📚 Sound: Key Concepts and Exam Focus | 声：核心考点精讲
Sound is one of the most accessible and fascinating topics in physics. It brings together concepts of waves, energy transfer, human perception, and technological applications. A solid grasp of sound principles is essential for success in IB and CCEA science exams, where questions often test both qualitative understanding and quantitative problem-solving.
声音是物理学中最直观、最迷人的话题之一。它融合了波动、能量传递、人类感知和技术应用等概念。扎实掌握声学原理对于在IB和CCEA科学考试中取得成功至关重要，试题往往既考查定性理解，也考查定量问题解决。
This revision guide covers the core learning outcomes: the nature of sound waves, the wave equation, speed of sound in different media, frequency and pitch, amplitude and loudness, reflection, refraction and diffraction, resonance, the human ear, ultrasound, and the Doppler effect. Each section pairs clear English explanations with Chinese renditions to support bilingual learners. Let’s dive into the physics of sound.
本复习指南涵盖核心学习目标：声波的本质、波动方程、不同介质中的声速、频率与音调、振幅与响度、反射、折射和衍射、共振、人耳、超声波以及多普勒效应。每个小节都将清晰的英文解释与中文对应，以支持双语学习者。让我们一起深入学习声音的物理原理。
1. What is Sound? | 什么是声音？
Sound is a form of mechanical energy produced when an object vibrates. The vibration disturbs the particles in the surrounding medium, transferring energy from one location to another without any net movement of matter.
声音是物体振动时产生的一种机械能形式。振动会扰动周围介质中的粒子，将能量从一个位置传递到另一个位置，而物质本身并没有净移动。
Unlike electromagnetic waves, sound cannot travel through a vacuum. It requires a material medium such as a solid, liquid, or gas to propagate. This is because sound relies on particle interactions to transmit the compressions and rarefactions that make up the wave.
与电磁波不同，声音不能在真空中传播。它需要固体、液体或气体等物质介质才能传播。这是因为声音依赖粒子间的相互作用来传递构成声波的压缩和稀疏。
In everyday terms, sound is what we hear when our ears detect pressure variations in the air. These variations are interpreted by the brain, allowing us to recognise speech, music, and environmental cues.
日常所说的声音，是我们耳朵探测到空气压强变化时听到的东西。这些变化被大脑解读，使我们能够识别语音、音乐和环境信号。
2. Sound as a Longitudinal Wave | 声音作为纵波
Sound travels through a medium as a longitudinal wave. In a longitudinal wave, the particle displacement is parallel to the direction of energy propagation. This creates alternating regions of high pressure (compressions) and low pressure (rarefactions).
声音在介质中以纵波的形式传播。在纵波中，粒子的位移方向与能量传播方向平行。这就形成了高压区（压缩）和低压区（稀疏）交替出现的现象。
A single compression and the following rarefaction together make up one complete wave cycle. The distance between successive compressions (or successive rarefactions) is the wavelength, often represented by the Greek letter λ.
一个完整的压缩和紧随其后的稀疏共同构成一个完整的波形周期。相邻两个压缩区（或两个稀疏区）之间的距离就是波长，通常用希腊字母 λ 表示。
When representing longitudinal sound waves graphically, we often plot pressure against position or displacement against time. These graphs look very similar to transverse wave graphs, but it is important to remember that the actual particle motion is back and forth along the direction of travel.
在绘制纵波的图像时，我们常将压强-位置或位移-时间的关系绘制出来。这些图形看起来与横波图形非常相似，但务必记住，实际的粒子运动是沿着传播方向前后振动的。
3. The Wave Equation for Sound | 声波的波动方程
The relationship between the speed of sound (v), its frequency (f), and its wavelength (λ) is given by the universal wave equation. This equation applies to all periodic waves, including sound.
声速 (v)、频率 (f) 和波长 (λ) 之间的关系由普适的波动方程给出。该方程适用于包括声波在内的所有周期波。
v = f λ
In this equation, v is the speed in metres per second (m s⁻¹), f is the frequency in hertz (Hz), and λ is the wavelength in metres (m). A sound of frequency 440 Hz with a wavelength of 0.78 m has a speed of 343 m s⁻¹, roughly the speed of sound in air at room temperature.
