IB Edexcel Science: Sound Exam Essentials | IB Edexcel 科学：声 考点精讲

📚 IB Edexcel Science: Sound Exam Essentials | IB Edexcel 科学：声 考点精讲

Sound is a fundamental topic in both IB and Edexcel physics, bridging wave theory, human perception, and real-world applications. This revision guide consolidates the essential concepts you need to master—from the nature of longitudinal waves and the speed equation to decibel scales, standing waves in instruments, and the Doppler effect. Each section pairs concise explanations with bilingual paragraphs to support learners preparing for international science examinations.

声学是 IB 和 Edexcel 物理课程中的基础主题，连接了波动理论、人类感知和实际应用。本复习指南整合了你需要掌握的关键概念——从纵波的本质和声速方程，到分贝标度、乐器中的驻波以及多普勒效应。每个小节都提供简洁的中英双语配对段落，帮助学习者备战国际科学考试。

1. What is Sound? | 什么是声音？

Sound is a mechanical wave that transfers energy through the vibration of particles in a medium such as air, water, or solids. Unlike electromagnetic waves, sound cannot travel through a vacuum because it requires particles to propagate the disturbance. When a source vibrates, it causes compressions and rarefactions in the surrounding medium, creating alternating regions of high and low pressure that travel outward as a longitudinal wave.

声音是一种机械波，通过空气、水或固体等介质中粒子的振动来传递能量。与电磁波不同，声音不能在真空中传播，因为它需要粒子来传递扰动。当声源振动时，会使周围介质产生疏密相间的区域——压缩和稀疏，这些交替的高压和低压区域以纵波的形式向外传播。

Everyday examples of sound sources include vocal cords, loudspeaker cones, and musical instruments. The frequency of the vibration determines the pitch we perceive, while the amplitude relates to loudness. Understanding that sound is a pressure wave is the first step toward mastering wave equations and acoustics.

声源的常见例子包括声带、扬声器振膜和乐器。振动的频率决定我们感知到的音调高低，而振幅与响度有关。理解声音是一种压力波是掌握波动方程和声学的第一步。

2. Sound as a Longitudinal Wave | 声波是纵波

A longitudinal wave is one in which particles oscillate parallel to the direction of energy transfer. In the case of sound, air molecules move back and forth along the path of the wave, creating compressions (regions of high pressure) and rarefactions (regions of low pressure). This is distinct from transverse waves, such as light or water ripples, where particle displacement is perpendicular to wave travel.

纵波是粒子振动方向与能量传播方向平行的波。对于声波，空气分子沿波的传播路径来回运动，形成压缩区（高压区域）和稀疏区（低压区域）。这与横波（如光波或水波涟漪）不同，在横波中粒子的位移方向与波的传播方向垂直。

On an oscilloscope, a sound wave is often displayed as a sinusoidal graph of pressure variation against time. This graphical representation makes it easier to measure amplitude, period, and frequency. Remember that the distance between two consecutive compressions or two consecutive rarefactions equals one wavelength.

在示波器上，声波通常显示为气压随时间变化的正弦曲线图。这种图形表示使得测量振幅、周期和频率更加方便。记住，两个相邻压缩区或两个相邻稀疏区之间的距离等于一个波长。

Particle vibration direction ∥ wave propagation direction

3. Speed of Sound | 声速

The speed of sound v depends on the medium and its physical properties. In general, sound travels fastest in solids, slower in liquids, and slowest in gases. This is because particles are more tightly packed in solids, allowing vibrations to be transmitted more quickly. The speed of sound in air at room temperature is approximately 343 m s⁻¹. It increases with temperature and is also affected by humidity.

