off a straight surface, the wavefronts remain straight and parallel. When drawing ray diagrams, you should use solid lines for rays and dashed lines for normal lines, with arrows to show the direction of travel.

平面波在直线界面上反射时，波前保持平直且平行。绘制光路图时，用实线表示光线，虚线表示法线，并用箭头标出传播方向。

Reflection of light is used in mirrors, periscopes, and optical instruments. Reflection of sound causes echoes, which are used by bats for navigation and by sonar systems for underwater detection.

光的反射应用于镜子、潜望镜和光学仪器中。声的反射产生回声，蝙蝠利用回声导航，声呐系统利用回声进行水下探测。

6. Refraction of Waves | 波的折射

Refraction is the change in direction of a wave as it passes from one medium into another, caused by a change in wave speed. When a wave enters a denser medium at an angle, it slows down and bends towards the normal. When it enters a less dense medium, it speeds up and bends away from the normal.

折射是波从一种介质进入另一种介质时传播方向发生改变的现象，根源在于波速发生变化。当波以一定角度进入更密介质时，速度减慢，向法线方向偏折；进入较疏介质时，速度加快，向远离法线方向偏折。

It is important to distinguish refraction from reflection. In refraction, the wave actually passes into the new medium, whereas in reflection it stays in the original medium. A familiar example is a spoon appearing bent when placed in a glass of water.

务必区分折射与反射。折射中波确实进入了新介质，而反射中波仍停留在原介质中。一个常见例子是放入水杯中的勺子看起来像是折断了一样。

When a wave meets the boundary along the normal (at 90° to the surface), no bending occurs — the wave continues straight through, though its speed still changes. This fact is often tested in multiple-choice questions.

当波沿法线方向（与界面成 90°）射向边界时，不发生偏折——波仍然直线通过，但速度依然改变。这一点常出现在选择题中。

Refraction explains why a swimming pool appears shallower than it actually is, and why the Sun is visible briefly after it has set below the horizon due to atmospheric refraction.

折射解释了游泳池看起来比实际浅的原因，也解释了太阳落山后我们仍能短暂看到它的现象——这是由于大气折射所致。

7. Diffraction of Waves | 波的衍射

Diffraction is the spreading out of waves as they pass through a gap or around an obstacle. The amount of diffraction depends on the size of the gap or obstacle relative to the wavelength of the wave.

衍射是波通过狭缝或绕过障碍物时发生的展宽现象。衍射的程度取决于狭缝或障碍物的尺寸与波长的相对关系。

For significant diffraction to occur, the gap width should be approximately equal to the wavelength. If the gap is much larger than the wavelength, only slight spreading occurs at the edges. If the gap is smaller than the wavelength, the waves spread out almost circularly from the gap.

要发生明显的衍射，狭缝宽度应大致等于波长。若狭缝远大于波长，波仅在其边缘发生轻微展宽；若狭缝小于波长，波从狭缝处几乎呈圆形向外扩散。

Diffraction is more noticeable for sound waves than for light waves in everyday life because sound has a relatively long wavelength (around 0.3 m to 3 m), whereas light has an extremely short wavelength (about 5 × 10⁻⁷ m). You can hear around a corner, but you cannot see around it.

在日常生活中，声波的衍射比光波更明显，因为声波波长较长（约 0.3 m 至 3 m），而光波波长极短（约 5 × 10⁻⁷ m）。你能听见拐角处的声响，却无法看见拐角后的景象。

In the lab, diffraction of water waves can be observed using a ripple tank. When plane waves pass through two narrow gaps, circular waves spread out from each gap; where they overlap, interference patterns may form.

在实验室中，可用波动槽观察水波的衍射。当平面波通过两个窄缝时，每个窄缝处都有圆形波向外扩散；两列波重叠的区域可能形成干涉图样。

8. Sound Waves | 声波

Sound waves are longitudinal waves that require a medium to travel through; they cannot travel through a vacuum. Sound is produced when an object vibrates, causing adjacent air particles to oscillate and pass the disturbance along.

声波是纵波，需要介质才能传播；在真空中无法传播。物体振动时，带动周围空气粒子振动并传递扰动，从而产生声音。

The speed of sound depends on the medium. In air at room temperature, sound travels at approximately 340 m/s. Sound travels faster in liquids and even faster in solids because the particles are closer together and more strongly bonded, allowing vibrations to transfer more quickly.

声速取决于介质。在室温空气中，声速约为 340 m/s。声在水中传播得更快，在固体中更快，因为粒子间距更小、结合更紧密，振动传递更迅速。

Two key properties of sound waves are pitch and loudness. Pitch is determined by frequency — higher frequency gives higher pitch. Loudness is determined by amplitude — larger amplitude gives louder sound.

