📚 Sound: Key Concepts for IB & CIE Science | 声：IB CIE 科学考点精讲
Sound is a vibration that propagates as an audible mechanical wave of pressure and displacement, through a medium such as air, water or solids. In IB and CIE science syllabuses, understanding sound involves wave properties, the behaviour of longitudinal waves, the speed of sound in various materials, and phenomena such as interference, resonance and the Doppler effect. This revision guide breaks down each key concept you need to master, providing clear explanations and targeted exam insights.
声音是一种振动，以可听的机械波形式在空气、水或固体等介质中传播的压力和位移变化。在IB和CIE科学课程中，理解声音涉及波动性质、纵波的特性、不同介质中的声速，以及干涉、共振和多普勒效应等现象。这份考点精讲将逐一拆解你需要掌握的关键概念，提供清晰的解释和有针对性的考试洞见。
1. Introduction to Sound Waves | 声波简介
Sound waves are mechanical waves created by vibrating objects. They require a material medium to travel; they cannot propagate through a vacuum. The source of sound sets surrounding particles into oscillation, transferring energy without the net movement of matter. In both IB and CIE exams, you are expected to distinguish between transverse and longitudinal waves, and to classify sound correctly as a longitudinal wave.
声波是由振动物体产生的机械波。它们需要物质介质才能传播，不能在真空中行进。声源使周围的粒子产生振荡，在物质没有净位移的情况下传递能量。在IB和CIE考试中，你需要区分横波和纵波，并正确地将声归类为纵波。
A sound wave consists of alternating regions of compression (higher pressure, where particles are closer together) and rarefaction (lower pressure, where particles are spread apart). These compressions and rarefactions travel outward from the source as a longitudinal wave. Understanding this particle-based model is essential for explaining sound transmission and related calculations.
声波由交替的压缩区（高压区，粒子间距较小）和稀疏区（低压区，粒子间距较大）组成。这些压缩和稀疏以纵波形式从声源向外传播。理解这一基于粒子的模型对于解释声音传播及相关计算至关重要。
- English: Mechanical wave – needs a medium; cannot travel in a vacuum.
- 中文：机械波——需要介质，不能在真空中传播。
- English: Longitudinal wave – particle displacement is parallel to wave direction.
- 中文：纵波——粒子位移方向与波的传播方向平行。
2. Nature of Sound: Longitudinal Waves | 声的本质：纵波
In a longitudinal wave, the particles of the medium vibrate back and forth along the same line as the direction of energy transfer. For sound, this means air molecules oscillate horizontally as the pressure wave passes, creating compressions and rarefactions. You can model this with a slinky spring: pushing and pulling one end creates longitudinal pulses. CIE often asks students to label compressions and rarefactions on a diagram or to interpret oscilloscope traces.
在纵波中，介质粒子沿能量传递的方向来回振动。对于声，这意味着当压力波通过时，空气分子水平振荡，形成压缩和稀疏。你可以用弹簧玩具来模拟：推拉一端会产生纵向脉冲。CIE考试常要求学生在一张图上标注压缩区和稀疏区，或解释示波器上的波形。
While sound in fluids is purely longitudinal, in solids sound waves can also occur as transverse components (e.g. shear waves). For most exam questions at this level, however, treat sound in air as exclusively longitudinal. The oscilloscope display of a sound wave shows a graph of pressure variation against time or displacement against distance – always remember it is a graphical representation, not a picture of the wave itself.
