IB OCR Science: Sound Revision Notes | IB OCR 科学：声考点精讲

📚 IB OCR Science: Sound Revision Notes | IB OCR 科学：声考点精讲

Sound is a fundamental wave phenomenon tested across both IB and OCR science curricula. Understanding the mechanical, longitudinal nature of sound, its speed in different media, and the relationships between frequency, wavelength, and intensity is essential. This article covers key concepts from wave theory to applications such as ultrasound, the Doppler effect, and standing waves in musical instruments, equipping you with the knowledge needed for top marks in your exams.

声音是 IB 和 OCR 科学课程都会考查的基本波动现象。理解声波的机械纵波本质、在不同介质中的传播速度，以及频率、波长、强度之间的关系至关重要。本文涵盖从波动理论到超声、多普勒效应和乐器驻波等关键概念，帮助你在考试中取得优异成绩。

1. The Nature of Sound Waves | 声波的本质

Sound is a mechanical wave that requires a physical medium (solid, liquid, or gas) to propagate. Unlike electromagnetic waves, sound cannot travel through a vacuum because it relies on particle vibrations to transfer energy.

声音是一种机械波，需要实物介质（固体、液体或气体）才能传播。与电磁波不同，声音不能在真空中传播，因为它依靠粒子振动来传递能量。

Sound waves are produced by vibrating objects, such as vocal cords, loudspeaker cones, or a tuning fork. These vibrations disturb the surrounding medium, creating alternating regions of high and low pressure that travel outwards.

声波由振动的物体产生，例如声带、扬声器振膜或音叉。这些振动扰动周围的介质，形成交替的高压区和低压区，向外传播。

A key point for IB and OCR exams is that sound waves are longitudinal waves: the oscillations of particles are parallel to the direction of energy transfer. This contrasts with transverse waves, where particle motion is perpendicular.

IB 和 OCR 考试的一个关键点是声波属于纵波：粒子的振动方向与能量传播方向平行。这与粒子运动方向垂直于传播方向的横波形成对比。

2. Longitudinal Waves and Compression/Rarefaction | 纵波与疏密部

In a longitudinal sound wave, particles of the medium move back and forth along the wave’s direction. This motion creates compressions (regions of higher pressure and density) and rarefactions (regions of lower pressure and density).

在纵波声波中，介质粒子沿波的传播方向来回运动。这种运动形成压缩区（高压高密度区）和稀疏区（低压低密度区）。

When drawing or interpreting a sound wave graph, it is common to plot pressure or displacement against distance or time. A sinusoidal displacement graph shows compressions at the peaks and rarefactions at the troughs, while a pressure graph typically has maximum pressure at compressions.

在绘制或解读声波图像时，通常绘制压强或位移随距离或时间的变化。正弦位移图中，波峰对应压缩区，波谷对应稀疏区；而压强图通常在压缩区出现最大值。

The wavelength of a sound wave is the distance between two successive compressions or two successive rarefactions. The frequency, measured in hertz (Hz), is the number of complete vibrations per second.

声波的波长是两个相邻压缩区或相邻稀疏区之间的距离。频率以赫兹（Hz）为单位，是每秒完成振动的次数。

3. Speed of Sound and Its Dependence on Medium | 声速及其对介质的依赖

The speed of sound varies widely depending on the medium. In general, sound travels fastest in solids, slower in liquids, and slowest in gases. This is because the speed depends on the stiffness (bulk modulus, B) and density (ρ) of the material.

声速因介质不同而差异很大。一般来说，声音在固体中最快，液体中次之，气体中最慢。这是因为声速取决于材料的刚度（体积模量B）和密度（ρ）。

The theoretical speed of sound in a fluid or solid is given by:

v = √(B/ρ)

Here, B is the bulk modulus, measuring the material’s resistance to compression, and ρ is the density. In air at 20°C, the speed is approximately 343 m/s.