音调与响度是声波的两个重要属性。音调由频率决定——频率越高，音调越高；响度由振幅决定——振幅越大，声音越响。

Sound waves can be reflected (echoes), refracted (especially in air of varying temperature), and diffracted. The human ear can typically detect frequencies from about 20 Hz to 20,000 Hz; sounds above this range are called ultrasound.

声波可以反射（产生回声）、折射（尤其在温度不均匀的空气中）和衍射。人耳通常能听到约 20 Hz 至 20,000 Hz 的频率范围；超出此范围的声音称为超声波。

9. The Electromagnetic Spectrum | 电磁波谱

Electromagnetic waves are transverse waves that transfer energy through empty space. They do not require a medium to travel. In a vacuum, all electromagnetic waves travel at the same speed — exactly 3.0 × 10⁸ m/s (the speed of light).

电磁波是横波，能在真空中传递能量，无需介质。在真空中，所有电磁波以相同速度传播——精确值为 3.0 × 10⁸ m/s（光速）。

The electromagnetic spectrum is the continuous range of electromagnetic waves arranged by increasing frequency and decreasing wavelength. The seven main types, from lowest frequency to highest frequency, are:

电磁波谱是按频率递增、波长递减排列的连续电磁波范围。从最低频率到最高频率，七种主要类型依次为：

Type	Approximate Wavelength	Typical Use
Radio waves	> 0.1 m	Broadcasting and communication
Microwaves	~10⁻³ m	Cooking, mobile phones, radar
Infrared	~10⁻⁵ m	Remote controls, thermal imaging
Visible light	~10⁻⁶ m	Human vision
Ultraviolet	~10⁻⁸ m	Sterilisation, fluorescent lamps
X-rays	~10⁻¹⁰ m	Medical imaging, airport security
Gamma rays	< 10⁻¹² m	Cancer treatment, sterilising equipment

In exam questions, you may be asked to identify a type of electromagnetic wave from its use, or to arrange them in order of frequency or wavelength. Memorise the order: Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma — using the mnemonic “Rabbits Mate In Very Unusual eXpensive Gardens”.

考试中可能要求你根据用途判断电磁波类型，或按频率、波长排序。记住这个顺序：无线电波、微波、红外线、可见光、紫外线、X 射线、伽马射线——可用助记词 “Rabbits Mate In Very Unusual eXpensive Gardens”。

10. Applications and Exam Tips | 应用与考试要点

The properties of waves have numerous practical applications. Ultrasound is used in sonar to measure ocean depth, in prenatal scanning to create images of a fetus, and in breaking kidney stones. The principle is simple: a pulse is emitted, the time for the reflected echo is measured, and the distance is calculated from speed = distance ÷ time.

波的性质有着广泛的实际应用。超声波用于声呐测量海洋深度、产前扫描成像以及击碎肾结石。其原理很简单：发射脉冲，测量反射回波所需时间，再由速度 = 距离 ÷ 时间计算距离。

The equation above is worth remembering. For example, if a sonar pulse returns after 4 seconds and the speed of sound in water is 1500 m/s, the total journey is 1500 × 4 = 6000 m, so the depth is half of that: 3000 m.

上述公式值得牢记。例如，若声呐脉冲 4 秒后返回，水中声速为 1500 m/s，则总路程为 1500 × 4 = 6000 m，因此水深为其一半：3000 m。

When answering exam questions on waves, follow these tips. First, always quote the correct units. Second, use the wave equation with the correct rearrangement. Third, sketch wave diagrams clearly, labelling the normal when discussing reflection or refraction. Fourth, when comparing waves, state both a similarity and a difference explicitly. Finally, for electromagnetic waves, state that they all travel at the same speed in a vacuum.

作答波的考题时，请记住以下几点。第一，始终带上正确单位。第二，使用波动方程时注意正确变形。第三，绘制波图时保持清晰，讨论反射或折射时务必标出法线。第四，比较不同波时，同时明确写出一个相同点和一个不同点。最后，对于电磁波，要说明它们在真空中传播速度相同。

Mastering the properties of waves will give you a strong foundation across multiple IGCSE topics, including energy transfer, sound, light, and the electromagnetic spectrum. Regular practice with past paper questions is the most effective way to consolidate these concepts.

掌握波的特性将为你在 IGCSE 多個专题中打下坚实基础，包括能量传递、声音、光学和电磁波谱。定期练习历年真题是巩固这些概念最有效的方法。

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Properties of Waves | 波的特性