IB Physics: Basic Properties of Waves | IB物理：波的基本性质

📚 IB Physics: Basic Properties of Waves | IB物理：波的基本性质

波是IB物理DP课程中连接力学与电磁学的重要桥梁，也是考试中高频出现的考点。本文围绕”波的基本性质”这一主题，系统讲解波的定义、横波与纵波的区别、振幅、波长、频率、周期、波速、相位与相位差、波前与波线等核心概念，并针对IB考试中常见的图像题与易错点给出解题建议。全文采用中英双语对照，方便同学们在学习物理概念的同时积累英文术语。

Waves are an important bridge in the IB Physics DP course that connects mechanics with electromagnetism, and they appear frequently in examinations. This article focuses on the theme of “Basic Properties of Waves”, systematically explaining the definition of a wave, the difference between transverse and longitudinal waves, amplitude, wavelength, frequency, period, wave speed, phase and phase difference, wavefronts and rays, and other core concepts. It also provides problem-solving advice for the common graph questions and frequent mistakes found in IB exams. The full text is presented in bilingual Chinese-English format, making it convenient for students to accumulate English terminology while learning physics concepts.

一、什么是波：能量如何在不移动物质的情况下传播 | What Is a Wave: How Energy Travels Without Moving Matter

波的本质是一种能量的传递方式。当一列波在介质中传播时，介质中的每一个质点都在自己的平衡位置附近做周期性振动，但质点本身并不会随着波一起向前移动。以绳子上的波为例：你握住绳子的一端上下抖动，绳子上会出现一个凸起向另一端传去，但绳子上的每一个小段只是在上下振动，并没有沿着绳子水平移动。真正向前传播的是振动状态，也就是能量。

The essence of a wave is a way of transferring energy. When a wave travels through a medium, every particle in the medium oscillates periodically around its own equilibrium position, but the particles themselves do not move forward with the wave. Take a wave on a rope as an example: when you hold one end of the rope and shake it up and down, a hump appears and travels toward the other end, but every small segment of the rope only oscillates up and down; it does not move horizontally along the rope. What actually travels forward is the state of oscillation, that is, energy.

根据是否需要介质，波可以分为两大类。机械波（如声波、水波、绳波、地震波）必须依靠介质传播，在真空中无法传播；电磁波（如光、无线电波、X射线）则不需要介质，可以在真空中以光速传播。这个区别是IB考试选择题的常见陷阱：声音在真空中不能传播，而光可以。

Depending on whether a medium is required, waves can be divided into two broad categories. Mechanical waves (such as sound waves, water waves, rope waves, and seismic waves) must rely on a medium to propagate and cannot travel in a vacuum; electromagnetic waves (such as light, radio waves, and X-rays) do not need a medium and can travel at the speed of light in a vacuum. This distinction is a common trap in IB multiple-choice questions: sound cannot propagate in a vacuum, while light can.

此外，波还可以分为脉冲波（pulse）和连续波（continuous wave）。脉冲波只包含一个或少数几个扰动，例如拍打水面产生的单个涟漪；连续波则是持续周期性振动的结果，例如音叉持续振动产生的声波。在IB课程中，我们主要研究连续周期波，因为它可以用正弦函数精确描述。

In addition, waves can be divided into pulses and continuous waves. A pulse contains only one or a few disturbances, such as a single ripple produced by tapping the water surface; a continuous wave is the result of sustained periodic oscillation, such as the sound wave produced by a continuously vibrating tuning fork. In the IB course, we mainly study continuous periodic waves because they can be described precisely with sine functions.

二、横波与纵波：振动方向与传播方向的关系 | Transverse and Longitudinal Waves: Oscillation Direction vs. Propagation Direction

按质点振动方向与波传播方向的关系，波可以分为横波和纵波两大类。横波中，质点振动方向与波的传播方向垂直；纵波中，质点振动方向与波的传播方向平行（在同一直线上）。

According to the relationship between the direction of particle oscillation and the direction of wave propagation, waves can be divided into two major categories: transverse waves and longitudinal waves. In a transverse wave, the particles oscillate perpendicular to the direction of propagation; in a longitudinal wave, the particles oscillate parallel to the direction of propagation (along the same line).