其中B是体积模量，衡量材料抵抗压缩的能力，ρ是密度。在20°C的空气中，声速约为343 m/s。

For air, an empirical formula often used at typical temperatures is:

v ≈ 331 + 0.6T

where T is the temperature in degrees Celsius. This shows that sound moves faster in warmer air because the molecules have greater kinetic energy.

式中T为摄氏温度。这表明声音在较暖的空气中传播更快，因为分子具有更大的动能。

In solids, sound can travel as both longitudinal and transverse waves, with longitudinal speeds typically higher. For example, in steel, the longitudinal speed is around 5000–6000 m/s.

在固体中，声音既可以纵波也可以横波形式传播，纵波速度通常更高。例如，在钢中纵波速度约为5000–6000 m/s。

4. Frequency, Wavelength, and the Wave Equation | 频率、波长与波动方程

The relationship between speed (v), frequency (f), and wavelength (λ) is fundamental to all wave phenomena:

v = fλ

For a given medium, the speed of sound is nearly constant, so frequency and wavelength are inversely proportional. High-frequency sounds have short wavelengths, and low-frequency sounds have long wavelengths.

对于给定介质，声速几乎恒定，因此频率与波长成反比。高频声音波长短，低频声音波长长。

Human hearing typically spans from about 20 Hz to 20 kHz. Frequencies below 20 Hz are called infrasound, while those above 20 kHz are ultrasound. Many animals, such as bats and dogs, can detect ultrasound.

人类听觉范围通常约为20 Hz至20 kHz。低于20 Hz的频率称为次声波，高于20 kHz的称为超声波。蝙蝠和狗等许多动物能探测到超声波。

The wave equation can be used to calculate any one variable if the other two are known. In exam questions, always ensure that units are consistent (e.g., speed in m/s, frequency in Hz, wavelength in m).

如果已知其中两个变量，波动方程可用于计算第三个变量。在考试题目中，务必确保单位一致（如速度用m/s，频率用Hz，波长用m）。

5. Echo, Reflection, and Sonar | 回声、反射与声纳

When sound waves hit a large, hard surface, they are reflected as echoes. For a distinct echo to be heard, the time interval between the original sound and its reflection must be at least 0.1 s, which corresponds to a total path distance of at least 34 m (assuming 340 m/s speed and an obstacle at least 17 m away).

当声波遇到大型硬质表面时，会被反射形成回声。要听到清晰回声，原声与反射声之间的时间间隔至少需要0.1秒，对应总路径至少34 m（假设声速340 m/s，障碍物至少17 m远）。

The principle of echo is used in sonar (Sound Navigation and Ranging) to determine the depth of water or locate objects. A pulse of ultrasound is emitted, and the time taken for the echo to return is measured. The distance d is calculated using:

d = v × t / 2

where v is the speed of sound in water and t is the round-trip time.

回声原理被用于声纳（声音导航与测距），以确定水深或定位物体。发射一个超声波脉冲，测量回声返回的时间。利用公式 d = v × t / 2 计算距离，其中v是水中声速，t是往返时间。

Reflection of sound also explains phenomena like reverberation in large halls and the design of concert venues to optimise acoustics.

声音的反射也可解释大厅中的混响现象以及音乐厅优化声学效果的设计。

6. Pitch, Loudness, and Timbre | 音调、响度与音色

Pitch is the perceptual quality of sound related primarily to frequency. A higher frequency is heard as a higher pitch, and vice versa. However, pitch perception is logarithmic; doubling the frequency corresponds to an octave increase.

音调是与频率主要相关的听觉感知品质。频率越高，听到的音调越高，反之亦然。但音调感知是对数性的；频率加倍对应高一个八度。

Loudness is a subjective sensation that depends on the intensity and the sensitivity of the ear, but it is roughly correlated with the amplitude of the sound wave. Greater amplitude means more energy and generally a louder sound.

响度是一种主观感觉，取决于声强和人耳灵敏度，但它大致与声波的振幅相关。振幅越大，能量越大，通常声音越响。

Timbre (pronounced ‘tam-ber’) is the quality that allows us to distinguish between different sources producing the same pitch and loudness. It is determined by the harmonic content and the envelope of the sound. A violin and a piano playing the same note sound different because of their distinct harmonic spectra.