虽然流体中的声波纯粹是纵波，但在固体中声波也可能包含横波分量（例如剪切波）。不过，在这个阶段的考试中，通常将空气中的声视为纯纵波。示波器显示的声波图形是压力随时间或位移随距离变化的图像——请始终记住，这只是图形表示，不是波本身的形态。
3. Wave Properties: Frequency, Wavelength, and Speed | 波的性质：频率、波长和速度
The key quantities describing a sound wave are frequency (f), wavelength (λ), period (T), and speed (v). Frequency is the number of complete vibrations per second, measured in hertz (Hz). The audible range for humans is approximately 20 Hz to 20 000 Hz. Wavelength is the distance between two successive compressions (or rarefactions). These quantities are linked by the wave equation:
描述声波的关键物理量有频率（f）、波长（λ）、周期（T）和波速（v）。频率是每秒完整振动的次数，单位是赫兹（Hz）。人类可听范围大约是20 Hz到20000 Hz。波长是两个相邻压缩区（或稀疏区）之间的距离。这些量由波动方程联系：
v = f × λ
In air at room temperature (about 20 °C), the speed of sound is roughly 340 m s⁻¹. The period T is the time for one full oscillation, and T = 1/f. CIE and IB problems often require you to rearrange the wave equation or to calculate wavelength from frequency and speed, or to estimate distances using echo timing.
在室温空气中（约20°C），声速大约为340 m s⁻¹。周期T是一次全振荡所需的时间，且有T = 1/f。CIE和IB题目常要求你重新排列波动方程，或根据频率和速度计算波长，或利用回声时间估算距离。
| Symbol 符号 | Name 名称 | Unit 单位 |
| v | Speed 波速 | m s⁻¹ |
| f | Frequency 频率 | Hz |
| λ | Wavelength 波长 | m |
| T | Period 周期 | s |
4. The Speed of Sound in Different Media | 不同介质中的声速
The speed of sound depends on the medium’s properties: in general, v is higher in solids than liquids, and higher in liquids than gases. This is because particles in solids are more closely bound, transmitting vibrations more quickly. Elasticity and density are the key factors: sound travels faster in a less dense, more elastic medium. For air, temperature is the main variable; speed increases by about 0.6 m s⁻¹ for each 1 °C rise.
声速取决于介质的性质：一般来说，固体中的声速大于液体，液体中大于气体。这是因为固体中的粒子结合得更紧密，能更快地传递振动。弹性和密度是关键因素：声音在密度较低、弹性较大的介质中传播更快。对于空气，温度是主要变量；每升高1°C，声速约增加0.6 m s⁻¹。
Typical values at 20 °C: air ≈ 343 m s⁻¹; water ≈ 1482 m s⁻¹; steel ≈ 5960 m s⁻¹. In exam questions, you may be asked to explain why sound travels faster in warmer air, or to compare speeds in different materials. Theoretically, the speed of sound in an ideal gas is given by v = √(γRT/M), but this formula is usually only required in IB Higher Level or extended CIE.
20°C时的典型值：空气约为343 m s⁻¹；水约为1482 m s⁻¹；钢约为5960 m s⁻¹。考试中可能要求你解释为什么声音在更热的空气中传播更快，或比较不同材料中的声速。理论上，理想气体中的声速由 v = √(γRT/M) 给出，但该公式通常只在IB高等级或CIE扩展中出现。
5. Reflection and Echo | 反射与回声
Sound waves obey the law of reflection: the angle of incidence equals the angle of reflection. When a sound wave strikes a large, hard surface, it reflects, producing an echo if the reflected sound is heard with a sufficient time delay. For a distinct echo, the human ear typically needs a time gap of at least 0.1 s between the original and reflected sound. This corresponds to a minimum distance to the reflecting surface of around 17 m (since speed = distance/time, total path difference ≈ 34 m, so one-way ≈ 17 m).
声波遵守反射定律：入射角等于反射角。当声波遇到大而硬的分表面时，会发生反射，如果反射声与直达声之间有足够的时间间隔，就会产生回声。人耳通常需要至少0.1秒的时间差才能分辨出清晰回声。这对应的反射面最小距离约为17米（因为速度=距离/时间，往返路径差≈34 m，单程≈17 m）。
Echoes are used in sonar, echolocation by bats, and medical ultrasound imaging. CIE questions frequently involve calculating distances using the echo formula: distance = (v × t) / 2, where t is the round-trip time. Always remember to halve the total distance for the one-way distance. Reflection can also lead to reverberation in concert halls, which is managed by sound-absorbing materials.
