📚 A-Level AQA Science: Sound Key Points | A-Level AQA 科学：声 考点精讲
Sound is a longitudinal mechanical wave that travels through a medium by compressions and rarefactions. This article summarises the key AQA A-Level sound topics, including wave properties, speed, intensity, standing waves, Doppler effect, beats and ultrasound, with revision notes and worked concepts.
声是一种通过介质传播的纵波，以压缩和稀疏的方式传递能量。本文汇总了 AQA A-Level 物理中声学的核心考点，包括波的性质、声速、声强、驻波、多普勒效应、拍频和超声波，并提供精炼的复习要点与概念解析。
1. Nature of Sound Waves | 声波的本质
Sound waves are longitudinal mechanical waves that require a material medium for propagation. The oscillations of particles are parallel to the direction of energy transfer, creating regions of high pressure (compressions) and low pressure (rarefactions).
声波是纵波，需要介质传播。粒子的振动方向与能量传递方向平行，形成高压区（压缩）和低压区（稀疏）。
Unlike transverse waves, sound waves cannot travel through a vacuum. The audible frequency range for humans is typically 20 Hz to 20 000 Hz, while ultrasound refers to frequencies above this range.
与横波不同，声波不能在真空中传播。人类可听频率范围约为 20 Hz 到 20 000 Hz，超过此范围的称为超声波。
2. Properties of Sound Waves | 声波的性质
The pitch of a sound is determined by its frequency (f). A high frequency results in a high pitch. Loudness is related to the amplitude of the wave; a larger amplitude means a louder sound.
声音的音高由频率（f）决定，频率高则音调高。响度与振幅有关，振幅越大声音越响。
Like all waves, sound obeys the wave equation: v = f λ, where v is the speed of sound, f is frequency and λ is wavelength. This equation is fundamental when analysing resonance and standing wave patterns.
像所有波一样，声波满足波速公式：v = f λ，其中 v 是声速，f 是频率，λ 是波长。此方程在分析共振和驻波模式时至关重要。
3. Speed of Sound | 声速
The speed of sound depends on the medium, temperature and density. In air at 20 °C, the speed is approximately 343 m s⁻¹. In solids and liquids, sound travels faster because particles are closer together.
声速取决于介质、温度和密度。在 20 °C 的空气中，声速约为 343 m s⁻¹。在固体和液体中，由于粒子间距更近，声速更快。
An increase in temperature raises the kinetic energy of air molecules, leading to a higher speed. The relationship in air can be approximated by v ∝ √T, where T is the absolute temperature in kelvin.
温度升高使空气分子动能增加，声速增大。空气中声速近似与 √T 成正比，其中 T 是开尔文温度。
v = √(γ P / ρ)
（空气中 γ = 1.4，P 为压强，ρ 为密度）
4. Intensity and the Decibel Scale | 声强与分贝标度
Sound intensity I is the power transmitted per unit area, measured in W m⁻². The threshold of human hearing I₀ is 10⁻¹² W m⁻². Because the ear responds logarithmically, we use the decibel scale to express sound intensity level.
声强 I 是单位面积传递的功率，单位为 W m⁻²。人耳听觉阈 I₀ 为 10⁻¹² W m⁻²。由于人耳响应呈对数关系，我们使用分贝标度表示声强级。
L = 10 log₁₀ (I / I₀)
An increase of 10 dB corresponds to a factor of 10 in intensity. Doubling the intensity adds about 3 dB. This scale is used to measure noise levels and is often examined in relation to hearing damage.
声强每增加 10 dB，对应强度增大 10 倍。强度加倍约增加 3 dB。该标度用于测量噪声级，常结合听力损伤考点出现。
5. Standing Waves in Strings | 弦上的驻波
When a string fixed at both ends is plucked, a standing wave can form. The fundamental frequency (first harmonic) has a node at each end and an antinode in the middle. The wavelength of the fundamental is λ₁ = 2L, where L is the string length.
当两端固定的弦被拨动时，可形成驻波。基频（第一谐波）两端为波节，中间为波腹。基频波长 λ₁ = 2L，L 为弦长。
The frequencies of standing waves are given by:
fₙ = n v / (2L) (n = 1, 2, 3, …)
These form a harmonic series. The frequency of the second harmonic is 2f₁, the third is 3f₁, and so on.
谐波频率构成谐波系列。第二谐波频率为 2f₁，第三为 3f₁，以此类推。
| Harmonic n | Wavelength λₙ | Frequency fₙ |
|---|---|---|
| 1 | 2L | v / (2L) |
| 2 | L | 2v / (2L) |
| 3 | 2L/3 | 3v / (2L) |
6. Standing Waves in Air Columns | 空气柱中的驻波
Sound waves in a pipe can form standing waves. For a pipe open at both ends, the displacement antinodes are at both ends. The fundamental frequency corresponds to λ = 2L and f₁ = v / (2L). All harmonics (n=1,2,3…) are present.
