IB Physics: Core Concepts of Wave Behaviour | IB物理：波的行为核心概念讲解

📚 IB Physics: Core Concepts of Wave Behaviour | IB物理：波的行为核心概念讲解

Waves are one of the most elegant and powerful ideas in physics. They transfer energy without transferring matter, and they appear in everything from sound and light to seismic tremors and quantum particles. This guide explains the essential concepts of wave behaviour required for IB Physics.

波是物理学中最优雅且最强大的概念之一。波传递能量但不传递物质，从声音、光到地震波和量子粒子，波无处不在。本指南讲解 IB 物理所要求的波行为核心概念。

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1. What Is a Wave? | 什么是波？

A wave is a disturbance that travels through a medium or space, carrying energy and momentum from one location to another. The particles of the medium may oscillate about a fixed position, but they do not travel with the wave.

波是扰动在介质或空间中的传播，它把能量和动量从一个位置传递到另一个位置。介质中的粒子只围绕固定位置振动，并不随波一起移动。

There are two main types of wave: mechanical waves, which require a medium (for example sound waves in air), and electromagnetic waves, which can travel through a vacuum (for example light).

波主要有两类：机械波需要介质才能传播（例如空气中的声波），电磁波可以在真空中传播（例如光）。

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2. Transverse and Longitudinal Waves | 横波与纵波

In a transverse wave, the displacement of the medium is perpendicular to the direction of energy transfer. Examples include waves on a string, water surface waves, and all electromagnetic waves.

在横波中，介质粒子的位移方向与能量传播方向垂直。例如绳波、水表面波以及所有电磁波。

In a longitudinal wave, the displacement of the medium is parallel to the direction of energy transfer. Sound waves are the most common example, where compressions and rarefactions travel through the air.

在纵波中，介质粒子的位移方向与能量传播方向平行。声波是最常见的例子，它以疏密相间的形式在空气中传播。

v = f × λ

All waves obey the wave equation relating wave speed v, frequency f, and wavelength λ. Frequency is determined by the source, while wave speed depends on the medium.

所有波都满足波速 v、频率 f 和波长 λ 的关系式。频率由波源决定，波速由介质决定。

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3. Amplitude, Period, Frequency and Phase | 振幅、周期、频率与相位

Amplitude A is the maximum displacement from equilibrium. It determines the energy carried by the wave: for mechanical waves, energy is proportional to A².

振幅 A 是偏离平衡位置的最大位移。它决定波携带的能量：对于机械波，能量与 A² 成正比。

Period T is the time for one complete oscillation, and frequency f is the number of oscillations per second. They are related by f = 1/T.

周期 T 是一次完整振动所需的时间，频率 f 是每秒振动的次数。它们满足 f = 1/T。

Phase describes the position of a point on the wave cycle. Two points are in phase if they have the same displacement and velocity direction; they are in antiphase if they are separated by half a wavelength.

相位描述波循环中某个点的位置。如果两个点的位移和速度方向相同，则它们同相；如果相距半个波长，则它们反相。

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4. Superposition Principle | 叠加原理

The principle of superposition states that when two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements.

叠加原理指出：当两个或多个波在同一点相遇时，合位移等于各波单独位移的矢量和。

This principle is fundamental to interference, standing waves, and many other phenomena. It applies to both mechanical and electromagnetic waves, provided the waves are not of extreme intensity.

该原理是干涉、驻波以及其他许多现象的基础。它适用于机械波和电磁波，只要波的强度不过于极端。

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5. Reflection and Refraction | 反射与折射

Reflection occurs when a wave bounces off a boundary. The law of reflection states that the angle of incidence equals the angle of reflection.

反射发生在波遇到边界并被弹回时。反射定律指出：入射角等于反射角。

Refraction occurs when a wave changes direction as it enters a different medium, because its speed changes. When a wave slows down, it bends toward the normal; when it speeds up, it bends away from the normal.

折射发生在波进入不同介质时，由于波速改变而导致传播方向改变。当波减速时，它向法线方向偏折；当波加速时，它远离法线方向偏折。

n₁ sin θ₁ = n₂ sin θ₂

For light, Snell’s law gives the relationship between the angles of incidence and refraction, with n representing the refractive index of each medium.

对于光，斯涅耳定律给出了入射角与折射角之间的关系，其中 n 表示各介质的折射率。

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6. Total Internal Reflection | 全内反射

When light travels from a denser medium to a less dense medium, there is a critical angle. If the angle of incidence exceeds the critical angle, the light is completely reflected back into the denser medium.

当光从光密介质射向光疏介质时，存在一个临界角。如果入射角大于临界角，光将完全被反射回光密介质。

sin θ_c = n₂ / n₁ (for n₁ > n₂)

Total internal reflection is used in optical fibres, where light is trapped inside the fibre and travels long distances with very little loss. This technology is essential for modern internet communication and medical endoscopes.