回声被应用于声呐、蝙蝠的回声定位和医学超声成像。CIE考题经常涉及使用回声公式计算距离：距离 = (v × t) / 2，其中t为往返时间。请始终记得将总距离除以2以获得单向距离。反射也可能导致音乐厅中的混响，这可以通过吸声材料来控制。
6. Refraction and Diffraction of Sound | 声的折射与衍射
Refraction of sound occurs when a wave changes speed due to a change in the medium or a change in the properties of the same medium (e.g., temperature gradients in air). Sound bends towards cooler regions where it travels slower. At night, sound can be heard over longer distances because the ground is cooler than the air above, bending sound waves downward. In exams, you may need to interpret diagrams showing wavefronts bending due to a temperature gradient.
声的折射发生在波因介质改变或同一介质性质变化（如空气中的温度梯度）而改变速度时。声音会向传播较慢的较冷区域弯曲。夜晚，声音能传播到更远的距离，因为地面比上方的空气冷，导致声波向下弯曲。考试中可能需要你解释波前因温度梯度而弯曲的图示。
Diffraction is the spreading of sound waves around obstacles or through gaps. Significant diffraction occurs when the wavelength is comparable to or larger than the obstacle or aperture size. Low-frequency (long wavelength) sounds diffract more noticeably than high-frequency sounds – this is why you can hear the bass of a distant speaker even when you cannot see it. CIE may ask you to draw wavefronts around edges or to explain why you can hear around a corner.
衍射是声波绕过障碍物或穿过缝隙时扩展的现象。当波长与障碍物或开口尺寸相当或更大时，衍射效果显著。低频（长波长）声音的衍射比高频声音更明显——这就是为什么远处音响的低音你听得见却看不见声源。CIE可能要求你画出围绕边缘的波前图，或解释为什么在转角处也能听到声音。
7. Interference and Beats | 干涉与拍频
When two sound waves of the same frequency and a constant phase relationship overlap, they interfere constructively (louder) or destructively (softer) depending on their path difference. This produces a stationary pattern of loud and quiet regions. In the lab, this is often demonstrated with two speakers connected to the same signal generator, or with a tuning fork moved near a wall. IB students learn about double-source interference and the condition for constructive interference: path difference = nλ; destructive: path difference = (n + ½)λ.
当两个频率相同且相位关系恒定的声波相遇时，它们会根据程差产生相长干涉（更响）或相消干涉（更轻）。这会形成一种静止的响区和静区图案。实验室中通常用连接到同一信号发生器的两个扬声器来演示，或用音叉靠近墙壁移动。IB学生学习双源干涉，相长干涉的条件是程差 = nλ；相消干涉的条件是程差 = (n + ½)λ。
Beats occur when two waves of slightly different frequencies interfere. The resulting sound alternates in loudness at a frequency equal to the difference between the two frequencies. This beat frequency f_beat = |f₁ – f₂|. Beats are used by musicians to tune instruments: when the beat frequency falls to zero, the two notes are in tune. IB and CIE often include beat-frequency calculations or ask you to explain why beats disappear when frequencies match.
当两个频率略有不同的波干涉时，会产生拍频。合成的声音响度以等于两频差的频率周期性变化。拍频 f_beat = |f₁ – f₂|。音乐家利用拍频来调音：当拍频降至零时，两个音高一致。IB和CIE常包含拍频计算，或要求解释为什么当频率一致时拍频消失。
8. 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 (units: W m⁻²). The human ear can detect a huge range of intensities, from about 10⁻¹² W m⁻² (threshold of hearing) to 1 W m⁻² or more (pain threshold). To manage this range, the decibel (dB) scale is used, which is logarithmic. The sound intensity level in dB is given by:
声强（I）是波携带的每单位面积上的功率（单位：W m⁻²）。人耳可探测的声强范围极大，从约10⁻¹² W m⁻²（听觉阈）到1 W m⁻²或更高（痛觉阈）。为处理这一宽范围，使用分贝（dB）标度，它是对数标度。以分贝为单位的声强级由下式给出：
β = 10 log₁₀ (I / I₀)
where I₀ = 1 × 10⁻¹² W m⁻² is the reference intensity. 其中 I₀ = 1 × 10⁻¹² W m⁻² 是基准声强。
A doubling of sound intensity corresponds to an increase of about 3 dB, while a tenfold increase in intensity adds 10 dB. CIE and IB exam questions often require you to calculate intensity or intensity level, or to compare loudness in terms of dB differences. Remember that perceived loudness also depends on frequency; the ear is most sensitive around 3 kHz. Digital sound level meters approximate the ear’s response using frequency weighting (A-weighting).
