📚 Determining the Wavelength and Speed of Sound | 测定声波的波长与声速
In A-level physics, measuring the wavelength and speed of sound in air is a core practical skill. It combines wave theory, stationary waves, resonance and careful measurement technique. One of the most common CIE experiments uses a resonance tube and a tuning fork of known frequency, while an alternative uses two microphones and an oscilloscope to compare phases.
在 A-level 物理中，测量空气中声波的波长和声速是一项核心实验技能。它综合了波动理论、驻波、共振和细致的测量技术。CIE 最常见的一个实验使用共振管和已知频率的音叉，另一种方法则使用两个麦克风和示波器来比较相位。
1. Experimental Aim and Principle | 实验目的与原理
The aim of this experiment is to determine the wavelength λ of a sound wave of known frequency f, and then use the wave equation v = fλ to calculate the speed of sound in air.
本实验的目的是测定已知频率 f 的声波波长 λ，然后利用波动方程 v = fλ 计算空气中的声速。
The experiment relies on the formation of stationary waves in a closed air column. When the air column length is adjusted so that a node forms at the water surface and an antinode forms near the open end, resonance occurs and the sound becomes noticeably louder.
实验依赖于在封闭空气柱中形成驻波。当调整空气柱长度，使水面处形成波节、开口端附近形成波腹时，就会发生共振，声音会明显增强。
2. Apparatus and Setup | 仪器与装置
A typical resonance tube experiment uses a long glass tube, a water reservoir connected by rubber tubing, a metre rule, a tuning fork of known frequency, a rubber pad, and a thermometer.
典型的共振管实验使用一根长玻璃管、一个通过橡胶管连接的水槽、一把米尺、一个已知频率的音叉、一个橡胶垫和一个温度计。
For the two-microphone method, you also need a signal generator, a loudspeaker, two microphones and a dual-trace oscilloscope.
对于双麦克风方法，还需要信号发生器、扬声器、两个麦克风和一台双踪示波器。
The glass tube should be vertical, and the water level must be adjustable so that the length of the air column can be changed smoothly.
玻璃管应竖直放置，水面高度必须可调，以便平滑地改变空气柱的长度。
3. Resonance Tube Method: First and Second Resonance | 共振管法：第一与第二共振
First, strike the tuning fork gently on the rubber pad and hold it just above the open end of the tube.
首先，将音叉在橡胶垫上轻轻敲击，并将其置于玻璃管开口端正上方。
Raise or lower the water reservoir to change the air column length. Listen for the first position at which the sound becomes clearly louder; this is the first resonance. Record the air column length L₁ from the water surface to the top of the tube.
升高或降低水槽以改变空气柱长度。仔细听第一次声音明显增强的位置，这就是第一共振。记录水面到管口的空气柱长度 L₁。
Continue lowering the water level until a second loud resonance is heard. Record this longer air column length L₂.
继续降低水面，直到听到第二次响亮共振。记录这个较长的空气柱长度 L₂。
Repeat each measurement several times and take average values to reduce random uncertainty.
每项测量重复多次并取平均值，以减小随机不确定度。
4. End Correction and Wavelength Calculation | 端部修正与波长计算
In a real tube, the antinode at the open end is formed a small distance e beyond the end. This distance is called the end correction.
在实际管子中，开口端的波腹形成于管口外一小段距离 e 处。这个距离称为端部修正。
For the first resonance, the effective length is L₁ + e, and this equals one quarter of the wavelength. For the second resonance, the effective length is L₂ + e, and this equals three quarters of the wavelength.
对于第一共振，有效长度为 L₁ + e，它等于四分之一波长。对于第二共振，有效长度为 L₂ + e，它等于四分之三波长。
L₁ + e = λ/4 and
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