管中声波可形成驻波。两端开口的管，两端均为位移波腹。基频对应 λ = 2L，f₁ = v / (2L)。所有整次谐波均存在。
For a pipe closed at one end, there is a displacement node at the closed end and an antinode at the open end. The fundamental wavelength is λ₁ = 4L, and the frequencies are:
fₙ = n v / (4L) (n = 1, 3, 5, …)
Only odd harmonics exist. This difference is frequently tested in AQA questions on resonance tubes and musical instruments.
此时只存在奇次谐波。这一区别在共振管和乐器题目中常考。
7. Harmonics and Overtones | 谐波与泛音
The term ‘overtone’ refers to any frequency higher than the fundamental. The first overtone is the second harmonic for strings and open pipes, but for a closed pipe the first overtone is the third harmonic (n=3).
“泛音”指任何高于基频的频率。对于弦和开口管，第一泛音是第二谐波；而对于闭口管，第一泛音是第三谐波（n=3）。
Understanding the harmonic structure helps explain the timbre of different instruments. Timbre is determined by the relative amplitudes of the harmonics present.
理解谐波结构有助于解释不同乐器的音色。音色由所包含谐波的相对振幅决定。
8. The Doppler Effect | 多普勒效应
The Doppler effect is the change in observed frequency when a source of sound and an observer move relative to each other. The observed frequency f’ is given by:
多普勒效应是当声源与观察者相对运动时，观测到的频率发生变化的现象。观测频率 f’ 由下式给出：
f’ = f (v ± vᵒ) / (v ∓ vˢ)
where v is the speed of sound, vᵒ is the speed of the observer, vˢ is the speed of the source. Use the plus sign in the numerator if the observer moves towards the source (minus if away). In the denominator, use the minus sign if the source moves towards the observer (plus if away).
其中 v 为声速，vᵒ 为观察者速度，vˢ 为波源速度。若观察者朝向波源运动，分子取正号；远离则取负号。分母中，波源朝向观察者运动时取负号，远离时取正号。
This effect is applied in radar speed guns, echolocation and the shift in sound from a moving vehicle.
该效应应用于雷达测速、回声定位以及车辆驶过时音调的变化。
9. Beats | 拍频
When two sound waves of slightly different frequencies superpose, the amplitude varies periodically, creating beats. The beat frequency is the absolute difference between the two frequencies:
两列频率稍有差异的声波叠加时，振幅会周期性变化，形成拍。拍频等于两频率之差的绝对值：
f_beat = | f₁ – f₂ |
Beats are used to tune musical instruments by matching frequencies until the beat disappears.
拍现象用于乐器调音，通过调整频率直至拍消失来确定音高一致。
10. Diffraction and Interference of Sound | 声的衍射与干涉
Sound waves can diffract around obstacles and spread out after passing through gaps. Significant diffraction occurs when the wavelength is comparable to the size of the obstacle or opening. Low‑frequency sounds diffract more because of longer wavelengths.
声波能绕过障碍物衍射，通过缝隙后扩散。当波长与障碍物或缝隙尺寸相当时，衍射显著。低频声波波长长，衍射更明显。
Interference of two coherent sound sources produces a pattern of constructive and destructive interference. A common demonstration uses two loudspeakers connected to a signal generator; walking across the room you hear loud and quiet regions.
两相干声源的干涉产生加强和减弱的图案。常见演示使用两个连接信号发生器的扬声器，在室内走动会听到响区和静区。
The condition for constructive interference is a path difference of nλ; destructive interference occurs at path difference (n + ½)λ.
干涉加强条件为波程差等于 nλ；减弱条件为波程差等于 (n + ½)λ。
11. Applications of Ultrasound | 超声的应用
Ultrasound refers to sound with frequency above 20 kHz. It is widely used in medical imaging (sonography), industrial flaw detection and cleaning. Ultrasonic waves reflect at boundaries between different media, allowing imaging of internal structures.
超声波指频率高于 20 kHz 的声波。广泛用于医学成像（超声检查）、工业探伤和清洗。超声波在不同介质界面反射，可对内部结构成像。
In AQA exams, you may be asked to calculate the distance or resolution using v = 2d / t for pulse‑echo methods, or to explain why high frequency gives better resolution.
在 AQA 考试中，可能要求用脉冲回波法公式 v = 2d / t 计算距离，或解释为什么高频能提供更好的分辨率。
12. Measuring the Speed of Sound | 测量声速
One standard AQA experiment uses a resonance tube with a tuning fork. The shortest length of the air column that produces resonance corresponds to λ/4 for a closed pipe. By finding the first resonance length L₁ and second resonance length L₂ (≈ 3λ/4), the wavelength can be determined.
AQA 标准实验之一是共振管配合音叉。闭管产生共振的最短空气柱长度对应 λ/4。通过找到第一共振长度 L₁ 和第二共振长度 L₂（约为 3λ/4），可确定波长。
The speed is then calculated using v = f λ. Alternatively, an oscilloscope with two microphones can measure time delay over a known distance. Accuracy is improved by repeating measurements and averaging.
然后利用 v = f λ 计算声速。也可用示波器和两个麦克风测量已知距离上的时间延迟。通过重复测量取平均值提高精确度。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply