📚 Repeatable | 可重复性
In A-level Physics, the term 'repeatable' refers to the closeness of agreement between results obtained by the same experimenter, using the same apparatus, under the same conditions, and in a short period of time. Understanding repeatability is essential for evaluating the quality of experimental data and for designing reliable investigations.
在A-level物理中，'可重复性'指的是同一实验者、使用同一装置、在相同条件下、短时间内获得的多次结果之间的一致性。理解可重复性对于评估实验数据质量和设计可靠的探究至关重要。
1. Definition of Repeatability | 可重复性的定义
Repeatability is a measure of precision. If an experiment is repeatable, repeating the measurement procedure gives very similar values. Mathematically, it is quantified by the spread of repeated readings, often expressed as the standard deviation or range.
可重复性是精密度的一种度量。如果实验是可重复的，重复测量过程会得到非常相近的数值。在数学上，它通过重复读数的离散程度来量化，通常表示为标准偏差或极差。
For example, if you measure the period of a pendulum five times and obtain values 1.02 s, 1.01 s, 1.03 s, 1.02 s, 1.02 s, the small spread shows good repeatability.
例如，如果你测量单摆周期五次，得到 1.02 s、1.01 s、1.03 s、1.02 s、1.02 s，较小的离散程度表明可重复性好。
2. Repeatability vs Reproducibility | 可重复性与可再现性的区别
Repeatability involves the same experimenter, same equipment and same conditions. Reproducibility means that different experimenters, different apparatus or different laboratories can obtain consistent results when following the same procedure. Both are important for validating scientific findings.
可重复性涉及同一实验者、同一设备和相同条件。可再现性是指不同的实验者、不同的装置或不同的实验室在遵循相同步骤时也能得到一致的结果。两者对于验证科学发现都很重要。
| Repeatable 可重复性 | Reproducible 可再现性 |
| Same experimenter 同一实验者 | Different experimenters 不同实验者 |
| Same apparatus 同一装置 | Different apparatus 不同装置 |
| Same conditions 相同条件 | May vary conditions 条件可能不同 |
| Usually short time scale 通常短时间内 | Longer time scale 较长时间尺度 |
3. Errors and Uncertainty | 误差与不确定度
Uncertainty is the interval within which the true value is expected to lie. Random errors cause readings to spread around the true value, reducing repeatability. Systematic errors shift all readings in one direction, affecting accuracy but not necessarily repeatability.
不确定度是真值预期所在的区间。随机误差使读数围绕真值离散，降低可重复性。系统误差使所有读数朝一个方向偏移，影响准确度但不一定影响可重复性。
The uncertainty of a repeated measurement can be estimated as half the range, or more rigorously as the standard deviation of the mean.
重复测量的不确定度可以估计为极差的一半，或更严谨地使用平均值的标准偏差。
Δx = (largest − smallest) / 2
or, for a sample of n readings:
s = √[Σ(xᵢ − x̄)² / (n − 1)]
where xᵢ is each reading, x̄ is the mean and n is the number of readings.
其中 xᵢ 是每次读数，x̄ 是平均值，n 是读数次数。
4. Random Errors and Repeatability | 随机误差与可重复性
Random errors arise from unpredictable changes in the experiment, such as fluctuations in temperature, vibration, or judgement when reading a scale. These errors cause readings to be scattered around the mean. The presence of large random errors means poor repeatability.
随机误差源于实验中不可预测的变化，如温度波动、振动或读取刻度时的判断偏差。这些误差使读数在平均值附近散布。较大的随机误差意味着可重复性较差。
Increasing the number of readings allows random errors to be reduced by averaging, improving the reliability of the mean. However, it does not eliminate systematic errors.
增加读数次数可以通过求平均来减小随机误差的影响，从而提高平均值的可靠性。但这并不能消除系统误差。
5. Systematic Errors and Repeatability | 系统误差与可重复性
A systematic error is a consistent, repeatable error caused by faulty equipment, calibration errors, or a flaw in the experimental method. For example, a balance that is not zeroed gives every mass reading 0.05 g too high. This error is the same in every trial, so it does not affect repeatability, but it affects accuracy.
系统误差是由设备故障、校准误差或实验方法缺陷引起的、一致且可重复的误差。例如，未调零的天平会使每次质量读数偏高 0.05 g。这种误差在每次试验中都相同，因此不影响可重复性，但影响准确度。
Therefore, repeatable results can still be inaccurate if a systematic error is present.
因此，如果存在系统误差，可重复的结果仍然可能是不准确的。
6. Improving Repeatability in Experiments | 提高实验可重复性的方法
Use digital instruments with higher resolution to reduce judgment errors, which improves repeatability.
使用分辨率更高的数字仪器来减少判读误差，从而提高可重复性。
Take multiple readings and use the mean value in subsequent calculations.
多次读数并在后续计算中使用平均值。
Control environmental conditions such as temperature, pressure and humidity.
控制温度、压力和湿度等环境条件。
Follow a standardised procedure to ensure that each trial is performed in the same way.
遵循标准化步骤，确保每次试验以相同方式进行。
Check equipment calibration before starting the experiment.
在开始实验前检查设备的校准情况。
7. Example: Measuring g | 实例：测量重力加速度
In a simple pendulum experiment, the period T of a pendulum of length L is related to g by:
在单摆实验中，摆长 L 的周期 T 与重力加速度 g 的关系为：
T = 2π √L / g
Rearranging gives:
整理后得到：
g = 4π² L / T²
To obtain a repeatable value of T, you should time several oscillations (e.g. 10 or 20 swings) and repeat the measurement several times. The spread of the calculated values of g indicates the repeatability of the experiment.
为了获得可重复的 T 值，你应该测量多个周期（例如 10 或 20 次摆动）并重复测量多次。计算出的 g 值的离散程度反映了实验的可重复性。
8. Example: Hooke's Law | 实例：胡克定律
In a Hooke's law experiment, the extension x of a spring is measured for a range of weights F. If the experiment is repeatable, repeating the loading process with the same masses gives the same extensions at each load.
在胡克定律实验中，测量弹簧在多种重量 F 下的伸长量 x。如果实验是可重复的，使用相同砝码重复加载过程时，每次载荷下的伸长量应该相同。
Factors that could reduce repeatability include permanent stretching of the spring, hysteresis, or reading errors from the ruler. Using a pointer and mirror scale can reduce parallax error and improve repeatability.
可能降低可重复性的因素包括弹簧的永久拉伸、滞后现象或从尺子上读数时的误差。使用指针和镜面标尺可以减少视差误差并提高可重复性。
9. Recording and Reporting Data | 数据记录与报告
When reporting repeatable measurements, it is important to include all raw data, the calculated mean, and the uncertainty. This allows others to judge how repeatable the results were.
在报告可重复的测量时，重要的是包括所有原始数据、计算出的平均值和不确定度。这使他人能够判断结果的可重复程度。
For example, a set of readings may be recorded as:
例如，一组读数可以记录为：
| Reading 1 | 1.02 s | Published by TutorHao | A-Level Physics Revision Series | aleveler.com
