📚 AS Physics Unit 4 Insert June 2019 Experiment Investigation | AS 物理 Unit 4 2019年6月插页实验探究
The June 2019 Insert for Edexcel AS Physics Unit 4 (Waves and Our Universe) provided a detailed description of an experiment to determine the speed of sound in air using a resonance tube. This investigation is a classic demonstration of stationary waves in a closed pipe and requires careful measurement, clear understanding of wave theory, and rigorous analysis of uncertainties. This article unpacks every aspect of that insert-based experiment, guiding you through the equipment, procedure, theory, and common pitfalls so you can master the practical skills and answer related exam questions with confidence.
2019年6月爱德思AS物理Unit 4（波与我们的宇宙）的插页提供了一个使用共振管测定空气中声速的详细实验描述。该探究是闭管中驻波的经典演示实验，需要细致的测量、对波动理论的清晰理解以及严谨的误差分析。本文将拆解那份插页实验的各个方面，带你走过设备、步骤、理论和常见陷阱，助你掌握实验技能并自信应对相关考题。
1. Experimental Context | 实验背景
The resonance tube experiment exploits the formation of stationary waves in a column of air closed at one end. When a vibrating tuning fork is held above the open end, the sound wave reflects from the water surface, and at certain tube lengths the incident and reflected waves superpose to produce a loud resonance. By measuring the difference in tube lengths for consecutive resonances, the wavelength of sound can be found, and using a known frequency the speed of sound is calculated. This practical is a direct application of the Unit 4 topic on stationary waves and is frequently assessed for data analysis, graph plotting, and uncertainty evaluation.
共振管实验利用一端封闭的空气柱中驻波的形成原理。当振动的音叉置于开口端上方时，声波在水面处反射，在特定的管长下入射波与反射波叠加产生响亮的共振。通过测量相邻共振的管长差即可求得声波的波长，再结合已知频率便可计算出声速。该实验是对Unit 4驻波内容的直接应用，常被用来考查数据分析、图形绘制和误差评估。
2. Equipment List | 设备清单
The insert specified the following apparatus:
插页列出了以下仪器：
- Resonance tube (graduated, approx. 1 m long) with a movable reservoir or adjustable water level – 带刻度的共振管（约1米长）和可移动的水箱或可调水位
- Tuning fork of known frequency (e.g. 480 Hz or 512 Hz) – 已知频率的音叉（如480 Hz或512 Hz）
- Rubber pad or mallet for striking the fork – 用于敲击音叉的橡胶垫或木槌
- Metre rule or built‑in scale on the tube – 米尺或管身自带刻度
- Thermometer (to record room temperature) – 温度计（记录室温）
- Clamp and stand to hold the tube vertically – 铁架台和夹子，垂直固定管子
- Water and a beaker or reservoir to adjust the water level slowly – 水以及烧杯或水箱，用于缓慢调节水位
Only basic lab equipment is required, making this a common but highly examinable practical.
只需基础实验设备，因此这是一个常见但高频考查的实验。
3. Experimental Setup | 实验装置
Clamp the resonance tube vertically so that its lower end is connected via a flexible tube to a water reservoir that can be raised or lowered. Fill the tube partially with water so the air column length can be varied by moving the reservoir. Place the tuning fork just above the open end of the tube, ensuring it does not touch the glass. The setup must allow slow, continuous adjustment of the water level to pinpoint the exact column length at which resonance occurs.
将共振管垂直夹持，其下端通过软管与一个可升降的水箱相连。管内注入部分水，通过移动水箱改变空气柱的长度。将音叉置于管口上方，确保不接触玻璃。装置应能缓慢连续地调节水位，从而精确确定产生共振时的气柱长度。
4. Procedure Step‑by‑Step | 实验步骤
Step 1: Strike the tuning fork gently on the rubber pad and hold it horizontally about 1 cm above the open end of the tube.