声强加倍对应约3 dB的增加，声强变为原来的10倍则增加10 dB。CIE和IB的考试题经常要求计算声强或声强级，或根据分贝差异比较响度。记住，感知响度还取决于频率；人耳对约3千赫兹的声音最敏感。数字声级计使用频率加权（A计权）来近似人耳的响应。
9. Standing Waves and Resonance | 驻波与共振
Standing waves form when an incident wave and its reflection superpose in a bounded medium, such as a string, an open pipe, or a pipe closed at one end. In musical instruments, standing sound waves determine the pitch. For a string fixed at both ends, harmonics follow: fₙ = n(v/2L), with n = 1,2,3… For a pipe open at both ends, the same formula applies, where v is the speed of sound and L is the pipe length. For a pipe closed at one end, only odd harmonics exist: fₙ = n(v/4L), n = 1,3,5… .
当入射波与其反射波在有限介质（如弦、开管或一端封闭的管）中叠加时，会形成驻波。在乐器中，驻波的声音决定了音高。对于两端固定的弦，谐波遵循：fₙ = n(v/2L)，n = 1,2,3…。对于两端打开的开管，公式相同，其中v是声速，L是管长。对于一端封闭的管，只有奇次谐波：fₙ = n(v/4L)，n = 1,3,5…。
Resonance occurs when an object is forced to vibrate at its natural frequency, causing a dramatic increase in amplitude. Pushing a swing in time, shattering a glass with a singer’s voice, and the vibration of an air column in a tube are all examples. In a tube closed at one end, resonance happens when the length of the air column is an odd multiple of quarter-wavelengths. Typical exam questions involve using a tuning fork over a graduated cylinder to find the speed of sound via resonance positions.
共振发生在物体被迫以其固有频率振动时，导致振幅急剧增大。按节拍推秋千、歌唱声音震碎玻璃杯、管内空气柱的振动都是例子。在一端封闭的管中，当空气柱长度为四分之一波长的奇数倍时会发生共振。典型考题包括用音叉在有刻度的圆筒上方通过共振位置求声速。
10. Doppler Effect | 多普勒效应
The Doppler effect is the change in observed frequency when a source of sound moves relative to an observer. If source and observer approach each other, the observed frequency is higher (pitch sounds higher). If they recede, frequency is lower. The general equation for a moving source and stationary observer is:
多普勒效应是当声源与观察者相对运动时，观察频率发生变化的现象。如果声源和观察者互相靠近，则观察频率更高（音调听起来更高）。如果它们远离，频率变低。对于运动的声源和静止观察者，一般方程为：
f’ = f × (v / (v ± v_s))
where v is the speed of sound, v_s is the speed of the source, and the sign is minus for approaching, plus for receding. IB Higher Level requires using this equation. CIE usually expects a qualitative understanding or simple calculations based on the relative motion.
其中 v 是声速，v_s 是声源速度，当声源靠近时取减号，远离时取加号。IB高等级要求使用该方程。CIE通常期望定性理解或基于相对运动的简单计算。
Applications include the siren of a passing ambulance (pitch drops), radar speed guns, and the redshift of light from distant galaxies (which also exhibits a Doppler effect for electromagnetic waves). When both source and observer move, the formula becomes more complex, but the principle remains the same. Be careful with sign conventions: draw a clear diagram and define the positive direction.