在该方程中，v 是速度，单位为米每秒（m s⁻¹）；f 是频率，单位为赫兹（Hz）；λ 是波长，单位为米（m）。频率为440 Hz、波长为0.78 m的声波，其速度为343 m s⁻¹，大致相当于室温下空气中的声速。
Exam questions frequently ask students to rearrange this equation to solve for an unknown quantity. Remember to convert units—wavelengths are sometimes given in centimetres, so convert to metres before substituting into the formula.
考试题目经常要求学生变换该方程来求解未知量。切记要换算单位——波长有时以厘米给出，因此代入公式前要先转换为米。
4. Speed of Sound in Different Media | 不同介质中的声速
The speed of sound varies significantly depending on the medium through which it travels. In general, sound travels fastest in solids, slower in liquids, and slowest in gases. This is due to differences in the elasticity and density of the materials.
声速会因传播介质的不同而显著变化。一般来说，声音在固体中传播最快，在液体中次之，在气体中最慢。这是由于材料的弹性和密度差异所致。
Table 1 shows typical values for the speed of sound in common media.
表1 列出了常见介质中的典型声速值。
| Medium / 介质 | Speed (m s⁻¹) / 速度 |
|---|---|
| Air at 20°C | 343 |
| Water at 25°C | 1498 |
| Steel | 5960 |
| Glass | 5640 |
| Helium at 0°C | 965 |
In gases, the speed of sound increases with temperature. For air, an approximate relationship is v = 331 + 0.6T, where T is the temperature in degrees Celsius. This explains why sound travels faster on a warm day.
在气体中，声速随温度升高而增大。对于空气，近似关系为 v = 331 + 0.6T，其中 T 为摄氏温度。这就解释了为什么声音在温暖的天气里传播得更快。
The stiffness (elastic modulus) of a solid is the primary factor enabling the rapid transmission of sound. Denser materials can sometimes slow sound down, but a higher elastic modulus usually dominates, giving solids the highest speeds.
固体的刚度（弹性模量）是实现声音快速传播的主要因素。密度较大的材料有时会使声音减慢，但较高的弹性模量通常占主导地位，因此固体的声速最高。
5. Frequency and Pitch | 频率与音调
Frequency is the number of complete wave cycles passing a point per second, measured in hertz (Hz). The frequency of a sound wave determines the pitch that we perceive. High-frequency sounds correspond to high-pitched notes, while low-frequency sounds are heard as low-pitched notes.
频率是每秒通过某一点的完整波形周期数，单位为赫兹（Hz）。声波的频率决定了我们感知到的音调。高频声波对应高音，低频声波则被听作低音。
The human ear can typically detect frequencies ranging from 20 Hz to 20 000 Hz (20 kHz). Sounds below 20 Hz are called infrasound, and those above 20 kHz are called ultrasound. Many animals, such as dogs and bats, can hear frequencies beyond the human range.
人耳通常能探测到20 Hz至20 000 Hz（20 kHz）的频率范围。低于20 Hz的声音称为次声波，高于20 kHz的称为超声波。许多动物，如狗和蝙蝠，能听到超出人类范围的频率。
In music, the note A above middle C is standardised at 440 Hz. Doubling the frequency produces an octave higher; halving it gives an octave lower. This logarithmic relationship underpins musical scales.
在音乐中，中央C上方的A音被标准化为440 Hz。频率加倍可产生高八度音，减半则得到低八度音。这种对数关系是音阶的基础。
6. Amplitude, Intensity, and Loudness | 振幅、强度与响度
The amplitude of a sound wave corresponds to the maximum displacement of particles from their equilibrium positions. In a pressure wave, amplitude relates to the maximum pressure variation. Greater amplitude means more energy is being transferred.