全内反射应用于光纤中，光被限制在光纤内部，可以以极小的损耗传播很长距离。这项技术对现代互联网通信和医用内窥镜至关重要。

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7. Diffraction | 衍射

Diffraction is the spreading of waves as they pass through an aperture or around an obstacle. The amount of spreading depends on the size of the aperture relative to the wavelength.

衍射是波通过狭缝或绕过障碍物时发生的展宽现象。展宽的程度取决于狭缝尺寸与波长的相对大小。

For a single slit of width a, the first minimum of the diffraction pattern occurs at an angle θ given by:

对于宽度为 a 的单缝，衍射图样的第一级极小值出现在角度 θ，满足：

a sin θ = λ

When the slit is much wider than the wavelength, diffraction is negligible. When the slit is comparable to the wavelength, the wave spreads significantly. This is why sound waves diffract around doorways, but light waves, with much shorter wavelengths, show less obvious diffraction.

当狭缝远大于波长时，衍射可以忽略；当狭缝与波长相近时，波会显著展宽。这就是为什么声波能绕过门洞传播，而波长更短的光波则表现出较不明显的衍射。

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8. Interference | 干涉

Interference is the result of superposition of two coherent waves. Constructive interference occurs when waves arrive in phase and their amplitudes add; destructive interference occurs when waves arrive in antiphase and their amplitudes cancel.

干涉是两列相干波叠加的结果。当两波同相到达时发生相长干涉，振幅相加；当两波反相到达时发生相消干涉，振幅相互抵消。

In Young’s double-slit experiment, bright and dark fringes are formed on a screen. For two slits separated by distance d, the bright fringes satisfy:

在杨氏双缝实验中，屏幕上会形成明暗相间的条纹。对于间距为 d 的双缝，明纹满足：

d sin θ = n λ (n = 0, 1, 2, …)

The fringe spacing s on a screen at distance L is given by s = λL/d. Interference requires the sources to be coherent, meaning they have a constant phase relationship.

在距离 L 处的屏幕上，条纹间距为 s = λL/d。干涉要求波源相干，即它们之间具有恒定的相位关系。

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9. Standing Waves | 驻波

A standing wave is produced when two identical waves travel in opposite directions through the same medium. At certain frequencies, the superposition creates points called nodes, where the displacement is always zero, and antinodes, where the displacement oscillates with maximum amplitude.

当两列完全相同但传播方向相反的波在同一介质中相遇时，会形成驻波。在特定频率下，叠加产生位移始终为零的节点，以及振幅最大的波腹。

For a string fixed at both ends of length L, the allowed wavelengths are λₙ = 2L/n, where n is a positive integer. The corresponding frequencies are fₙ = nv/(2L).

对于两端固定的长度为 L 的弦，允许的波长为 λₙ = 2L/n，其中 n 为正整数。相应频率为 fₙ = nv/(2L)。

Standing waves are the basis of musical instruments: plucked strings, organ pipes, and even the vibrating membranes of drums all rely on standing-wave patterns to produce specific pitches.

驻波是乐器发声的基础：拨动的琴弦、管风琴的管以及鼓的振动膜都依赖驻波模式来产生特定的音调。

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10. The Doppler Effect | 多普勒效应

The Doppler effect is the observed change in frequency of a wave when the source and the observer are moving relative to each other. When the source moves toward the observer, the waves are compressed and the observed frequency increases; when it moves away, the frequency decreases.

多普勒效应是指当波源与观察者之间存在相对运动时，观察到的波频率发生变化的现象。当波源向观察者靠近时，波被压缩，观察到的频率升高；当波源远离时，频率降低。

For sound waves, the observed frequency f’ when the source moves with speed u and the observer is stationary is:

对于声波，当波源以速度 u 运动而观察者静止时，观察到的频率 f’ 为：

f’ = f × v / (v ∓ u)

where v is the speed of sound. The minus sign is used when the source approaches, and the plus sign when it recedes. The Doppler effect also applies to light and is used by astronomers to measure the speeds of stars and galaxies, revealing the expansion of the universe.

其中 v 是声速。波源靠近时用减号，远离时用加号。多普勒效应同样适用于光，天文学家利用它来测量恒星和星系的速度，从而揭示了宇宙的膨胀。

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Mastering these core wave concepts is essential for IB Physics. Understanding how waves travel, superimpose, reflect, refract, diffract, and interfere gives you a powerful toolkit for solving problems in both mechanics and electromagnetism. Practice drawing wave diagrams, identifying phase relationships, and applying the wave equation until these ideas become second nature.

掌握这些波的核心理念对 IB 物理至关重要。理解波如何传播、叠加、反射、折射、衍射和干涉，将为你解决力学与电磁学问题提供强大的工具。请多加练习绘制波形图、判断相位关系以及运用波速公式，直到这些概念成为你的本能。

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