A-Level Physics: Sound | A-Level 物理：声考点精讲

📚 A-Level Physics: Sound | A-Level 物理：声考点精讲

Sound waves are a fundamental topic in A-Level Physics, exploring how mechanical vibrations travel through media, produce audible sensations, and exhibit wave phenomena such as interference, resonance, and the Doppler effect. This revision guide covers all essential concepts, equations, and applications you need to master for your exams.

声波是A-Level物理的基础课题，探索机械振动如何在介质中传播、产生听觉，并表现出干涉、共振和多普勒效应等波动现象。本考点精讲涵盖你需要掌握的所有核心概念、方程式和应用。

1. Nature of Sound Waves | 声波的本质

Sound is a longitudinal mechanical wave that requires a medium (solid, liquid, or gas) to propagate. It consists of compressions (high-pressure regions) and rarefactions (low-pressure regions). Unlike electromagnetic waves, sound cannot travel through a vacuum.

声音是一种纵波，需要介质（固体、液体或气体）才能传播。它由疏密相间的压缩区（高压区域）和稀疏区（低压区域）组成。与电磁波不同，声音不能在真空中传播。

The audible range for humans is typically from 20 Hz to 20,000 Hz. Frequencies below this range are infrasound, and those above are ultrasound, both of which have important practical applications.

人类的可听范围通常在20赫兹到20,000赫兹之间。低于此范围的为次声波，高于此范围的为超声波，两者都有重要的实际应用。

2. Wave Equation and the Speed of Sound | 波动方程与声速

The wave equation v = f λ relates the speed of sound (v), frequency (f), and wavelength (λ). For sound waves, the speed depends on the medium and its properties, such as density and temperature.

波动方程 v = f λ 关联声速 (v)、频率 (f) 和波长 (λ)。对于声波，速度取决于介质及其属性，如密度和温度。

v = f λ

In air, the speed of sound is approximately 340 m/s at room temperature, and it increases by about 0.6 m/s for each degree Celsius rise: v = 331 + 0.6T (with T in °C).

在空气中，室温下声速约为340米/秒，且温度每升高1摄氏度约增加0.6米/秒：v = 331 + 0.6T (T 以°C计)。

v = 331 + 0.6T

3. Characteristics of Sound: Pitch, Loudness, and Timbre | 声的特性：音调、响度与音色

The pitch of a sound is determined by its frequency: a higher frequency produces a higher pitch. Loudness is related to the amplitude of the wave; a greater amplitude results in a louder sound. Timbre (quality) depends on the waveform and harmonic content, allowing us to distinguish different instruments playing the same note.

声音的音调由其频率决定：频率越高，音调越高。响度与声波的振幅有关；振幅越大，声音越响。音色（品质）取决于波形和谐波成分，使我们能够区分演奏同一音符的不同乐器。

A pure tone is represented by a sinusoidal waveform on an oscilloscope. Complex sounds, such as musical instruments, combine a fundamental frequency with overtones or harmonics, producing a distinctive pattern.

纯音在示波器上表现为正弦波形。复杂的声音，如乐器声，结合了基频和泛音或谐波，产生独特的波形图谱。

4. Superposition and Interference of Sound | 声的叠加与干涉

When two or more sound waves meet, they superpose. Constructive interference occurs when waves are in phase (path difference = nλ), resulting in increased amplitude. Destructive interference occurs when they are out of phase (path difference = (n+½)λ), leading to reduced or zero amplitude.

当两个或多个声波相遇时会发生叠加。同相波叠加（路径差 = nλ）产生相长干涉，振幅增大；反相波叠加（路径差 = (n+½)λ）产生相消干涉，振幅减小或为零。

Δx = nλ (constructive), Δx = (n + ½)λ (destructive)

A common demonstration uses two loudspeakers connected to the same signal generator. Moving a microphone along a line reveals alternating loud and quiet zones due to interference.

常见的演示是使用连接到同一信号发生器的两个扬声器。沿线移动麦克风会因干涉而出现交替的响区和静区。

5. Standing Waves in Strings | 弦中的驻波

When a string is fixed at both ends and vibrated, standing waves are formed with nodes (zero displacement) at the ends and antinodes (maximum displacement) in between. The fundamental frequency is f₁ = v/(2L), where v is the wave speed on the string and L is the length.

当一根两端固定的弦振动时，会形成驻波，两端为波节（位移为零），中间为波腹（位移最大）。基频为 f₁ = v/(2L)，其中 v 是弦上波速，L 是长度。

f₁ = v / (2L)

The allowed frequencies are harmonics: fₙ = n f₁ = n v/(2L) for n = 1, 2, 3,… The wave speed on a string is given by v = √(T/μ), where T is tension and μ is mass per unit length.

