📚 Longitudinal and Transverse Waves | 纵波与横波
Waves transfer energy from one place to another without transferring matter. In A-Level Physics, one of the most important distinctions is between transverse and longitudinal waves, because it affects how a wave can be represented, how it interacts with materials, and whether it can be polarised.
波将能量从一处传递到另一处，而不传递物质。在 A-Level 物理中，最重要的区别之一是横波与纵波的区别，因为它会影响波的表示方式、与物质的相互作用以及是否能被偏振。
1. Wave Basics | 波的基本概念
A progressive wave is a moving disturbance that carries energy away from a source. The particles of the medium oscillate about fixed equilibrium positions, but they do not travel with the wave; only the energy and wave shape move forward.
行波是一种从波源向外传播能量的运动扰动。介质中的粒子围绕固定平衡位置振动，并不随波前进；只有能量和波形向前传播。
Two main types of progressive wave are defined by the direction of particle oscillation relative to the direction of energy travel.
行波根据粒子振动方向与能量传播方向的关系，分为两种主要类型。
2. Transverse Waves | 横波
In a transverse wave, the particles oscillate perpendicular to the direction of energy transfer. Examples include waves on a stretched string, water ripples, and all electromagnetic waves such as visible light, radio waves, and X-rays.
在横波中，粒子振动方向与能量传递方向垂直。例如拉紧的绳子上的波、水波涟漪以及所有电磁波，如可见光、无线电波和 X 射线。
A transverse wave can be drawn as a series of crests and troughs. The crest is the point of maximum positive displacement, and the trough is the point of maximum negative displacement.
横波可以画成一系列波峰和波谷。波峰是最大正位移点，波谷是最大负位移点。
3. Longitudinal Waves | 纵波
In a longitudinal wave, the particles oscillate parallel to the direction of energy transfer. Sound waves, ultrasound, and compression waves in a slinky spring are common examples.
在纵波中，粒子振动方向与能量传递方向平行。声波、超声波和弹簧中的压缩波都是常见例子。
Longitudinal waves form compressions and rarefactions. A compression is a region where particles are closer together than normal, and a rarefaction is a region where they are farther apart.
纵波形成压缩区和稀疏区。压缩区是粒子比正常间距更近的区域，稀疏区是粒子间距比正常更远的区域。
Although longitudinal waves do not have crests and troughs, their displacement along the direction of travel can still be plotted as a sine-like curve.
尽管纵波没有波峰和波谷，但粒子沿传播方向的位移仍然可以绘制成正弦曲线的形式。
4. Comparing Transverse and Longitudinal Waves | 横波与纵波对比
The table summarises the key differences between the two wave types. Study it carefully, because CIE exam questions often ask you to compare them.
下表总结了两种波的主要区别。请认真学习，因为 CIE 考试题目经常要求对它们进行比较。
| Property / 性质 | Transverse wave / 横波 | Longitudinal wave / 纵波 |
|---|---|---|
| Oscillation direction / 振动方向 | Perpendicular to energy direction / 垂直于能量方向 | Parallel to energy direction / 平行于能量方向 |
| Shape features / 形状特征 | Crests and troughs / 波峰与波谷 | Compressions and rarefactions / 压缩区与稀疏区 |
| Examples / 例子 | Light, water ripples, string waves / 光、水波、绳波 | Sound, ultrasound, P earthquake waves / 声波、超声波、地震 P 波 |
| Can be polarised? / 能否偏振 | Yes / 可以 | No / 不可以 |
5. Displacement-Position Graphs | 位移-位置图像
A displacement-position graph shows how the displacement of particles varies with distance along the wave at one instant of time. For a transverse wave, upward displacement forms crests and downward displacement forms troughs.
位移-位置图像显示在某一瞬间粒子位移随波传播距离的变化。对于横波，向上的位移形成波峰，向下的位移形成波谷。
For a longitudinal wave, the graph still has a sinusoidal shape, but the displacement is parallel to the wave direction. Points of zero displacement with a negative gradient correspond to the centres of compressions, while zero displacement with a positive gradient corresponds to rarefactions.
对于纵波，图像仍然呈正弦形状，但位移方向与波传播方向平行。位移为零且斜率为负的点对应压缩区的中心，而位移为零且斜率为正的点对应稀疏区。
Reading the wavelength from this graph is the same for both wave types: the distance between two adjacent points that are in phase, such as two adjacent crests or two adjacent compressions.
从该图像读取波长的方法对两种波是相同的：两个相邻同相点之间的距离，例如两个相邻波峰或两个相邻压缩区之间的距离。
6. Wave Quantities: Amplitude, Wavelength, Frequency, Speed | 波的特征量：振幅、波长、频率、速度
The amplitude is the maximum displacement of a particle from its equilibrium position. Wavelength is the distance between two consecutive points that are in phase, for example crest to crest or compression to compression.
振幅是粒子离开平衡位置的最大位移。波长是两个相邻同相点之间的距离，例如波峰到波峰或压缩区到压缩区。
The period T is the time for one complete oscillation, and the frequency f is the number of complete oscillations per second. They are related by:
周期 T 是一次完整振动所需的时间，频率 f 是每秒完整振动的次数。它们之间的关系为：
f = 1 / T
The speed v of a wave is the distance travelled by the wave energy per unit time. For all progressive waves, speed, frequency, and wavelength are linked by the wave equation:
波速 v 是波的能量在单位时间内传播的距离。对于所有行波，速度、频率和波长由波动方程联系：
v = fλ
7. The Wave Equation and a Worked Example | 波动方程与示例
If a wave source has a higher frequency, the wavelength becomes shorter when speed remains constant. Always convert frequency to hertz and wavelength to metres before substituting into the equation.
