📏 波长与频率：波的两个关键尺码📏 Wavelength & Frequency: Two Key Measurements
上一片里，波带着能量一路向前跑。可波到底有多“大”？这一片拿出两把尺子：波长 λ 和频率 f，量一量波的两个关键尺码。Last leaf, a wave carried energy from place to place. But how big is a wave, exactly? This leaf takes out two rulers: wavelength λ and frequency f — the two key measurements of any wave.
第 1 步：波长 λ——一个完整波有多长Step 1: Wavelength λ — the length of one full wave
先量长度：一个完整的波，从“头”到“头”有多长？First, the length: how long is one full wave, head to head?
相邻两个波峰（或两个波谷）之间的距离，就是一个波长 λ。“一个完整波”就是从波峰出发、正好重复一次的那一段。单位是米——机械波的波长，就是波在一个振动周期里跑过的路程。The distance between two neighbouring crests (or two troughs) is one wavelength λ. “One full wave” means exactly one repeating stretch, starting from a crest. It is measured in metres — the wavelength is how far the wave travels in one vibration period.
长度量完了，波还藏着一个“快慢”的问题：它一秒钟振动几次？Length done — now the pace: how many times does the wave vibrate each second?
第 2 步：频率 f——每秒振动几次Step 2: Frequency f — vibrations per second
甩跳绳时，手每秒甩几下，绳上就产生几个波——这就是频率 f，单位是赫兹（Hz）。甩得越快，f 越大，波在绳上排得越密；甩得慢，波就稀疏。频率由波源决定：手就是波源。Swing a skipping rope: the number of shakes your hand gives each second is the number of waves born on the rope — that is the frequency f, measured in hertz (Hz). Swing faster, f is larger, and the waves pack tighter; swing slowly and the waves spread out. The source (your hand) sets the frequency.
一个说“一截多长”，一个说“一秒几次”——它们其实锁在同一个公式里。One says “how long a stretch”, the other “how many per second” — and they are locked together by a single formula.
第 3 步：v = λf——三者联动Step 3: v = λf — the three move as one
波速 v = 波长 λ × 频率 f。比如每秒振动 3 次、每个波长 4 米，波速就是 12 m/s。关键是：在同一种介质里（波速不变），频率越高，波长就越短——就像甩得快，波被“挤”密了；甩得慢，波长就被拉长。Wave speed v = wavelength λ × frequency f. Vibrate 3 times a second with a 4-metre wavelength and the speed is 12 m/s. The key: in the same medium (speed fixed), a higher frequency means a shorter wavelength — fast swings squeeze the waves together, slow swings stretch them out.
🎮 你来当波的调音师（1 分钟）🎮 Your turn: tune a wave (1 minute)
道理讲完了。拖动频率和波速两个滑块，看波长 λ 怎么实时变化、波形怎么变密变疏；再完成下面 4 个小任务。Theory done. Drag the frequency and wave-speed sliders and watch λ change live as the wave packs or spreads; then take the 4 tasks below.
一句话记住它：波速 = 波长 × 频率（v = λf）。波速不变时，频率越高，波长越短。Remember it in one line: wave speed = wavelength × frequency (v = λf). At a fixed speed, a higher frequency means a shorter wavelength.
波长 λ：一个完整波的长度（波峰到波峰），单位米Wavelength λ: the length of one full wave (crest to crest), in metres频率 f：波源每秒振动的次数，单位赫兹 HzFrequency f: vibrations the source makes per second, in hertz (Hz)三者联动：波速看介质，频率看波源，波长 = 波速 ÷ 频率All three connect: the medium sets speed, the source sets frequency, wavelength = speed ÷ frequency
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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