声速 v 取决于介质及其物理性质。一般来说，声音在固体中传播最快，液体中次之，气体中最慢。这是因为固体中的粒子排列更紧密，使得振动能够更快地传递。室温下声音在空气中的传播速度约为 343 m s⁻¹。声速随温度升高而增加，也受湿度影响。

The fundamental wave equation links speed, frequency, and wavelength: v = f λ. For a given medium, frequency and wavelength are inversely related. When sound passes from one medium to another, its frequency remains constant (determined by the source), but its wavelength changes, resulting in a change in speed.

基本波动方程将速度、频率和波长联系起来：v = f λ。对于给定的介质，频率和波长成反比关系。当声音从一种介质进入另一种介质时，频率保持不变（由声源决定），但波长发生变化，从而导致速度改变。

v = f λ

In exam questions, you will often calculate wavelength or frequency using this relationship. Be careful with units: speed in metres per second, frequency in hertz (Hz), and wavelength in metres.

考试题目中，你常常会用这个关系式计算波长或频率。注意单位：速度单位为米每秒，频率单位为赫兹（Hz），波长单位为米。

4. Frequency, Wavelength, and Amplitude | 频率、波长与振幅

Frequency (f) is the number of complete oscillations per second, measured in hertz (Hz). The audible range for humans is typically 20 Hz to 20 000 Hz. Wavelength (λ) is the spatial period of the wave—the distance between two points in phase, such as compression to compression. Amplitude is the maximum displacement of particles from their equilibrium position and is linked to the energy carried by the wave: a larger amplitude means a louder sound.

频率（f）是每秒完整振动的次数，以赫兹（Hz）为单位。人类的听觉范围通常为 20 Hz 到 20 000 Hz。波长（λ）是波的空间周期——两个同相点之间的距离，例如从压缩区到压缩区。振幅是粒子偏离其平衡位置的最大位移，与波携带的能量有关：振幅越大，声音越响。

On a pressure-time graph, frequency is the inverse of period (T): f = 1/T. Amplitude is the peak value of pressure variation. When studying sound, it is crucial to distinguish between the physical quantity (amplitude) and the perceptual quality (loudness), and similarly between frequency and pitch. Pitch increases with frequency, but the relationship is not strictly linear due to the ear’s response.

在压力-时间图上，频率是周期（T）的倒数：f = 1/T。振幅是压力变化的峰值。学习声音时，区分物理量（振幅）和感知质量（响度）以及频率和音调之间的关系至关重要。音调随频率升高而升高，但由于人耳的响应特性，这种关系并非严格线性。

5. Sound Intensity and the Decibel Scale | 声强与分贝标度

Sound intensity I is the power per unit area carried by a wave, measured in watts per square metre (W m⁻²). For a point source radiating uniformly, intensity follows the inverse square law: I = P / (4πr²), where P is the power of the source and r is the distance from it. Doubling the distance reduces intensity to one quarter.

声强 I 是波在单位面积上传输的功率，单位为瓦特每平方米（W m⁻²）。对于均匀辐射的点声源，声强遵循平方反比定律：I = P / (4πr²)，其中 P 是声源的功率，r 是到声源的距离。距离加倍时，声强减小为原来的四分之一。

The human ear perceives intensity on a logarithmic scale, so we use the decibel (dB) scale. The sound level β in decibels is defined as: β = 10 log₁₀ (I / I₀), where I₀ = 1.0 × 10⁻¹² W m⁻² is the threshold of hearing. A sound of 0 dB is barely audible, while 120 dB causes pain. Common exam tasks involve comparing intensities given decibel differences: a 10 dB increase means intensity is multiplied by 10.

人耳以对数标度感知声强，因此我们采用分贝（dB）标度。声级 β 的定义为：β = 10 log₁₀ (I / I₀)，其中 I₀ = 1.0 × 10⁻¹² W m⁻² 是可听阈值。0 dB 的声音几乎听不见，而 120 dB 会引起痛感。常见的考试题型涉及根据分贝差值比较强度：声级每增加 10 dB，强度增大 10 倍。

β = 10 log₁₀ (I / I₀)

6. The Human Ear and Hearing Range | 人耳与听觉范围

The human ear converts pressure variations in air into electrical signals interpreted by the brain. The outer ear collects sound and directs it to the eardrum, causing it to vibrate. These vibrations are transmitted through the middle ear bones to the cochlea in the inner ear, where hair cells trigger nerve impulses. The frequency range of healthy human hearing declines with age, particularly at high frequencies.