典型的横波包括：电磁波（光的振动方向垂直于传播方向）、绳波（绳子质点上下振动而波水平传播）、水面波（严格来说是横波与纵波的组合，但IB课程通常简化处理）。典型的纵波包括：声波（空气分子沿传播方向前后振动，形成疏密相间的区域）和地震P波。

Typical transverse waves include: electromagnetic waves (the oscillation of light is perpendicular to its direction of propagation), rope waves (the particles of the rope oscillate vertically while the wave travels horizontally), and water surface waves (strictly speaking a combination of transverse and longitudinal motion, though the IB course usually simplifies this). Typical longitudinal waves include: sound waves (air molecules oscillate back and forth along the direction of propagation, forming alternating regions of compression and rarefaction) and seismic P-waves.

比较项目 / Comparison	横波 / Transverse	纵波 / Longitudinal
振动方向 / Oscillation direction	垂直于传播方向 / Perpendicular to propagation	平行于传播方向 / Parallel to propagation
结构特征 / Structural feature	波峰与波谷 / Crests and troughs	疏部与密部 / Rarefactions and compressions
典型例子 / Typical examples	电磁波、绳波 / EM waves, rope waves	声波、地震P波 / Sound, seismic P-waves
能否在真空中传播 / Propagation in vacuum	电磁横波可以 / EM transverse waves can	机械纵波不可以 / Mechanical longitudinal waves cannot

IB考试中常考的一个细节是：纵波图像与横波图像在示意图上的区别。纵波通常用”疏密相间的条纹”表示，而横波用”正弦曲线”表示。如果题目给出正弦曲线并要求判断波的类型，需要注意题目是否明确指出振动方向与传播方向的关系，不能仅凭图像形状下结论。

A detail frequently tested in IB exams is the difference between the schematic diagrams of longitudinal and transverse waves. Longitudinal waves are usually represented by alternating bands of compression and rarefaction, while transverse waves are represented by a sine curve. If a question provides a sine curve and asks you to identify the type of wave, note whether the question explicitly states the relationship between the oscillation direction and the propagation direction; you cannot draw a conclusion from the shape of the graph alone.

三、振幅：波携带能量的”音量旋钮” | Amplitude: The “Volume Knob” of Wave Energy

振幅（amplitude）是描述波强弱的核心物理量，符号为A，国际单位是米（m）。振幅定义为介质质点偏离平衡位置的最大位移，也就是从平衡位置到波峰（或波谷）的距离。注意：振幅不是波峰到波谷的距离，后者是两倍振幅。

Amplitude is the core physical quantity that describes the strength of a wave, with the symbol A and the SI unit metre (m). Amplitude is defined as the maximum displacement of a particle in the medium from its equilibrium position, that is, the distance from the equilibrium position to a crest (or trough). Note: amplitude is NOT the distance from crest to trough; that distance is twice the amplitude.

振幅决定了波携带能量的多少。对于机械波，波携带的能量与振幅的平方成正比（E ∝ A²）。这意味着：如果振幅变为原来的2倍，能量变为原来的4倍；振幅变为原来的3倍，能量变为原来的9倍。这个”平方关系”是IB考试计算题的高频考点。在声音中，振幅对应响度；在光中，振幅对应亮度。

Amplitude determines how much energy a wave carries. For mechanical waves, the energy carried by a wave is proportional to the square of the amplitude (E ∝ A²). This means: if the amplitude doubles, the energy becomes four times larger; if the amplitude triples, the energy becomes nine times larger. This “square relationship” is a high-frequency calculation point in IB exams. In sound, amplitude corresponds to loudness; in light, amplitude corresponds to brightness.

易错提示：IB考题有时会把”振幅加倍，能量变为几倍”与”频率加倍，能量变为几倍”放在一起考查。对于相同的波，能量与振幅平方成正比，也与频率的平方（或说每秒振动的次数相关）有关，但题目通常会限定其他条件不变。做题时先看清题目问的是”振幅变化”还是”频率变化”。

Mistake reminder: IB questions sometimes combine “if amplitude doubles, how many times does the energy become” with “if frequency doubles, how many times does the energy become” in the same item. For the same wave, energy is proportional to the square of amplitude and is also related to frequency, but questions usually state that other conditions remain unchanged. When solving, first read carefully whether the question asks about a change in “amplitude” or a change in “frequency”.