音色使我们能够区分发出相同音调和响度的不同声源。它由泛音成分和声音的包络决定。小提琴和钢琴演奏同一音符听起来不同，正是由于它们独特的谐波频谱。

7. The Decibel Scale and Sound Intensity | 分贝标度与声强

Sound intensity (I) is the power transmitted per unit area, measured in watts per square metre (W/m²). Because the range of intensities the human ear can detect is enormous (from 10⁻¹² W/m² to over 1 W/m²), a logarithmic decibel scale is used.

声强（I）是每单位面积传递的功率，单位为瓦特/平方米（W/m²）。由于人耳可探测的声强范围极大（从10⁻¹² W/m²到1 W/m²以上），故采用对数标度的分贝尺度。

The sound intensity level L in decibels (dB) is defined by:

L = 10 log₁₀(I / I₀)

where I₀ = 1 × 10⁻¹² W/m² is the threshold of hearing.

其中I₀ = 1 × 10⁻¹² W/m² 是听觉阈值。

Some typical sound levels:

Source	I (W/m²)	L (dB)
Threshold of hearing	10⁻¹²	0
Whisper	10⁻¹⁰	20
Normal conversation	10⁻⁶	60
Heavy traffic	10⁻⁴	80
Rock concert	10⁻¹	110
Threshold of pain	1	120

Because the scale is logarithmic, an increase of 10 dB corresponds to a 10-fold increase in intensity, and an increase of 20 dB corresponds to a 100-fold increase. Hearing protection becomes necessary above about 85 dB.

由于标度是对数的，增加10 dB意味着声强增大10倍，增加20 dB则增大100倍。当声级超过约85 dB时就需要听力保护。

8. Ultrasound and Infrasound | 超声波与次声波

Ultrasound refers to sound with frequencies above the human hearing range (>20 kHz). It has numerous applications: medical imaging (diagnostic ultrasound), breaking up kidney stones (lithotripsy), industrial cleaning, and non-destructive testing by detecting internal flaws in materials.

超声波指频率超过人类听觉范围（>20 kHz）的声音。它有许多应用：医学成像（诊断超声）、击碎肾结石（碎石术）、工业清洗，以及通过探测材料内部缺陷进行无损检测。

In medical ultrasound, a transducer emits high-frequency pulses that reflect off tissues. The time delay and intensity of echoes are used to construct an image. This relies on the principle of reflection and the constant value of speed of sound in soft tissue (~1540 m/s).

在医学超声中，换能器发射高频脉冲，这些脉冲在组织界面反射。通过回声的时间延迟和强度构建图像。这利用了反射原理和软组织中声速的恒定值（约1540 m/s）。

Infrasound, with frequencies below 20 Hz, is produced by natural events like earthquakes, volcanic eruptions, and ocean waves. Some animals (e.g., elephants) use infrasound for long‑distance communication. While inaudible, intense infrasound can cause physical discomfort or resonance in body cavities.

次声波频率低于20 Hz，由地震、火山喷发和海浪等自然事件产生。某些动物（如大象）利用次声波进行远距离交流。尽管听不到，但强烈的次声波可能引起身体不适或体腔共振。

9. The Doppler Effect | 多普勒效应

The Doppler effect is the change in observed frequency when there is relative motion between a sound source and an observer. When the source moves towards the observer, the wavefronts are compressed, resulting in a higher frequency (higher pitch). When it moves away, the wavefronts are stretched, giving a lower frequency (lower pitch).

多普勒效应是指当声源与观察者之间有相对运动时，观测到的频率发生变化的现象。声源向观察者移动时，波前被压缩，导致频率升高（音调变高）；当声源远离时，波前被拉伸，频率降低（音调变低）。

The observed frequency f’ for a stationary observer and moving source is given by:

f’ = f × (v / (v ± vₛ))

where f is the source frequency, v is the speed of sound, and vₛ is the speed of the source. Use minus (–) when the source moves towards the observer, plus (+) when moving away.