声波的振幅对应于粒子偏离其平衡位置的最大位移。在压强波中，振幅与最大压强变化相关。振幅越大，传递的能量就越多。
Sound intensity is the power carried by the wave per unit area, measured in watts per square metre (W m⁻²). Loudness is the subjective perception of intensity and depends on both the amplitude and the frequency sensitivity of the ear.
声强是声波单位面积上传递的功率，单位为瓦每平方米（W m⁻²）。响度是对强度的主观感知，它不仅取决于振幅，还取决于人耳对频率的灵敏度。
Because the human ear can detect an enormous range of intensities, a logarithmic scale called the decibel (dB) is used. The threshold of hearing is 0 dB, a normal conversation is about 60 dB, and sounds above 120 dB can cause pain and damage.
由于人耳能感知范围极大的强度变化，因此采用对数标度——分贝（dB）。听阈为0 dB，正常交谈约为60 dB，而超过120 dB的声音可能引起疼痛和损伤。
Doubling the amplitude does not double the perceived loudness; loudness roughly scales with the logarithm of intensity. A 10 dB increase corresponds to a perceived doubling of loudness for most listeners.
振幅加倍并不会使感知响度加倍；响度大致与强度的对数成正比。对大多数人来说，声级每增加10 dB，响度感觉大约加倍。
7. Waveforms, Harmonics, and Timbre | 波形、谐波与音色
Pure tones have a single frequency and produce a smooth sinusoidal waveform. However, most real-world sounds consist of a fundamental frequency combined with a series of higher-frequency harmonics (overtones). The mix of these harmonics defines the timbre or ‘colour’ of the sound.
纯音只有单一频率，产生平滑的正弦波形。然而，大多数真实声音都由基频加上一系列高频谐波（泛音）组成。这些谐波的混合决定了声音的音色或“色彩”。
Figure 1 compares waveforms of a tuning fork (near pure tone), a violin, and a clarinet playing the same note. Although they share the same fundamental frequency, the amplitude distribution of harmonics makes each instrument instantly recognisable.
图1 对比了音叉（接近纯音）、小提琴和单簧管演奏同一音符时的波形。尽管它们的基频相同，但谐波振幅的分布使每种乐器能立即被辨认出来。
Square, sawtooth, and triangular waves are examples of complex periodic waveforms used in sound synthesis. Each has a unique harmonic spectrum that can be represented using Fourier analysis.
方波、锯齿波和三角波是声音合成中使用的复杂周期波形示例。每种波形都有独特的谐波频谱，可以通过傅里叶分析来表示。
8. Reflection, Echoes, and Reverberation | 反射、回声与混响
When sound strikes a hard surface, it reflects according to the law of reflection—the angle of incidence equals the angle of reflection. A distinct reflected sound arriving more than about 0.1 s after the direct sound is perceived as an echo.
声音撞到硬表面时，会按照反射定律反射——入射角等于反射角。反射声在直达声之后到达，若延迟超过约0.1秒，就会被人耳感知为回声。
The minimum distance for an echo can be calculated using the speed of sound. Since the sound must travel to the reflector and back, the minimum distance is d = (v × t) / 2, where t is the minimum time delay for an echo (0.1 s). In air, this equates to about 17 m.
产生回声的最小距离可以用声速来计算。由于声音必须往返于反射面，最小距离 d = (v × t) / 2，其中 t 是产生回声所需的最小延迟（0.1 s）。在空气中，这大约相当于17 m。
Reverberation is the persistence of sound after the source has stopped, caused by multiple overlapping reflections in an enclosed space. Concert halls are carefully designed to balance reverberation time for optimal sound quality.
混响是声源停止后声音的持续现象，由封闭空间内多次重叠的反射造成。音乐厅会精心设计，以平衡混响时间，达到最佳音质。
9. Refraction and Diffraction of Sound | 声音的折射与衍射
Sound refraction occurs when a wave changes speed and direction as it passes from one medium to another or through a medium with varying properties. Temperature gradients in the atmosphere can bend sound waves, sometimes causing sounds to be heard over unexpectedly long distances.