步骤1：轻敲音叉使其振动，将其水平置于管口上方约1 cm处。
Step 2: Slowly lower the water level by moving the reservoir downward while listening for a sudden increase in loudness. The first resonance will occur when the air column length L₁ is approximately one‑quarter of the wavelength.
步骤2：缓慢降低水位（向下移动水箱），同时仔细听声音的突然增强。第一次共振发生时，空气柱长度L₁约等于波长的四分之一。
Step 3: Measure and record the length L₁ from the top of the tube to the water meniscus. Use the built‑in scale and a magnifying glass if necessary to avoid parallax error.
步骤3：测量并记录从管口到水面弯月面的长度L₁。使用自带刻度，必要时借助放大镜避免视差。
Step 4: Continue lowering the water level to find the second resonance at L₂ (approximately 3λ/4) and the third resonance at L₃ (5λ/4), if the tube is long enough. Each resonance should be verified by oscillating the water level up and down to ensure the loudest point is captured.
步骤4：继续下降水位找到第二次共振（约3λ/4）的L₂，如果管足够长还可找到第三次共振（5λ/4）的L₃。每次共振都应通过上下微调水位来确认最响点。
5. Data Collection | 数据收集
Record the air column lengths L₁, L₂, L₃ in metres to the nearest millimetre. Note the frequency f of the tuning fork (e.g. 480 Hz). Also record the ambient temperature, as the speed of sound varies with temperature. It is good practice to repeat each measurement at least three times and calculate a mean to reduce random error. A sample table from the insert may look like this:
记录各次共振的空气柱长度L₁、L₂、L₃，以米为单位精确到毫米。记录音叉频率f（如480 Hz）。同时记录环境温度，因为声速随温度变化。最好对每个长度至少重复测量三次并计算平均值以减小随机误差。插页中的典型表格如下：
| Resonance | L / m (trial 1) | L / m (trial 2) | L / m (trial 3) | Mean L / m |
|---|---|---|---|---|
| 1st (L₁) | 0.178 | 0.179 | 0.177 | 0.178 |
| 2nd (L₂) | 0.543 | 0.544 | 0.542 | 0.543 |
From the means, the half‑wavelength distance (L₂ − L₁) can be determined with its absolute uncertainty.
根据平均值可确定半波长间距（L₂ − L₁）及其绝对不确定度。
6. Theory and Calculations | 理论与计算
For a tube closed at one end, the closed end is a displacement node and the open end is an antinode. The first resonance occurs when the air column length satisfies L₁ + c = λ/4, where c is an end correction (approximately 0.3d for a tube of diameter d). The second resonance satisfies L₂ + c = 3λ/4. Subtracting the two equations eliminates the end correction:
对于一端封闭的管子，封闭端为位移波节，开口端为波腹。第一次共振时气柱长度满足 L₁ + c = λ/4，其中c为管口修正值（约为0.3d，d为管直径）。第二次共振满足 L₂ + c = 3λ/4。两式相减消去修正项：
L₂ − L₁ = λ/2
Hence the wavelength is:
因此波长为：
λ = 2(L₂ − L₁)
Once λ is known, the speed of sound v is calculated using the wave equation:
求得λ后，利用波动方程计算声速v：
v = f × λ
If a third resonance L₃ is measured, the difference (L₃ − L₁) = λ can also be used to improve precision. In the insert, students were expected to derive these relationships and use a graphical method to find λ.
如果测量了第三次共振L₃，也可通过 (L₃ − L₁) = λ 来提高精度。在插页中，学生需要推导这些关系并用图形法求出λ。
7. Graphical Analysis | 图形分析
The insert guided candidates to plot a graph of resonance length L on the y‑axis against resonance order number n (where n = 1, 3, 5…) on the x‑axis. The gradient of the line of best fit gives λ/4, because the theoretical relationship is L + c = nλ/4. Hence:
插页引导考生绘制共振长度L（y轴）对共振序数n（x轴，n = 1, 3, 5…）的图形。最佳拟合线的斜率等于 λ/4，因为理论关系为 L + c = nλ/4。因此：
λ = 4 × gradient
The y‑intercept can be used to estimate the end correction c, though this is not required for the speed calculation. Plotting multiple points reduces the effect of random errors and allows uncertainty in λ to be found from the maximum and minimum gradient lines.