应用包括经过的救护车警报声（音调下降）、雷达测速枪，以及遥远星系的光线红移（电磁波也呈现多普勒效应）。当声源和观察者都运动时，公式会更复杂，但原理相同。注意符号约定：画出清晰的示意图并规定正方向。
11. Ultrasound and its Applications | 超声波及其应用
Ultrasound is sound with frequencies above 20 000 Hz, beyond the human audible range. It has the same physical properties as audible sound but has several practical advantages: it can be focused into narrow beams, it reflects well from boundaries between different media, and it does not cause hearing disturbance. In medical imaging, ultrasound pulses are sent into the body, and the echoes are used to form images of soft tissues, such as a fetus in the womb.
超声波是指频率高于20 000 Hz的声音，超出人类可听范围。它与可听声具有相同的物理性质，但有若干实用优势：可聚焦成窄束，在不同介质的分界面反射良好，且不会引起听觉干扰。在医学成像中，超声波脉冲发射到体内，通过回声形成软组织的图像，如子宫中的胎儿。
Industrial applications include flaw detection in materials, cleaning delicate objects, and measuring thickness. Bats and dolphins use ultrasound for echolocation. In an exam, you might be asked to calculate the distance to an object using ultrasound echo time, or to explain why high frequencies give better resolution. Also note that ultrasound can cause cavitation, which is used in cleaning and lithotripsy (breaking kidney stones).
工业应用包括材料缺陷检测、精密物体的清洗和厚度测量。蝙蝠和海豚使用超声波进行回声定位。考试中可能要求你利用超声回声时间计算到物体的距离，或解释为什么高频能提供更好的分辨率。还需注意，超声可引起空化效应，用于清洗和碎石术（击碎肾结石）。
12. Exam Tips and Common Misconceptions | 考试技巧与常见误区
Many students confuse the oscilloscope trace of a sound wave with a diagram of a longitudinal wave. Remember: the trace shows pressure variation or displacement against time – it looks like a transverse wave but still represents a longitudinal sound wave. Never claim ‘sound is a transverse wave because the trace shows peaks and troughs’. Make sure to label compressions and rarefactions correctly on diagrams.
许多学生将声波的示波器波形与纵波图相混淆。请记住：波形显示的是压力或位移随时间的变化——它看起来像横波，但仍表示纵波的声音。绝不能说“因为波形有波峰和波谷，所以声音是横波”。请确保在图中正确标出压缩区和稀疏区。
Common calculation pitfalls include forgetting to halve the distance in echo problems, using the wrong sign in Doppler equations, or mixing up frequency and period. Always convert units to SI (metres, seconds, hertz) before substituting into formulas. When interpreting intensity levels in dB, recall that every 10 dB increase means a tenfold intensity increase, not a doubling. And for standing waves, a pipe closed at one end only has odd harmonics; do not try to fit even harmonics there.
常见的计算陷阱包括：在回声问题中忘记将距离除以2，在多普勒方程中使用错误的正负号，或混淆频率和周期。在代入公式前，始终将单位转换为国际单位制（米、秒、赫兹）。在解释分贝的声强级时，记住每增加10 dB意味着声强变为10倍，而不是两倍。对于驻波，一端封闭的管只有奇次谐波；不要在那里试图套用偶次谐波。
Finally, practice drawing and interpreting wavefront diagrams for reflection, refraction, and diffraction. These visual questions are common in CIE papers. For IB, ensure you can derive or apply the standing wave formulas and understand the nature of sound propagation. Review the environmental impact of noise pollution and how sound intensity decreases with distance from a point source (inverse square law, I ∝ 1/r²).
最后，练习绘制和解释反射、折射和衍射的波前图。这些视觉题在CIE试卷中很常见。对于IB，确保你能推导或应用驻波公式，并理解声音传播的本质。复习噪声污染的环境影响，以及声强如何随点声源距离的增加而减小（平方反比定律，I ∝ 1/r²）。
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