四、波长与频率：描述波周期性的两个核心量 | Wavelength and Frequency: Two Core Quantities of Wave Periodicity

波长（wavelength）是波在一个完整周期内传播的距离，符号为λ（希腊字母lambda），国际单位是米（m）。在横波图像上，波长等于相邻两个波峰（或相邻两个波谷、或任意两个相邻的同相点）之间的距离。频率（frequency）是单位时间内通过某一点的完整波的个数，符号为f，单位是赫兹（Hz），1 Hz 表示每秒1个完整周期。

Wavelength is the distance a wave travels during one complete period, with the symbol λ (the Greek letter lambda) and the SI unit metre (m). On a transverse wave graph, the wavelength equals the distance between two adjacent crests (or two adjacent troughs, or any two adjacent points in the same phase). Frequency is the number of complete waves passing a given point per unit time, with the symbol f and the unit hertz (Hz); 1 Hz means one complete period per second.

频率与周期（period）互为倒数：T = 1/f，其中T是周期，单位是秒（s）。周期是完成一次完整振动所需的时间。例如，一个频率为50 Hz的波，其周期为T = 1/50 = 0.02 s，也就是说每0.02秒就有一个完整的波通过。

Frequency and period are reciprocals of each other: T = 1/f, where T is the period in seconds (s). The period is the time needed to complete one full oscillation. For example, a wave with a frequency of 50 Hz has a period of T = 1/50 = 0.02 s, meaning one complete wave passes every 0.02 seconds.

波长和频率的大小与波的种类密切相关。可见光的波长范围大约在400纳米（紫光）到700纳米（红光）之间，频率约为4.3×10¹⁴到7.5×10¹⁴ Hz；人耳能听到的声音频率范围大约为20 Hz到20000 Hz。波长越短、频率越高的波，在相同介质中的能量往往越集中。

Wavelength and frequency are closely related to the type of wave. Visible light has wavelengths ranging from about 400 nanometres (violet) to 700 nanometres (red), with frequencies of roughly 4.3×10¹⁴ to 7.5×10¹⁴ Hz; the human ear can hear sound frequencies from about 20 Hz to 20000 Hz. Shorter-wavelength, higher-frequency waves tend to carry more concentrated energy in the same medium.

IB考试中，波长和频率的概念经常与图像题结合。一张位移-距离图像（displacement-distance graph）的横轴是距离，图中相邻波峰的距离就是波长；一张位移-时间图像（displacement-time graph）的横轴是时间，图中相邻波峰的时间间隔就是周期。这两类图像的区别是IB学生的经典易错点，我们将在第九节详细展开。

In IB exams, the concepts of wavelength and frequency are often combined with graph questions. In a displacement-distance graph, the horizontal axis is distance, and the distance between adjacent crests in the graph is the wavelength; in a displacement-time graph, the horizontal axis is time, and the time interval between adjacent crests is the period. The difference between these two types of graphs is a classic point of confusion for IB students, and we will discuss it in detail in Section Nine.

五、波速与波方程 v = fλ：连接三个基本量的桥梁 | Wave Speed and the Wave Equation v = fλ

波速（wave speed）是波在介质中传播的快慢，符号为v，单位是米每秒（m/s）。波速由介质本身的性质决定，而不是由波源决定。例如，在相同温度和压强下，声音在空气中的速度约为340 m/s，在水中约为1500 m/s，在钢铁中约为5000 m/s。光在真空中的速度恒为3×10⁸ m/s。

Wave speed is how fast a wave propagates through a medium, with the symbol v and the unit metres per second (m/s). The wave speed is determined by the properties of the medium itself, not by the source of the wave. For example, at the same temperature and pressure, sound travels at about 340 m/s in air, about 1500 m/s in water, and about 5000 m/s in steel. Light travels at a constant 3×10⁸ m/s in a vacuum.

