📚 IB Physics: Core Concepts of Waves and Wave Graph Analysis | IB物理：波动核心概念与波的图像分析
Waves are everywhere in physics, from sound and light to quantum matter waves. Understanding the core concepts of waves and the ability to interpret wave graphs are essential skills for IB Physics students.
波在物理学中无处不在，从声音、光到量子物质波。理解波动的核心概念以及解读波的图像，是 IB 物理学生必备的关键技能。
1. What is a Wave? | 什么是波？
A wave is a disturbance that travels through a medium or space, transporting energy and momentum from one point to another without any bulk movement of the medium itself.
波是一种在介质或空间中传播的扰动，它将能量和动量从一点传递到另一点，而介质本身并没有发生整体的平移。
For example, if you drop a stone into a still pond, circular ripples spread outward. The water molecules mainly move up and down; the wave itself travels horizontally.
例如，当你向平静的池塘中投下一块石头，圆形涟漪会向外扩散。水分子主要做上下振动，而波本身则沿水平方向传播。
A wavefront is an imaginary line connecting points that are in the same phase; a ray is a line perpendicular to the wavefront and points in the direction of propagation.
波前是连接同相各点的假想线；射线是与波前垂直且指向传播方向的线。
2. Transverse and Longitudinal Waves | 横波与纵波
Waves are classified by the direction of particle oscillation relative to the direction of wave propagation.
波按照质点振动方向与波传播方向的关系进行分类。
- Transverse wave: particles oscillate perpendicular to the direction of travel. Examples include waves on a string, electromagnetic waves, and water surface waves.
- 横波：质点振动方向与传播方向垂直。例如绳波、电磁波和水面波。
- Longitudinal wave: particles oscillate parallel to the direction of travel. Examples include sound waves and seismic P-waves.
- 纵波：质点振动方向与传播方向平行。例如声波和地震 P 波。
In a longitudinal wave, regions of compression and rarefaction travel along the medium.
在纵波中，一系列疏密相间的区域（压缩区与稀疏区）沿介质传播。
3. Key Quantities: Amplitude, Wavelength, Period, Frequency | 关键物理量：振幅、波长、周期、频率
To describe a wave fully we need several quantities that characterise both its size and its rhythm.
为了完整地描述一个波，我们需要几个既能刻画其大小又能刻画其节奏的物理量。
- Amplitude (A): the maximum displacement of a particle from its equilibrium position. It is related to the energy carried by the wave.
- 振幅 (A)：质点偏离平衡位置的最大位移。它与波携带的能量有关。
- Wavelength (λ): the distance between two consecutive points in the same phase, e.g. crest to crest or trough to trough.
- 波长 (λ)：两个相邻同相点之间的距离，例如波峰到波峰或波谷到波谷。
- Period (T): the time required for one complete oscillation of a particle, or for the wave to advance by one wavelength.
- 周期 (T)：质点完成一次全振动所需的时间，或波前进一个波长所需的时间。
- Frequency (f): the number of complete oscillations per unit time; f = 1/T, with unit hertz (Hz).
- 频率 (f)：单位时间内完成全振动的次数；f = 1/T，单位是赫兹 (Hz)。
f = 1/T
The frequency of a wave is determined by the source and does not change when the wave enters a different medium.
波的频率由波源决定，当波进入不同介质时频率不会改变。
4. The Wave Equation: v = fλ | 波速公式：v = fλ
Imagine following a fixed point on the wave, such as a wave crest. In one period T, the crest travels exactly one wavelength λ.
设想跟踪波上的某个固定点，例如一个波峰。在一个周期 T 内，该波峰恰好前进一个波长 λ。
Therefore the wave speed is:
因此波速为：
v = λ/T = fλ
Since f = 1/T, we also write v = fλ.
因为 f = 1/T，所以也可写作 v = fλ。
Hz in air at 20 °C has a speed of about 343 m s⁻¹, so its wavelength is λ = v/f ≈ 0.78 m.
例如，在 20 °C 空气中，频率为 440 Hz 的声波速度约为 343 m s⁻¹，因此其波长 λ = v/f ≈ 0.78 m。
Important: v depends on the medium, while f is fixed by the source. When a wave crosses into a medium with a different speed, λ changes accordingly.
重要：波速取决于介质，而频率由波源决定。当波进入波速不同的介质时，波长会相应地改变。
5. Two Essential Wave Graphs: y–x and y–t | 两种关键波形图：y–x 图与 y–t 图
IB Physics often tests your ability to switch between two types of wave graph.
IB 物理经常考查你在两类波形图之间进行切换的能力。
Displacement–position graph (y–x graph): a "snapshot" of the wave at one instant. The horizontal axis is distance along the wave, and the vertical axis is the displacement of particles from equilibrium.
位移–位置图（y–x 图）：波在某一个时刻的“快照”。横轴表示沿波传播方向的距离，纵轴表示质点相对平衡位置的位移。
Displacement–time graph (y–t graph): shows how a single particle (or a single point of the medium) moves over time. The horizontal axis is time, and the vertical axis is displacement.
位移–时间图（y–t 图）：显示介质中一个质点（或一个固定点）在时间上的振动情况。横轴是时间，纵轴是位移。
Many students confuse these two graphs. The key is to remember: the x-axis tells you what is fixed.
许多学生容易混淆这两张图。关键在于记住：横轴告诉你“什么量是固定的”。
6. How to Extract Information from the Graphs | 如何从图像中提取信息
From a y–x graph you can directly read the amplitude A and the wavelength λ. The period T cannot be read unless the wave speed v is given.
从 y–x 图中可以直接读出振幅 A 和波长 λ。除非给出了波速 v，否则无法直接读出周期 T。
From a y–t graph you can directly read the amplitude A and the period T. The wavelength λ cannot be read unless the wave speed v is known.
从 y–t 图中可以直接读出振幅 A 和周期 T。除非已知波速 v，否则无法直接读出波长 λ。
To relate the two graphs, use:
要关联这两张图，需要用到：
v = λ/T
| Quantity | From y–x graph | From y–t graph |
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