声音折射发生在声波从一种介质进入另一种介质，或在性质变化的介质中传播时速度与方向发生改变时。大气中的温度梯度会使声波弯曲，有时导致声音在出乎意料的长距离外仍能被听到。
Diffraction is the spreading out of sound waves when they pass through an opening or around an obstacle. Because audible sound has wavelengths ranging from about 17 m (20 Hz) to 0.017 m (20 kHz), low-frequency sounds diffract more noticeably around everyday objects.
衍射是声波穿过缝隙或绕过障碍物时发生扩展的现象。由于可听声音的波长范围从约17 m（20 Hz）到0.017 m（20 kHz），低频声波在绕过日常物体时衍射现象更为明显。
This explains why you can hear bass notes from a stereo around a corner more easily than treble notes. Long wavelengths bend around the obstacle, whereas short wavelengths cast sharper acoustic shadows.
这就解释了为什么你可以在角落处听到音响的低音，却较难听到高音。长波长会绕过障碍物，而短波长则会产生更清晰的声影区。
10. Resonance and Standing Waves in Air Columns | 共振与气柱驻波
Resonance occurs when an object is forced to vibrate at its natural frequency, resulting in a dramatic increase in amplitude. In sound, resonance is responsible for the rich tones of musical instruments and the phenomenon of standing waves in air columns.
当一个物体被迫以其固有频率振动时，就会发生共振，导致振幅急剧增大。在声学中，共振是乐器发出丰富音色的原因，也是气柱中驻波现象的基础。
A standing wave is formed when two identical waves travelling in opposite directions interfere. In a pipe closed at one end, the closed end must be a displacement node (pressure antinode), while the open end is a displacement antinode (pressure node). This gives rise to only odd harmonics.
驻波是由两列相同但反向传播的波发生干涉而形成的。在一端封闭的管中，封闭端必须是位移波节（压强波腹），而开口端是位移波腹（压强波节）。这导致只能产生奇次谐波。
For a pipe of length L closed at one end, the resonant wavelengths are given by λ = 4L / n, where n = 1, 3, 5, … The fundamental frequency is f₁ = v / (4L). Open pipes support both even and odd harmonics, with λ = 2L / n and n = 1, 2, 3, …
对于长度为 L 的一端封闭管，共振波长为 λ = 4L / n，其中 n = 1, 3, 5, …。基频为 f₁ = v / (4L)。两端开口的管则支持偶次和奇次谐波，λ = 2L / n，n = 1, 2, 3, …
11. The Human Ear and Hearing | 人耳与听觉
The human ear is a remarkable organ that converts sound pressure waves into electrical signals the brain can interpret. It is divided into three main sections: the outer ear, the middle ear, and the inner ear.
人耳是一个非常精巧的器官，能将声压波转换成大脑可解读的电信号。它主要分为三个部分：外耳、中耳和内耳。
The outer ear consists of the pinna and the ear canal, which funnel sound to the eardrum. The eardrum vibrates in response, transmitting these vibrations to three tiny bones in the middle ear—the hammer, anvil, and stirrup—which amplify the pressure variations.
外耳由耳廓和耳道组成，将声音汇聚到鼓膜。鼓膜随之振动，将这些振动传递给中耳内的三块小骨——锤骨、砧骨和镫骨——它们会放大压强的变化。
In the inner ear, the cochlea contains fluid and thousands of hair cells tuned to different frequencies. Movement of the fluid bends these hair cells, triggering nerve impulses that travel via the auditory nerve to the brain. The semicircular canals are responsible for balance, not hearing.
内耳的耳蜗含有液体和数以千计对不同频率敏感的毛细胞。液体的流动使毛细胞弯曲，触发电神经冲动，通过听神经传至大脑。半规管负责平衡，而非听觉。
12. Ultrasound: Properties and Applications | 超声波的性质与应用
Ultrasound refers to sound waves with frequencies above the upper limit of human hearing, typically greater than 20 kHz. These high-frequency waves have short wavelengths, which allows them to be focused into narrow beams and to produce detailed images.