波速、波长和频率之间满足著名的波方程：v = fλ。这个公式的物理含义非常直观：在一个周期T内，波前进一个波长λ的距离，因此波速等于波长除以周期，即v = λ/T = λf。这是IB物理中最重要的公式之一，几乎所有波的计算题都会用到它。

Wave speed, wavelength and frequency are related by the famous wave equation: v = fλ. The physical meaning of this formula is very intuitive: during one period T, the wave advances a distance of one wavelength λ, so the wave speed equals the wavelength divided by the period, that is, v = λ/T = λf. This is one of the most important formulas in IB Physics, and almost every wave calculation question uses it.

解题要点：当波从一种介质进入另一种介质时（例如从空气进入水），频率保持不变（因为频率由波源决定），但波速会改变，因此波长也会相应改变。例如，光从空气进入水中时，速度减小，波长变短，但颜色（频率）不变。这个”频率不变、波长随速度变化”的规律是IB考试的高频考点。

Key point for problem solving: when a wave enters a different medium (for example, from air into water), the frequency remains unchanged (because the frequency is determined by the source), but the wave speed changes, so the wavelength changes accordingly. For example, when light travels from air into water, its speed decreases, its wavelength becomes shorter, but its colour (frequency) stays the same. This rule that “frequency is unchanged while wavelength varies with speed” is a high-frequency point in IB exams.

物理量 / Quantity	符号 / Symbol	单位 / Unit	决定因素 / Determined by
波速 / Wave speed	v	m/s	介质 / Medium
频率 / Frequency	f	Hz	波源 / Source
波长 / Wavelength	λ	m	v 与 f 共同决定 / v and f together
周期 / Period	T	s	T = 1/f
振幅 / Amplitude	A	m	能量供给 / Energy supply

六、周期与角频率：从”每秒几次”到”每秒多少弧度” | Period and Angular Frequency: From Cycles per Second to Radians per Second

周期T描述一次完整振动所需的时间，频率f描述每秒完成的振动次数，两者互为倒数。但在描述简谐波时，IB课程还引入了一个重要概念：角频率（angular frequency）ω，单位是弧度每秒（rad/s），定义式为ω = 2πf = 2π/T。角频率表示每秒转过的”相位角”弧度数，它把”每秒钟几个周期”转换成了”每秒钟多少弧度”。

The period T describes the time needed for one complete oscillation, and the frequency f describes the number of oscillations completed per second; the two are reciprocals of each other. However, when describing simple harmonic waves, the IB course also introduces an important concept: angular frequency ω, with the unit radians per second (rad/s), defined as ω = 2πf = 2π/T. Angular frequency represents the number of radians of “phase angle” swept per second; it converts “how many cycles per second” into “how many radians per second”.

为什么要引入角频率？因为波上任意一点的振动可以用正弦函数描述：y = A sin(ωt + φ₀)，其中y是位移，A是振幅，ωt是随时间变化的相位，φ₀是初相位。使用角频率可以让公式中的自变量直接对应”角度”，从而与三角函数的数学工具无缝衔接。这也是为什么后续学习叠加、驻波和干涉时，相位概念如此重要。

Why introduce angular frequency? Because the oscillation of any point on a wave can be described by a sine function: y = A sin(ωt + φ₀), where y is the displacement, A is the amplitude, ωt is the phase that changes with time, and φ₀ is the initial phase. Using angular frequency makes the independent variable in the formula directly correspond to “angle”, seamlessly connecting with the mathematical tool of trigonometric functions. This is also why the concept of phase is so important when you later study superposition, standing waves and interference.

IB考试中，角频率的计算通常出现在两类题目中：一是给出周期或频率求ω；二是在波的叠加或振动图像中，利用ω = 2π/T 把图像信息转换成解析式。注意计算器要设置为弧度模式（radian mode），这是IB学生在三角函数相关题目中最常见的低级失误。

In IB exams, angular frequency calculations usually appear in two types of questions: first, given the period or frequency, find ω; second, in wave superposition or oscillation graph questions, use ω = 2π/T to convert graphical information into an analytic expression. Remember to set your calculator to radian mode; this is the most common careless mistake made by IB students in trigonometry-related questions.

