IB Physics: Wave Properties — Wavelength, Frequency, and Wave Speed | IB物理：波的特性——波长、频率与波速

📚 IB Physics: Wave Properties — Wavelength, Frequency, and Wave Speed | IB物理：波的特性——波长、频率与波速

A wave is a mechanism by which energy is transferred from one location to another without any net transfer of matter. In IB Physics, the most fundamental descriptors of a wave are its wavelength, frequency and speed, which are linked by a single elegant relationship. Mastering these definitions and their applications will allow you to solve a wide range of wave problems confidently.

波是一种将能量从一处传递到另一处的机制，过程中没有物质的净迁移。在IB物理中，波最基本的描述量是波长、频率与波速，它们之间由一个简洁的关系式联系在一起。熟练掌握这些定义及其应用，将帮助你自信地解决各类波动问题。

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1. What Is a Wave? | 什么是波？

A wave is a travelling disturbance that carries energy and momentum from one point to another without transporting matter. Waves can be classified as mechanical waves, which require a medium (such as sound in air or waves on a string), and electromagnetic waves, which can travel through a vacuum (such as light).

波是一种传播中的扰动，它将能量和动量从一点传递到另一点，而不运输物质。波可分为机械波和电磁波：机械波需要介质（如空气中的声波、绳上的波），而电磁波可以在真空中传播（如光）。

Every wave is characterised by a set of measurable quantities, the most important being wavelength, frequency, amplitude and speed. In this article, we focus on wavelength, frequency and wave speed, and on the relationship between them.

每种波都由一组可测量的物理量来表征，其中最重要的是波长、频率、振幅和波速。本文将重点讨论波长、频率和波速，以及它们之间的关系。

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2. Wavelength (λ) | 波长（λ）

The wavelength, denoted by the Greek letter λ (lambda), is the distance between two successive points that are in phase. For example, the distance from one crest to the next crest, or from one trough to the next trough, is one wavelength.

波长用希腊字母 λ 表示，是指两个相邻同相点之间的距离。例如，从一个波峰到下一个波峰，或从一个波谷到下一个波谷的距离，就是一个波长。

On a displacement–distance graph, the wavelength is the horizontal distance between identical repeating features of the wave. The SI unit of wavelength is the metre (m), though in optics we often use nanometres (nm, where 1 nm = 1 × 10⁻⁹ m) because visible light wavelengths are extremely small.

在位移—距离图像上，波长是波的两个相同重复特征之间的水平距离。波长的国际单位是米（m），但在光学中我们常用纳米（nm，1 nm = 1 × 10⁻⁹ m），因为可见光的波长非常小。

An important point: wavelength is a property of the wave in a particular medium. When a wave moves from one medium into another, its speed changes and the wavelength changes accordingly, while its frequency remains constant. For instance, when light enters glass from air, it slows down and its wavelength decreases.

一个重要的要点：波长是波在特定介质中的性质。当波从一种介质进入另一种介质时，波速改变，波长也随之改变，但频率保持不变。例如，当光从空气进入玻璃时，速度减慢，波长变短。

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3. Frequency (f) and Period (T) | 频率（f）与周期（T）

The frequency f of a wave is the number of complete oscillations (or cycles) that pass a fixed point in one second. Its SI unit is the hertz (Hz), where 1 Hz = 1 s⁻¹. A wave with a frequency of 50 Hz means 50 complete cycles pass a given point every second.

波的频率 f 是指在单位时间内通过某一固定点的完整振动次数。频率的国际单位是赫兹（Hz），1 Hz = 1 s⁻¹。频率为 50 Hz 的波意味着每秒有 50 个完整周期通过某一点。

The period T is the time required for one complete oscillation to pass a fixed point. Frequency and period are reciprocal quantities:

周期 T 是一个完整振动通过某一点所需要的时间。频率与周期互为倒数：

f = 1 / T 或 T = 1 / f

The frequency of a wave is completely determined by the source that produces it. A tuning fork labelled 440 Hz always generates sound waves with a frequency of 440 Hz, regardless of the medium through which the sound travels. This is a crucial concept in IB exam questions.