超声波是指频率超过人耳听觉上限（通常大于20 kHz）的声波。这些高频波具有短波长，因而可以被聚焦成窄波束，并生成精细的图像。
In medicine, ultrasound imaging (sonography) uses the reflection of ultrasonic pulses to create real-time images of organs and foetuses. A gel is applied to the skin to minimise impedance mismatch and maximise transmission into the body.
在医学领域，超声成像（声波成像）利用超声脉冲的反射来生成器官和胎儿的实时图像。皮肤上会涂抹耦合凝胶，以减少阻抗失配，最大程度地将声波传导入体内。
Industrial applications include non-destructive testing of materials, where ultrasound reveals hidden cracks or flaws. Ultrasonic cleaning uses cavitation—the rapid formation and collapse of tiny bubbles—to remove dirt from delicate items.
工业应用包括材料的无损检测，利用超声波揭示隐藏的裂纹或缺陷。超声波清洗则利用空化效应——微小气泡的迅速形成与坍塌——来清除精密物品上的污垢。
Animals such as bats and dolphins use ultrasound for echolocation. They emit high-frequency clicks and interpret the returning echoes to navigate and hunt in complete darkness.
蝙蝠和海豚等动物利用超声波进行回声定位。它们发射高频嘀嗒声，并通过解读返回的回声，在完全黑暗中导航和捕食。
13. The Doppler Effect | 多普勒效应
The Doppler effect is the change in observed frequency of a wave when there is relative motion between the source and the observer. For sound, this is commonly experienced as the change in pitch of an ambulance siren as it passes by.
多普勒效应是指当波源与观察者之间存在相对运动时，观测到的频率发生变化的现象。对于声音，救护车警笛驶过时音调的变化就是一种常见体验。
When the source moves toward the observer, the wavefronts are compressed, leading to a higher observed frequency. When the source moves away, the wavefronts are stretched, producing a lower observed frequency.
当波源向观察者移动时，波前受到压缩，导致观测到的频率升高。当波源远离时，波前被拉伸，从而产生较低的观测频率。
The observed frequency f’ can be calculated using the formula:
观测频率 f’ 可用以下公式计算：
f’ = f (v ± vₒ) / (v ∓ vₛ)
where f is the source frequency, v is the speed of sound in the medium, vₒ is the velocity of the observer (positive if moving towards the source), and vₛ is the velocity of the source (positive if moving towards the observer). The sign conventions ensure that approaching motion increases f’.
其中 f 为波源频率，v 为介质中的声速，vₒ 为观察者的速度（若朝波源移动则取正值），vₛ 为波源的速度（若朝观察者移动则取正值）。符号约定确保相互靠近时 f’ 增大。
If the source speed exceeds the speed of sound, a shock wave is created, resulting in a sonic boom. This occurs when the wavefronts pile up into a cone-shaped shock front.
如果波源速度超过声速，就会产生冲击波，形成音爆。此时波前会堆积成锥形激波前沿。
14. Exam Tips and Common Pitfalls | 考试技巧与常见错误
When tackling sound questions in IB and CCEA exams, always begin by identifying what type of wave you are dealing with—sound is longitudinal, not transverse. Many students lose marks by incorrectly drawing or describing particle motion.
在应对IB和CCEA考试中的声音题目时，首先要明确你面对的是哪种波——声音是纵波，而不是横波。许多学生因错误画出或描述粒子运动而丢分。
Ensure that you can apply the wave equation confidently in both directions. Rearrange v = f λ to find any unknown, and double-check that all units are in metres, hertz, and metres per second.
要能熟练地双向运用波动方程。变换 v = f λ 求解未知量，并仔细检查所有单位是否都统一为米、赫兹和米每秒。
A classic error is confusing pitch and loudness. Pitch is determined by frequency; loudness is related to amplitude and intensity. Explaining this distinction clearly can secure high marks in theory questions.
一个经典错误是混淆音调和响度。音调由频率决定，响度与振幅和强度有关。清楚解释这一区别能在理论题中获得高分。
When discussing echolocation or ultrasound, always mention that the sound pulse must travel to the target and back, so the total distance is twice the
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