七、相位与相位差：两列波之间的”步调”关系 | Phase and Phase Difference: The “Step” Relationship Between Two Waves

相位（phase）描述的是一个振动质点在某一时刻所处的”振动状态”，包括它的位移大小、运动方向等。两个质点如果位移和运动方向完全相同，我们说它们”同相”（in phase）；如果位移大小相同但运动方向相反，我们说它们”反相”（antiphase）。同相的两点之间相距整数个波长，反相的两点之间相距半个波长的奇数倍。

Phase describes the “oscillation state” of a vibrating particle at a given moment, including its displacement and direction of motion. If two particles have exactly the same displacement and direction of motion, we say they are “in phase”; if they have the same magnitude of displacement but opposite directions of motion, we say they are “in antiphase”. Two in-phase points are separated by an integer number of wavelengths, while two antiphase points are separated by an odd number of half-wavelengths.

相位差（phase difference）是两列波（或同一列波上的两个点）在同一时刻相位之差，通常用弧度或度表示。对于同一列波上相距Δx的两个点，相位差Δφ = 2πΔx/λ。例如，相距四分之一波长的两个点，相位差为π/2（90度）；相距半波长的两个点，相位差为π（180度）。

Phase difference is the difference in phase between two waves (or two points on the same wave) at the same moment, usually expressed in radians or degrees. For two points on the same wave separated by a distance Δx, the phase difference is Δφ = 2πΔx/λ. For example, two points separated by a quarter of a wavelength have a phase difference of π/2 (90 degrees); two points separated by half a wavelength have a phase difference of π (180 degrees).

相位差是理解干涉现象的基础：当两列相干波在某点相遇时，如果它们的相位差为0或2π的整数倍，该点振动加强；如果相位差为π的奇数倍，该点振动减弱甚至抵消。这就是双缝干涉实验中明暗条纹交替出现的根本原因。IB考试常以”计算两点的相位差”或”判断两列波是同相还是反相”的形式考查这一概念。

Phase difference is the foundation for understanding interference: when two coherent waves meet at a point, if their phase difference is 0 or an integer multiple of 2π, the vibration at that point is reinforced; if the phase difference is an odd multiple of π, the vibration is weakened or even cancelled. This is the fundamental reason why bright and dark fringes alternate in the double-slit interference experiment. IB exams often test this concept by asking you to “calculate the phase difference between two points” or “determine whether two waves are in phase or in antiphase”.

易错提示：计算相位差时，一定要先确认两点之间相距几个波长，再用公式Δφ = 2πΔx/λ。如果题目给出的距离是波长的分数形式（如λ/4），可以直接换算；如果题目给出的两列波的频率不同，则不能直接套用这个公式，因为此时相位差随时间变化。

Mistake reminder: when calculating phase difference, always first confirm how many wavelengths separate the two points, then apply the formula Δφ = 2πΔx/λ. If the distance is given as a fraction of the wavelength (such as λ/4), you can convert directly; if the two waves in the question have different frequencies, you cannot apply this formula directly, because the phase difference changes with time in that case.

八、波前与波线：描述波传播的几何工具 | Wavefronts and Rays: Geometric Tools for Describing Wave Propagation

波前（wavefront）是波在同一时刻到达的、相位相同的各点连成的面（或线）。对于点波源产生的波，波前是以波源为圆心的同心圆（二维）或同心球面（三维）；对于远处传来的波，波前近似为平面。相邻波前之间的距离等于一个波长。

A wavefront is the surface (or line) connecting all points that the wave reaches at the same moment with the same phase. For a point source, the wavefronts are concentric circles (in two dimensions) or concentric spheres (in three dimensions) centred on the source; for waves arriving from far away, the wavefronts are approximately planar. The distance between adjacent wavefronts equals one wavelength.

波线（ray）是表示波的传播方向的线，始终与波前垂直。在均匀介质中，波线是直线；当波遇到障碍物或进入不同介质时，波线会发生偏折。用波前和波线描述波的好处是：可以把复杂的波动问题转化为几何问题，这正是惠更斯原理（Huygens’ principle）的思想基础 – 波前上的每一点都可以看作新的子波源，子波的包络面形成新的波前。

A ray is a line that indicates the direction of wave propagation and is always perpendicular to the wavefront. In a uniform medium, rays are straight lines; when a wave encounters an obstacle or enters a different medium, the rays bend. The advantage of describing waves with wavefronts and rays is that complex wave problems can be converted into geometry problems. This is the conceptual basis of Huygens’ principle: every point on a wavefront can be treated as a new source of secondary waves, and the envelope of these secondary waves forms the new wavefront.