如果波源频率较高，在速度保持不变时波长会变短。代入公式之前，始终将频率换算为赫兹，波长换算为米。
Worked example: A sound wave travels at 340 m s⁻¹ in air and has frequency 680 Hz. Calculate its wavelength.
示例：声波在空气中传播速度为 340 m s⁻¹，频率为 680 Hz。计算其波长。
λ = v / f = 340 / 680 = 0.50 m
8. Phase and Phase Difference | 相位与相位差
Phase describes the position of a point on a wave cycle relative to the start of the cycle. Two points are in phase if they have the same displacement and are moving in the same direction, such as two crests separated by a whole number of wavelengths.
相位描述波周期中某一点相对于周期起点的位置。如果两点具有相同的位移且运动方向相同，则它们同相，例如间隔整数倍波长的两个波峰。
Phase difference compares the positions of two points on a wave. It can be measured in degrees or radians. For two points separated by a distance Δx along the wave:
相位差比较波上两点的位置。它可以用度数或弧度来度量。对于波上相距 Δx 的两点：
phase difference = 2π × Δx / λ
In degrees this becomes:
用度数表示则为：
phase difference = 360° × Δx / λ
A phase difference of 180° or π radians means the points are in antiphase: one is at a crest while the other is at a trough.
相位差为 180° 或 π 弧度表示两点反相：一个在波峰，另一个在波谷。
9. Polarisation | 偏振
Polarisation is the restriction of a transverse wave’s oscillations to one plane only. A polarising filter only allows oscillations in one direction to pass through, absorbing or blocking oscillations in other directions.
偏振是将横波的振动限制在单一平面内的现象。偏振片只允许一个方向的振动通过，吸收或阻挡其他方向的振动。
Only transverse waves can be polarised because their oscillations are perpendicular to the direction of travel. Longitudinal waves cannot be polarised, since their oscillations are already along one line only.
只有横波才能被偏振，因为它们的振动方向垂直于传播方向。纵波不能被偏振，因为它们的振动本身只沿一条线方向。
When unpolarised light passes through a polarising filter, the transmitted intensity can be found using Malus’s law:
当非偏振光通过偏振片时，透射光强可以用马吕斯定律计算：
I = I₀ cos² θ
Here I₀ is the intensity incident on the analyser, and θ is the angle between the polarisation direction of the light and the transmission axis of the analyser.
其中 I₀ 是入射到检偏器上的光强，θ 是光的偏振方向与检偏器透射轴之间的夹角。
10. Sound and Ultrasound as Longitudinal Waves | 声波与超声波作为纵波
Sound waves are longitudinal mechanical waves. They require a medium to travel through, because they propagate by passing compressions and rarefactions through the particles of the material.
声波是纵波，也是机械波。它们需要介质才能传播，因为它们通过介质粒子的压缩区和稀疏区来传递能量。
Sound travels at different speeds in different media, typically fastest in solids, slower in liquids, and slowest in gases. In air at room temperature, the speed is about 340 m s⁻¹.
声波在不同介质中的传播速度不同，通常在固体中最快，液体中较慢，气体中最慢。在室温空气中，声速约为 340 m s⁻¹。
Ultrasound is sound with frequency above the human hearing range, normally above 20 kHz. It is still longitudinal and cannot be polarised.
超声波是频率高于人类听觉范围的声音，通常高于 20 kHz。它仍然是纵波，不能被偏振。
11. Electromagnetic Waves as Transverse Waves | 电磁波作为横波
All electromagnetic waves, including visible light, microwaves, and X-rays, are transverse waves. The oscillating electric field and magnetic field are perpendicular to each other and both are perpendicular to the direction of energy travel.
所有电磁波，包括可见光、微波和 X 射线，都是横波。振荡的电场和磁场彼此垂直，并且都垂直于能量传播方向。
In a vacuum, all electromagnetic waves travel at the same speed c:
在真空中，所有电磁波以相同的速度 c 传播：
c = 3.00 × 10⁸ m s⁻¹
The fact that light can be polarised is strong evidence for its transverse nature. Polaroid sunglasses and polarising filters for cameras use this effect to reduce glare.
光能被偏振这一事实是光具有横波特性的有力证据。偏光太阳镜和相机偏振镜利用这一效应来减少眩光。
12. Exam Tips and Common Misconceptions | 考试提示与常见误区
A common misconception is that particles in a wave travel from the source to the receiver. In fact, particles only oscillate about fixed positions, while energy moves through the medium.
一个常见误区是认为波中的粒子会从波源运动到接收器。事实上，粒子只围绕固定位置振动，而能量在介质中传播。
Another common mistake is to say that longitudinal waves can be polarised. Remember: polarisation is a test that distinguishes transverse waves from longitudinal waves.
另一个常见错误是认为纵波可以被偏振。请记住：偏振是区分横波与纵波的一种检验方法。
When drawing or interpreting displacement-position graphs, do not mix up the shape of a transverse wave with the actual particle motion of a longitudinal wave. Label compressions and rarefactions clearly where required.
在绘制或解释位移-位置图像时，不要把横波的形状与纵波的实际粒子运动混为一谈。需要时，请清楚地标出压缩区和稀疏区。
Finally, always show units in calculations. A wavelength in centimetres must be converted to metres before using v = fλ with a speed in metres per second.
最后，计算时始终标明单位。在使用 v = fλ 且
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