人耳将空气中的气压变化转换成大脑解读的电信号。外耳收集声音并将其引导到鼓膜，使鼓膜振动。这些振动通过中耳的听小骨传递到内耳的耳蜗，耳蜗内的毛细胞触发神经冲动。健康人耳的听力频率范围会随年龄增长而缩小，特别是高频部分。

Infrasound refers to sound waves with frequencies below 20 Hz, and ultrasound refers to frequencies above 20 kHz. Animals such as dogs and bats can detect ultrasound, which is used for echolocation. In medicine and industry, ultrasound has numerous applications, including imaging and cleaning.

次声波指频率低于 20 Hz 的声音，超声波指频率高于 20 kHz 的声音。狗和蝙蝠等动物能够探测超声波，用于回声定位。在医学和工业中，超声波有众多应用，包括成像和清洗。

7. Ultrasound and Its Applications | 超声波及其应用

Ultrasound waves are high-frequency sound waves beyond the range of human hearing. They obey the same wave principles, including reflection and refraction at boundaries. One major application is medical sonography, where pulses of ultrasound are sent into the body, and the reflected echoes are used to form images of internal organs or a fetus. The time delay and intensity of echoes provide information about tissue depth and density.

超声波是超出人耳听觉范围的高频声波。它们遵循相同的波动原理，包括在界面处的反射和折射。一个重要应用是医学超声检查，向体内发射超声波脉冲，反射回波用于生成内脏器官或胎儿的图像。回声的时间延迟和强度提供了关于组织深度和密度的信息。

In industry, ultrasound is used for flaw detection in metals and for cleaning delicate items. The formula d = v × t / 2 is essential for echo-ranging problems, where d is distance to the reflecting surface, v is the speed of sound in the medium, and t is the round-trip time. Make sure you understand the factor of 1/2 when solving such problems.

在工业中，超声波用于金属探伤和精密物品清洗。公式 d = v × t / 2 对于回声定位问题至关重要，其中 d 是到反射面的距离，v 是介质中的声速，t 是往返时间。在解决这类问题时，确保你理解 1/2 因子的意义。

8. Reflection, Refraction, and Diffraction of Sound | 声波的反射、折射和衍射

Sound waves obey the same boundary behaviors as all waves. Reflection occurs when sound hits a hard surface, giving rise to echoes. The law of reflection applies: angle of incidence equals angle of reflection. Smooth, large surfaces produce clear echoes, while rough surfaces scatter sound, reducing reverberation.

声波遵循与所有波相同的边界行为。当声音遇到硬表面时会发生反射，产生回声。反射定律适用：入射角等于反射角。光滑的大表面产生清晰的回声，而粗糙的表面散射声音，减少混响。

Refraction happens when sound travels from one medium into another with different speeds, or when air temperature layers change. At night, sound may bend downwards due to cooler air near the ground, allowing distant sounds to be heard more clearly. Diffraction is the spreading of sound around obstacles and through openings. Because sound wavelengths are relatively long (from a few centimetres to several metres), diffracted sound can be heard even when a source is behind a barrier, which is why you can hear someone speaking in a room before you see them.