IB考试中，波前图经常用于考查反射、折射和衍射。例如：平面波遇到平面障碍物时，反射波的波前仍然是平面，但传播方向改变；平面波通过狭缝时，如果狭缝宽度与波长相当，波前会弯曲成圆弧状，这就是衍射。看到波前图时，先判断波的类型（平面波还是圆形波）、再判断波前的疏密（疏代表波长大、频率低），就能快速读懂题目。

In IB exams, wavefront diagrams are often used to test reflection, refraction and diffraction. For example: when a plane wave meets a flat obstacle, the wavefronts of the reflected wave remain planar but the direction of propagation changes; when a plane wave passes through a slit, if the slit width is comparable to the wavelength, the wavefronts bend into circular arcs, which is diffraction. When you see a wavefront diagram, first identify the type of wave (plane or circular), then check the spacing of the wavefronts (wide spacing means large wavelength and low frequency); this allows you to read the question quickly.

九、两类波图像辨析：位移-距离图与位移-时间图 | Distinguishing Two Wave Graphs: Displacement-Distance vs Displacement-Time

IB考试中，波的概念几乎总是通过图像来考查，而最经典的易错点就是分不清位移-距离图像（displacement-distance graph）和位移-时间图像（displacement-time graph）。两者的图像形状完全一样，都是正弦曲线，区别在于横轴：前者横轴是距离x，后者横轴是时间t。

In IB exams, wave concepts are almost always tested through graphs, and the most classic point of confusion is failing to distinguish between a displacement-distance graph and a displacement-time graph. The two graphs look exactly the same, both being sine curves; the difference lies in the horizontal axis: the former has distance x on the horizontal axis, while the latter has time t.

从位移-距离图像中，我们可以直接读出波长λ（相邻波峰的水平距离），但读不出周期；从位移-时间图像中，我们可以直接读出周期T（相邻波峰的时间间隔），但读不出波长。如果题目同时给出两张图（这是IB考试的常见出题方式），则可以利用v = fλ = λ/T 计算出波速。

From a displacement-distance graph, we can read the wavelength λ directly (the horizontal distance between adjacent crests), but we cannot read the period; from a displacement-time graph, we can read the period T directly (the time interval between adjacent crests), but we cannot read the wavelength. If a question provides both graphs (a common format in IB exams), you can calculate the wave speed using v = fλ = λ/T.

特征 / Feature	位移-距离图 / Disp.-Distance	位移-时间图 / Disp.-Time
横轴 / Horizontal axis	距离 x (m)	时间 t (s)
它拍摄的是 / It shows	某一时刻整列波的”照片” / A snapshot of the whole wave	某个质点的振动”录像” / The oscillation record of one particle
相邻波峰间距 / Crest spacing	波长 λ / Wavelength	周期 T / Period
纵轴 / Vertical axis	各质点的位移 y	该质点的位移 y

还有一个重要的细节：在位移-距离图像上，波的传播方向与质点的振动方向之间的关系需要借助”波形推移法”来判断。例如，若波向右传播，则位于波峰右侧、正在上升途中的质点，其振动方向为向上；若波向左传播，则判断结果相反。IB简答题常要求你画出某个质点的运动方向箭头，掌握波形推移法是拿分关键。

There is another important detail: on a displacement-distance graph, the relationship between the direction of wave propagation and the direction of particle oscillation is determined by the “waveform shift method”. For example, if the wave travels to the right, a particle on the right side of a crest that is on its way up is moving upward; if the wave travels to the left, the result is reversed. IB short-answer questions often ask you to draw the direction arrow of a particle’s motion; mastering the waveform shift method is the key to scoring.