允许的频率为谐频：fₙ = n f₁ = n v/(2L)（n = 1, 2, 3,…）。弦上的波速公式为 v = √(T/μ)，T 为张力，μ 为单位长度质量。

v = √(T/μ)

6. Standing Waves in Air Columns | 空气柱中的驻波

In pipes, standing sound waves can form. For a pipe open at both ends, the fundamental frequency is f₁ = v/(2L), and all harmonics are present. For a pipe closed at one end, f₁ = v/(4L), and only odd harmonics (f₁, 3f₁, 5f₁,…) are produced.

在管中可形成驻波。两端开口的管，基频为 f₁ = v/(2L)，存在所有谐波；一端闭口的管，基频为 f₁ = v/(4L)，只存在奇数谐波（f₁, 3f₁, 5f₁,…）。

Antinodes form at open ends, and nodes at closed ends. The effective length of an air column may be slightly longer due to end corrections, typically added as 0.3 × diameter for each open end.

开口端为波腹，闭口端为波节。由于末端修正效应，空气柱的有效长度可能略长，通常每个开口端增加0.3倍直径的长度。

7. Resonance and Harmonics | 共振与谐波

Resonance occurs when a periodic driving force matches the natural frequency of a system, causing maximum amplitude of oscillation. In sound, resonance is exploited in musical instruments and can cause objects to vibrate sympathetically, such as a tuning fork setting another identical fork into vibration.

当周期性驱动力与系统的固有频率相匹配时，会发生共振，导致振荡振幅达到最大。在声学中，共振被用于乐器中，并可引起物体共鸣，例如一个音叉使另一个相同频率的音叉振动。

The quality factor (Q factor) describes how sharp the resonance peak is: a high Q means low damping and a sharp peak. Resonance tubes and Helmholtz resonators are common laboratory examples.

品质因数（Q 因数）描述了共振峰的尖锐程度：高 Q 值意味着低阻尼和尖锐的峰值。共振管和亥姆霍兹共振器是常见的实验示例。

8. Doppler Effect | 多普勒效应

The Doppler effect is the change in frequency observed when there is relative motion between a sound source and an observer. When they move towards each other, the observed frequency is higher; when apart, it is lower.

多普勒效应是当声源与观察者之间存在相对运动时观测到的频率变化。当两者相互靠近时，观测频率升高；相互远离时，频率降低。

The general formula for a stationary medium is: f’ = f (v ± v_o) / (v ∓ v_s), where f is the source frequency, v is the speed of sound, v_o is the observer’s velocity relative to the medium (positive if moving towards source), and v_s is the source velocity (positive if moving towards observer). Choose the signs so that relative approach yields a higher observed frequency.

在静止介质中的通用公式为：f’ = f (v ± v_o) / (v ∓ v_s)，其中 f 为声源频率，v 为声速，v_o 为观察者相对于介质的速度（朝向声源为正），v_s 为声源速度（朝向观察者为正）。选取符号应使两者接近时观测频率更高。

f’ = f × (v ± v_o) / (v ∓ v_s)

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

Sound intensity I is defined as power per unit area: I = P / A. The human ear can detect a vast range of intensities, so a logarithmic decibel scale is used: dB = 10 log₁₀ (I / I₀), where I₀ = 1 × 10⁻¹² W m⁻² is the threshold of hearing.

声强 I 定义为单位面积的功率：I = P / A。人耳能检测极广范围的声强，因此使用对数分贝标度：dB = 10 log₁₀ (I / I₀)，其中 I₀ = 1 × 10⁻¹² 瓦每平方米为听阈。

dB = 10 log₁₀ (I / I₀)

A 10 dB increase corresponds to a tenfold increase in intensity, but only about a doubling in perceived loudness. For example, 60 dB is 10⁶ times the reference intensity.

声强每增加10分贝，对应的强度增至10倍，但感知的响度仅增大约一倍。例如，60分贝的声强是基准强度的10⁶倍。

10. Diffraction and Ultrasound | 衍射与超声波

Sound waves diffract around obstacles and spread through openings. Since audible sound has wavelengths from about 17 m (20 Hz) to 1.7 cm (20 kHz), it can easily diffract around everyday objects. This is why we can hear sounds around corners.

声波会绕过障碍物发生衍射，并通过开口传播。由于可听声波波长范围约从17米（20 Hz）到1.7厘米（20 kHz），它很容易绕射日常物体，这就是我们能听到拐角处声音的原因。

Ultrasound, with frequencies above 20 kHz, has very short wavelengths, enabling it to be focused into narrow beams. It is used in medical imaging (e.g., prenatal scans), industrial flaw detection, and SONAR for underwater ranging.

频率高于20 kHz的超声波波长非常短，可聚焦成细束，广泛应用于医学成像（如产前检查）、工业探伤以及水下测距声呐。

The principle of ultrasound imaging relies on the reflection (echo) of high-frequency sound waves from boundaries between different tissues. The time delay and intensity of echoes are used to construct an image.

超声波成像的原理依赖于高频声波在不同组织交界面的反射（回声）。回波的延时和强度被用来构建影像。

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A-Level Physics: Sound | A-Level 物理：声 考点精讲