当声音从一个介质进入速度不同的另一个介质时，或当空气温度层变化时，会发生折射。夜间，由于近地面空气较冷，声音可能向下弯曲，使远处的声音听得更清楚。衍射是声音绕过障碍物和穿过开口时的弯曲现象。由于声波波长相对较长（从几厘米到几米），即便声源在障碍物后方，你也能听到衍射声，这就是为什么你能在看见一个人之前先听到他在房间里说话。

9. Interference of Sound Waves | 声波的干涉

When two sound waves of similar frequency and constant phase difference meet, they superpose to produce interference. Constructive interference occurs when compressions meet compressions, leading to an increased amplitude and a louder sound. Destructive interference occurs when compression meets rarefaction, resulting in reduced amplitude or even silence. This phenomenon can be demonstrated with two loudspeakers connected to the same signal generator.

当两列频率相近、相位差恒定的声波相遇时，它们叠加产生干涉。当压缩区遇到压缩区时，发生相长干涉，振幅增大，声音更响。当压缩区遇到稀疏区时，发生相消干涉，振幅减小甚至消声。这一现象可以用两个连接到同一信号发生器的扬声器来演示。

Path difference plays a key role: constructive interference requires a path difference of nλ (n = 0,1,2,…), while destructive interference requires (n + ½)λ. In exam questions, you may be asked to predict sound-level changes at different positions in a room. Beats are a special case of interference in time, where two slightly different frequencies produce a periodically varying loudness; the beat frequency is |f₁ – f₂|.

波程差起着关键作用：相长干涉需要波程差为 nλ（n = 0,1,2,…），而相消干涉需要 (n + ½)λ。考试题目可能要求你预测房间内不同位置的声级变化。拍是一种特殊的时间干涉现象，两个频率略有不同的声波会产生周期性变化的响度；拍频为 |f₁ – f₂|。

10. Standing Waves in Strings | 弦上的驻波

A standing wave forms when two identical waves travel in opposite directions along a string and superpose. For a string fixed at both ends (e.g., guitar, violin), the ends must be nodes (points of zero displacement). The fundamental frequency f₁ corresponds to the simplest standing wave pattern: length L = λ/2, so λ = 2L. Using v = fλ, the fundamental frequency is f₁ = v/(2L) where v is the wave speed on the string.

当两列相同的波沿弦向相反方向传播并叠加时，会形成驻波。对于两端固定的弦（如吉他、小提琴），两端必须是波节（位移为零的点）。基频 f₁ 对应最简单的驻波图样：长度 L = λ/2，因此 λ = 2L。利用 v = fλ，基频为 f₁ = v/(2L)，其中 v 是弦上的波速。

Higher harmonics are multiples of the fundamental: f₂ = 2f₁, f₃ = 3f₁, etc. These are called the second harmonic, third harmonic, etc. The wavelength for the nth harmonic is λₙ = 2L/n. The wave speed v on a stretched string is given by v = √(T/μ), where T is the tension and μ is the linear mass density (mass per unit length). This formula explains why tightening a string raises pitch and using a thicker string lowers it.

更高的谐波是基频的整数倍：f₂ = 2f₁，f₃ = 3f₁，等等。这些分别称为第二谐波、第三谐波等。第 n 次谐波的波长为 λₙ = 2L/n。拉紧弦上的波速由 v = √(T/μ) 给出，其中 T 是张力，μ 是线密度（单位长度的质量）。这个公式解释了为什么拧紧琴弦会提高音调，而使用较粗的弦则会降低音调。

fₙ = n v/(2L), λₙ = 2L/n (n = 1,2,3,…)

11. Standing Waves in Pipes | 管中的驻波

Wind instruments rely on standing waves formed in air columns. For a pipe open at both ends, both ends are antinodes (points of maximum displacement). The fundamental mode has wavelength λ = 2L, giving f₁ = v/(2L). The harmonics follow fₙ = n f₁, with n = 1,2,3…, just like a string fixed at both ends, but with displacement antinodes at the ends instead of nodes.