十、IB考试高频考点与易错点清单 | Checklist of High-Frequency Exam Points and Common Mistakes

结合历年IB真题，我们把”波的基本性质”相关的高频考点和易错点整理如下。第一，振幅与波峰-波谷距离的关系：振幅是平衡位置到波峰的距离，等于波峰-波谷距离的一半。第二，能量与振幅的平方成正比：振幅加倍，能量变为4倍。第三，波速由介质决定、频率由波源决定：波进入新介质时频率不变、波长改变。

Based on past IB papers, we summarise the high-frequency exam points and common mistakes related to “Basic Properties of Waves” as follows. First, the relationship between amplitude and crest-to-trough distance: amplitude is the distance from the equilibrium position to a crest, equal to half the crest-to-trough distance. Second, energy is proportional to the square of amplitude: if amplitude doubles, energy becomes four times as large. Third, wave speed is determined by the medium and frequency is determined by the source: when a wave enters a new medium, the frequency stays the same but the wavelength changes.

第四，区分位移-距离图和位移-时间图：横轴是距离则读波长，横轴是时间则读周期。第五，纵波与横波的判断依据是振动方向与传播方向的关系，而不是图像形状。第六，相位差计算：Δφ = 2πΔx/λ，注意先判断两点间距与波长的倍数关系。第七，计算器务必使用弧度模式，三角函数相关的相位计算才能得到正确答案。

Fourth, distinguish the displacement-distance graph from the displacement-time graph: if the horizontal axis is distance, read the wavelength; if it is time, read the period. Fifth, the basis for identifying transverse versus longitudinal waves is the relationship between the oscillation direction and the propagation direction, not the shape of the graph. Sixth, phase difference calculation: Δφ = 2πΔx/λ; always determine the multiple relationship between the separation and the wavelength first. Seventh, always use radian mode on your calculator so that phase calculations involving trigonometric functions give the correct answer.

第八，v = fλ 的三个量中，题目通常给出两个求第三个，注意单位换算（如把纳米换算成米、把kHz换算成Hz）。第九，波前图中相邻波前间距代表波长，波前越密代表波长越短、频率越高。第十，遇到”波从一种介质进入另一种介质”的题目，先写”频率不变”再列方程，这是标准化解题的第一步。

Eighth, in the equation v = fλ, questions usually give two quantities and ask for the third; pay attention to unit conversions (such as converting nanometres to metres and kHz to Hz). Ninth, in wavefront diagrams, the spacing between adjacent wavefronts represents the wavelength; denser wavefronts mean shorter wavelength and higher frequency. Tenth, for questions about “a wave entering a different medium”, write down “frequency is unchanged” first and then set up the equation; this is the first step of a standardised solution.

Summary | 总结

本文系统梳理了IB物理”波的基本性质”的核心知识：波是能量的传递形式而非物质的移动；横波与纵波的区别在于振动方向与传播方向的关系；振幅决定波的能量强弱（E ∝ A²）；波长、频率、周期与波速通过v = fλ联系起来；相位与相位差是理解干涉的基础；波前与波线提供了描述波传播的几何语言。掌握这些概念，并熟练区分位移-距离图与位移-时间图，是解答IB波相关题目的关键。

This article systematically reviews the core knowledge of “Basic Properties of Waves” in IB Physics: a wave is a form of energy transfer rather than the movement of matter; the difference between transverse and longitudinal waves lies in the relationship between the oscillation direction and the propagation direction; amplitude determines the strength of wave energy (E ∝ A²); wavelength, frequency, period and wave speed are connected by v = fλ; phase and phase difference are the foundation for understanding interference; and wavefronts and rays provide a geometric language for describing wave propagation. Mastering these concepts and being able to distinguish displacement-distance graphs from displacement-time graphs are the keys to answering IB wave questions.

建议同学们在复习时，先把本文第二、四、五节的表格抄写一遍形成知识框架，再结合教材中的图像题做专项练习，最后用第十节的易错点清单进行自查。波的知识是后续学习干涉、衍射、驻波和波粒二象性的基础，打好这一章的基础，IB物理的高分之路就会更加顺畅。

We suggest that when revising, students first copy the tables in Sections Two, Four and Five to form a knowledge framework, then do targeted practice with the graph questions in the textbook, and finally use the checklist in Section Ten for self-assessment. The knowledge of waves is the foundation for later topics such as interference, diffraction, standing waves and wave-particle duality. Building a solid foundation in this chapter will smooth your path to a high score in IB Physics.

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