截距可用于估算管口修正值c，但声速计算不需要它。绘制多个数据点可减小随机误差的影响，并利用最大和最小斜率线求出λ的不确定度。
8. Sources of Uncertainty | 误差来源
Several uncertainties affect this experiment. The main random errors come from judging the exact point of maximum loudness and reading the meniscus with a fixed scale. A systematic error arises if the tuning fork frequency is not exactly the nominal value (e.g. due to temperature or damage). Parallax error when measuring the air column can be avoided by eye‑level reading. The end correction itself introduces a small systematic shift, but it cancels out when differences are taken. Also, the assumption that the open end is a perfect antinode is approximate; the node is slightly outside the tube, leading to an overestimation of the column length if uncorrected.
多种不确定度会影响本实验。主要随机误差来自判断最大响度点和用固定刻度读取弯月面。如果音叉频率并非标称值（如因温度或损坏），将产生系统误差。测量气柱长度时的视差可通过平视读数避免。管口修正本身会引入一个小的系统偏移，但取差值时抵消了。此外，假定开口端为完美波腹是近似的，实际上波节在管口稍外，若不修正会高估气柱长度。
To quantify uncertainty, the half‑range of repeated measurements can be used. The absolute uncertainty in λ is twice the uncertainty in (L₂ − L₁). The percentage uncertainty in v is the sum of the percentage uncertainties in f and λ.
为量化不确定度，可使用重复测量的半量程。λ的绝对不确定度为 (L₂ − L₁) 不确定度的两倍。v的百分不确定度是f和λ的百分不确定度之和。
9. Improvements and Safety | 改进与安全
Common improvements suggested in the insert mark scheme include: using a tuning fork of higher frequency (shorter wavelength) so more resonances can be observed within the tube length; using a set of tuning forks to obtain multiple independent values of v; and employing a microphone and oscilloscope to detect the resonance precisely by measuring the amplitude of the signal. Safety precautions are minimal, but care should be taken to avoid striking the tuning fork on hard surfaces (which can damage it) and to keep water away from electrical equipment if electronic sensors are used.
插页评分方案中常见的改进建议包括：使用更高频率的音叉（波长更短）以便在管长内观察到更多次共振；使用一组音叉获得多个独立的声速值；使用麦克风和示波器通过测量信号幅度来精准检测共振。安全预防措施不多，但需注意避免在硬物上敲击音叉（以防损坏），若使用电子传感器则须防水。
10. Conclusion and Exam Tips | 结论与考试技巧
The resonance tube experiment from the June 2019 Unit 4 insert is an elegant demonstration of stationary waves and provides a reliable method to determine the speed of sound. When answering exam questions on this practical, always refer to the specific steps shown in the insert, use correct terminology (node, antinode, end correction), and be prepared to calculate percentage differences between experimental and accepted values (e.g. 343 m s⁻¹ at 20 °C). Show clearly how you combine uncertainties and explain why certain procedures minimise error. Practising with past inserts will make these skills second nature.
2019年6月Unit 4插页中的共振管实验是对驻波的优雅演示，并提供了一种测定声速的可靠方法。在回答有关该实验的考题时，务必引用插页所示的具体步骤，使用正确的术语（波节、波腹、管口修正），并随时准备计算实验值与公认值（20 °C时343 m s⁻¹）之间的百分差异。清晰地展示如何合成不确定度，并解释某些操作为何能减小误差。通过练习历年插页，这些技巧将变得得心应手。
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