🥁 波的干涉：两列波相遇时的合奏🥁 Wave Interference: When Two Waves Meet
上一片量清了波的三个尺码：波长、频率、波速。可如果两列波同时来到同一片水面，会发生什么？答案很热闹——它们会“叠”在一起。Last leaf we measured a wave's three numbers: wavelength, frequency, speed. But what happens when two waves reach the same patch of water at once? The answer is lively — they add up.
第 1 步：两个波源，一片花纹Step 1: Two sources, one pattern
先看现象：两个波源一起工作时，水面出现了一片稳定的花纹。First the phenomenon: put two wave makers to work together, and a stable pattern appears on the water.
水波槽里放两个同相的波源，水面会形成放射状的花纹：某些方向的波纹总是更强，某些方向的水面几乎平静。这些花纹非常稳定——不是偶然，而是两列水波叠加的必然结果。Place two in-phase sources in a ripple tank and a fan-shaped pattern appears: ripples run stronger in some directions and the water stays nearly calm in others. The pattern is rock-steady — not luck, but the inevitable result of two waves adding up.
为什么有的方向更欢、有的方向安静？因为波相遇时会做“加法”。Why are some directions lively and others calm? Because waves do addition when they meet.
两列波在同一地点相遇，位移直接相加：波峰遇波峰，叠得更高，这叫相长；波峰遇波谷，正好抵消，这叫相消。加强的方向连成相长线（图中的亮纹），减弱的方向连成相消线（图上的安静水道）。Where two waves meet, their displacements simply add: a crest meeting a crest rises higher — constructive; a crest meeting a trough cancels out — destructive. Strong directions line up into constructive lines (bright ripples), weak directions into destructive lines (calm channels).
相消听起来“没用”？恰恰相反——它有一个你天天在用的应用。Destructive interference sounds useless? Quite the opposite — you use it every day.
第 3 步：用一列波干掉另一列——降噪耳机Step 3: One wave kills another — noise-cancelling headphones
降噪耳机先“听”一遍环境噪声，再发出一个形状相反的波：噪声的波峰正好撞上耳机的波谷。两者相加等于零，耳朵里就安静了。这就是相消的功劳——用一列波干掉另一列波。Noise-cancelling headphones first “listen” to the surrounding noise, then emit a wave of the opposite shape: each noise crest meets an emitted trough. The sum is zero — and your ears go quiet. That is destructive interference at work: one wave cancelling another.
🎮 你来当声学工程师（1 分钟）🎮 Your turn: be an acoustics engineer (1 minute)
道理讲完了。拖动两源间距和相位差，看干涉花纹怎么变、相长线相消线怎么挪；再完成下面 4 个观察任务。Theory done. Drag the source spacing and phase difference to see the pattern shift and its lines move; then take the 4 observation tasks below.
一句话记住它：两列波相遇就叠加——峰 + 峰更高（相长），峰 + 谷抵消（相消）。Remember it in one line: where two waves meet they add — crest + crest is higher, crest + trough cancels out.
相长：路程差 = 整数倍波长，两波同相到达、叠得更高Constructive: path difference = whole wavelengths, waves arrive in step and add up相消：路程差 = 半波长的奇数倍，峰谷相遇、抵消变平Destructive: path difference = odd half-wavelengths, crest meets trough and cancels应用：降噪耳机发出反相的波，把噪声“加”成零Application: headphones emit an opposite wave and add the noise to zero
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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