波的频率完全由产生它的波源决定。标称为 440 Hz 的音叉，无论声波在何种介质中传播，其频率始终为 440 Hz。这是IB考试中的一个关键概念。

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4. Wave Speed (v) | 波速（v）

The wave speed v is the distance travelled by a wavefront (e.g., the crest of a wave) per unit time, measured in metres per second (m s⁻¹). It tells us how quickly the disturbance propagates through the medium.

波速 v 是波前（例如波峰）在单位时间内传播的距离，单位是米每秒（m s⁻¹）。它描述了扰动在介质中传播的快慢。

Unlike frequency, the wave speed is determined by the medium, not by the source. For a string, the speed depends on the tension and the linear density; for sound in air, it depends on temperature and pressure. For all electromagnetic waves in a vacuum, the speed is the constant c = 3.00 × 10⁸ m s⁻¹.

与频率不同，波速由介质决定，而非由波源决定。对于弦上的波，速度取决于张力和线密度；对于空气中的声波，速度取决于温度和压强。对于所有电磁波，在真空中的速度均为常数 c = 3.00 × 10⁸ m s⁻¹。

It is essential to distinguish wave speed from the vibration speed of the particles in the medium. In a transverse wave on a string, the string particles oscillate up and down about their equilibrium positions, but the wave itself travels horizontally. The two speeds are completely different quantities.

必须区分波速与介质中质点的振动速度。在绳上的横波中，绳的质点围绕平衡位置上下振动，但波本身沿水平方向传播。这两个速度是完全不同的物理量。

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5. The Wave Equation v = fλ | 波动方程 v = fλ

Wavelength, frequency and wave speed are related by the wave equation. During one time period T, the wavefront advances forward by exactly one wavelength λ. Since the wave travels a distance of one wavelength in one period, the wave speed is:

波长、频率和波速由波动方程联系起来。在一个周期 T 内，波前正好前进一个波长 λ。由于波在一个周期内传播的距离为一个波长，因此波速为：

v = λ / T

Since f = 1 / T, we can rewrite this as the standard form:

由于 f = 1 / T，可将其改写为标准形式：

v = f λ

This equation applies to every type of wave — sound waves, water waves, waves on strings, and electromagnetic waves. If any two of the three quantities are known, the third can be found directly. For example, radio waves in vacuum with frequency 100 MHz (1.00 × 10⁸ Hz) have a wavelength of λ = c / f = 3.00 × 10⁸ / 1.00 × 10⁸ = 3.00 m.

这个方程适用于所有类型的波——声波、水波、弦波和电磁波。只要已知其中任意两个量，就可以直接求出第三个量。例如，频率为 100 MHz（1.00 × 10⁸ Hz）的无线电波在真空中的波长为 λ = c / f = 3.00 × 10⁸ / 1.00 × 10⁸ = 3.00 m。

For a fixed medium where v is constant, frequency and wavelength are inversely proportional: doubling the frequency halves the wavelength. This explains why blue light (shorter wavelength) has a higher frequency than red light in the same medium.

对于波速恒定的固定介质，频率与波长成反比：频率加倍则波长减半。这也解释了为什么在相同介质中蓝光（波长较短）的频率高于红光。

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6. Transverse vs Longitudinal Waves | 横波与纵波

Waves can be classified by the direction of particle oscillation relative to the direction of wave propagation. In a transverse wave, the particles oscillate perpendicular to the direction of propagation, while in a longitudinal wave, they oscillate parallel to it.

波可根据质点振动方向与波的传播方向的关系来分类。在横波中，质点振动方向垂直于传播方向；在纵波中，质点振动方向平行于传播方向。

Property	Transverse wave | 横波	Longitudinal wave | 纵波
Oscillation direction 振动方向	Perpendicular to propagation 垂直于传播方向	Parallel to propagation 平行于传播方向
Wave features 波的特征	Crests and troughs 波峰与波谷	Compressions and rarefactions 疏部与密部
Examples 典型例子	Electromagnetic waves, waves on a string 电磁波、弦波	Sound waves in air, seismic P-waves 空气中的声波、地震P波

In a longitudinal wave, the wavelength is measured as the distance between two successive compressions (or two successive rarefactions). The speed of a longitudinal wave depends on the elastic and inertial properties of the medium, just as the speed of a transverse wave on a string depends on tension and mass per unit length.

在纵波中，

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