管乐器依靠气柱中形成的驻波工作。对于两端开口的管子，两端都是波腹（最大位移点）。基模的波长为 λ = 2L，得出 f₁ = v/(2L)。谐波遵循 fₙ = n f₁，n = 1,2,3…，这与两端固定的弦类似，不过两端是位移波腹而不是波节。

For a pipe closed at one end (stopped pipe), the closed end is a node and the open end is an antinode. The fundamental mode requires L = λ/4, so λ = 4L and f₁ = v/(4L). Only odd harmonics are present: f₁, 3f₁, 5f₁, … because the open end must be an antinode and the closed end a node. This results in a different timbre compared to an open pipe.

对于一端封闭的管子（闭端管），闭端是波节，开口端是波腹。基模要求 L = λ/4，因此 λ = 4L，f₁ = v/(4L)。只存在奇次谐波：f₁, 3f₁, 5f₁, … 因为开口端必须是波腹，闭端必须是波节。这与开口管相比产生不同的音色。

Open pipe: fₙ = n v/(2L), n=1,2,3… Closed pipe: fₙ = n v/(4L), n=1,3,5…

12. Resonance | 共振

Resonance occurs when an object is forced to vibrate at its natural frequency by an external periodic driving force, resulting in a dramatic increase in amplitude. A classic demonstration is the resonance tube experiment, where a tuning fork is held over a cylinder of water with an adjustable air column length. As the column length is varied, the loudness jumps sharply when the air column’s natural frequency matches the fork’s frequency, forming a standing wave.

当物体受到与其固有频率相同的外部周期性驱动力作用时，会发生共振，导致振幅急剧增大。一个经典的演示实验是共振管实验：将音叉放在一个可调节气柱长度的水柱上方，当气柱长度变化到其固有频率与音叉频率相匹配时，响度急剧增大，形成驻波。

The condition for resonance in a closed pipe (air column closed at one end by water) is that the length L satisfies L = (2n-1)λ/4, for n = 1,2,3… Minimum resonating length gives L = λ/4. By measuring the lengths for successive resonances, you can determine the wavelength of the sound and hence speed using v = fλ. Resonance also explains why soldiers break step when marching across a bridge—to avoid matching the bridge’s natural frequency and causing destructive vibrations.

闭端管（一端被水封闭的气柱）的共振条件是长度 L 满足 L = (2n-1)λ/4，n = 1,2,3… 最小共振长度给出 L = λ/4。通过测量连续共振的长度，可以确定声波的波长，进而用 v = fλ 求出声速。共振也解释了为什么士兵过桥时要便步走——避免步伐频率与桥的固有频率匹配而引起破坏性振动。

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, the perceived pitch is higher when the source approaches and lower when it recedes. The general formula for a source moving with speed vₛ relative to a stationary observer in a medium (sound speed v) is: f’ = f (v / (v ± vₛ)), where the minus sign is used when the source moves toward the observer, and the plus sign when moving away. If the observer moves, the formula adjusts accordingly.

多普勒效应是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，当声源靠近时感知到的音调变高，远离时变低。对于在介质（声速 v）中以速度 vₛ 运动的声源和静止的观察者，一般公式为：f’ = f (v / (v ± vₛ))，当声源朝观察者运动时用减号，远离时用加号。如果观察者运动，公式相应调整。

Applications of the Doppler effect include radar speed guns, medical blood-flow measurement (Doppler ultrasonography), and astronomy (redshift/blueshift of light, which is a consequence of wave theory extended to electromagnetic waves). For sound, a familiar example is the changing pitch of a siren as an ambulance passes by. In IB and Edexcel exams, you might need to derive the frequency shift qualitatively or calculate the observed frequency for simple cases.

多普勒效应的应用包括雷达测速枪、医学血流测量（多普勒超声）以及天文学（光波的红移/蓝移，这是波动理论在电磁波中的延伸）。对于声音，熟悉的例子是救护车经过时警笛音调的变化。在 IB 和 Edexcel 考试中，你可能需要定性地推导频率变化，或者计算简单情况下的观测频率。

f’ = f × (v / (v − vₛ)) for source moving towards observer

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