其中f是声源频率，v是声速，vₛ是声源速度。声源靠近时用减号（–），远离时用加号（+）。

If both the source and the observer move, the general formula is:

f’ = f × (v ± vₒ) / (v ∓ vₛ)

Here vₒ is the observer’s speed relative to the medium. Use the upper signs when motion reduces separation, and lower signs when it increases separation. These conventions are often examined.

式中vₒ是观察者相对于介质的速度。当运动使距离减小时使用上方的符号，距离增大时使用下方的符号。这些符号规则经常考查。

Applications include radar speed guns, measuring blood flow via Doppler ultrasound, and the red/blue shift of light from stars (though the latter is an electromagnetic analogy).

应用包括雷达测速仪、通过多普勒超声测量血流，以及恒星光线的红移/蓝移（尽管后者是电磁波的类比）。

10. Standing Waves and Resonance in Air Columns | 空气柱中的驻波与共振

When sound waves reflect and interfere inside a confined space such as a pipe, standing waves can form. These are characterised by nodes (points of zero displacement) and antinodes (points of maximum displacement). Resonance occurs when the frequency of the driving source matches a natural frequency of the system.

当声波在管道等受限空间内反射并发生干涉时，会形成驻波。驻波的特征是波节（位移为零的点）和波腹（位移最大的点）。当驱动源的频率与系统的固有频率匹配时，就会发生共振。

For a pipe open at both ends (open pipe), the fundamental frequency corresponds to a standing wave with antinodes at both ends and a node in the middle. The length L of the pipe relates to wavelength by:

L = nλ/2, n = 1, 2, 3, …

For a pipe closed at one end (closed pipe), the closed end is a displacement node and the open end is an antinode. The length condition becomes:

L = (2n – 1)λ/4, n = 1, 2, 3, …

Thus, the fundamental frequency for an open pipe is f = v/(2L), while for a closed pipe it is f = v/(4L). Closed pipes produce only odd harmonics.

因此，开管的基频为f = v/(2L)，而闭管的基频为f = v/(4L)。闭管只产生奇次谐波。

Resonance can be demonstrated using a tuning fork held over a tube partly filled with water. Changing the water level adjusts the air column length, and loudness peaks when the column matches a resonant length.

共振可以用一个音叉放在部分装水的管子上方来演示。改变水位可调节空气柱的长度，当空气柱长度达到共振长度时，声音响度达到峰值。

11. Applications and Musical Instruments | 应用与乐器原理

String instruments (guitar, violin) produce sound from vibrating strings that are fixed at both ends. The frequencies of harmonics follow the relationship for a string:

fₙ = (n / 2L) √(T/μ)

where T is the tension, μ is the linear density (mass per unit length), and n = 1,2,3… This explains why tightening a string (increasing T) raises the pitch, and thinner, lighter strings (lower μ) give higher frequencies.

弦乐器（吉他、小提琴）通过两端固定的弦振动发声。谐频遵循弦的公式：fₙ = (n / 2L) √(T/μ)，其中T是张力，μ是线密度（单位长度质量），n=1,2,3… 这解释了为什么拧紧琴弦（增大T）会提高音调，而较细较轻的琴弦（μ较小）产生更高的频率。

Wind instruments operate on the principle of air column resonance. Brass and woodwind instruments can be modelled as open or closed pipes. Changing the effective length (by valves, slides, or holes) alters the pitch according to the standing-wave formulas.

管乐器基于空气柱共振原理工作。铜管乐器和木管乐器可以模拟为开管或闭管。通过活瓣、滑管或音孔改变有效长度，可根据驻波公式改变音高。

Acoustic engineering uses knowledge of sound reflection, absorption, and resonance to design concert halls with optimal reverberation times and to minimise unwanted echoes.

声学工程利用声音反射、吸收和共振的知识来设计具有最佳混响时间并尽量减少不必要回声的音乐厅。

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IB OCR Science: Sound Revision Notes | IB OCR 科学：声 考点精讲