Waves, Sound, and Physical Optics
AP Physics 2 Topic 14 7:50 English narration · English + 中文 subtitles burned in
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Transcript
Blow a soap bubble and look closely.
吹一个肥皂泡，凑近看。
The film is thinner than a hair and has no colour of its own, and the light falling on it is plain white light.
薄膜比头发还薄，本身没有任何颜色，照到它上面的也只是普通的白光。
Yet the bubble glows with bands of gold, green and violet that shift as it turns.
可是泡泡上却浮现出金色、绿色和紫色的条纹，随着转动不断变化。
So where do those colours come from?
那么，这些颜色到底是从哪里来的？
The answer is interference — waves adding together.
答案是干涉——波的叠加。
Today we build the whole picture: what a wave is, and how it behaves at a boundary. Then the Doppler effect, interference and standing waves, and how light bends.
今天我们把整幅图景搭起来：什么是波、波在界面上的行为、 多普勒效应、干涉与驻波，以及光是怎样弯折的。
Let's begin.
让我们开始吧。
Start with the idea itself.
先从这个概念本身说起。
A wave carries energy from one place to another without carrying matter with it.
波把能量从一处传到另一处，却不把物质一起带走。
Flick a rope and the pulse races away, but each piece of rope only moves up and down and stays put.
抖一下绳子，脉冲飞快跑开，但绳子的每一小段只是上下运动，仍留在原地。
One disturbance is a pulse; a repeating one is a wave.
一次扰动叫做脉冲，不断重复的扰动就是波。
Sound and water waves need a medium; light does not.
声波和水波需要介质才能传播，光则不需要。
Waves come in two kinds.
波分为两类。
In a transverse wave, like a wave on a rope, the material moves at right angles to the direction of travel.
在横波中，比如绳子上的波，介质的运动方向与传播方向成直角。
In a longitudinal wave, like sound, it moves back and forth along that same direction, squeezing the medium into compressions and stretching it into rarefactions.
在纵波中，比如声音，介质沿着同一方向来回运动，把介质挤压成密部、拉伸成疏部。
Now the words you must use precisely.
接下来是必须用准确的几个词。
Freeze the wave in space and you see the wavelength, the distance from one crest to the next. The height from the middle to a crest is the amplitude.
把波在空间里冻结，你看到的是波长， 也就是相邻两个波峰之间的距离；从中线到波峰的高度是振幅。
Watch one point over time and you see the period, while the frequency counts cycles each second.
改为盯住一个点随时间变化，你看到的是周期，而频率就是每秒的循环次数。
The speed equals the frequency times the wavelength.
波速等于频率乘以波长。
A bigger amplitude means more energy, and a louder sound; frequency sets pitch.
振幅越大，能量越多，声音也越响；频率决定音调。
What happens at a boundary?
波到达界面时会怎样？
Part of the wave transmits into the new material, and part reflects.
一部分进入新的介质，一部分反射回来。
If the wave slows down there, the reflection inverts — it comes back upside down. Picture a light string tied to a heavy one. But if it speeds up, the reflection stays upright.
如果波在新介质中变慢——比如细绳接到粗绳上——反射回来的脉冲会上下颠倒； 如果变快，反射脉冲则保持原样。
And the frequency never changes. A note going from air into water keeps its frequency, but its speed and wavelength both grow.
而频率永远不变：让一个音从空气进入水中， 频率保持不变，速度和波长都会变大。
Transverse waves have one more trick.
横波还有一个独有的本领。
Ordinary light vibrates in every direction at once.
普通的光同时在各个方向上振动。
Polarization: a polarizer passes only the vibrations lined up with it, so the light coming out is polarized — vibrating in one plane.
偏振片只让与它方向一致的振动通过，所以出来的光是偏振光，只在一个平面内振动。
That reduces the wave's intensity, the power delivered to each unit of area: an ideal polarizer halves it.
把其余部分挡掉会降低强度——强度就是每单位面积上传递的功率，理想偏振片会让强度减半。
Sound is longitudinal, so it can never be polarized.
声音是纵波，所以声音永远不能被偏振。
Light itself is an electromagnetic wave. It is an electric field and a magnetic field, oscillating at right angles to each other, and to the direction of travel.
光本身就是一种电磁波：一个电场和一个磁场互相垂直地振动，并且都垂直于传播方向。
They need no medium, and in a vacuum they all move at the speed of light.
这类波不需要任何介质，在真空中它们全都以光速传播。
They differ only in wavelength: radio, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays.
它们的差别只在波长： 无线电波、微波、红外线、可见光、紫外线、X射线和伽马射线。
The visible slice runs from red, the longest, down to violet.
可见光这一小段从波长最长的红色，一直到波长最短的紫色。
Now let the source move.
现在让波源动起来。
As an ambulance races toward you, each new wavefront starts closer to you than the last, so the waves bunch up: shorter wavelength, higher pitch.
当救护车朝你疾驰而来，每一个新的波前都比上一个离你更近， 于是波被挤在一起：波长更短，音调更高。
Behind it they stretch out: longer wavelength, lower pitch.
在它后面，波被拉开：波长更长，音调更低。
That is the Doppler effect.
这就是多普勒效应。
The faster the relative motion, the bigger the shift; move along with the source and nothing shifts at all.
相对运动越快，频率变化越大；如果你与波源一起运动，则完全没有变化。
When two waves meet they pass straight through each other; where they overlap they superpose, and the displacements simply add.
两个波相遇时会径直穿过彼此，在重叠处位移只是简单相加。
Crest on crest gives a bigger wave: constructive interference.
波峰对波峰得到更大的波：这是相长干涉。
Crest on trough cancels: destructive.
波峰对波谷则相互抵消：这是相消干涉。
Now sound two notes whose frequencies differ slightly — two tuning forks, four hertz apart.
现在让两个频率只差一点点的音同时响起——两支相差四赫兹的音叉。
They drift in and out of step, so the sound throbs loud and soft.
它们时而同步、时而不同步，声音就忽强忽弱地起伏。
That throb is called beats, and its frequency is the difference: four beats every second.
这种起伏叫做拍，它的频率就是两者之差：每秒四次。
Trap waves between two fixed ends and something new appears.
把波困在两个固定端之间，新的现象就出现了。
The wave travelling one way meets its own reflection coming back, and the two lock into a standing wave.
向一个方向传播的波遇到自己反射回来的波， 两者锁在一起形成驻波。
Some points never move at all: nodes. Between them the string swings hardest: antinodes.
有些点始终不动，叫做波节；它们中间的位置摆动最剧烈，叫做波腹。
Only certain wavelengths fit, and those are the harmonics.
只有特定的波长能够恰好容纳在两端之间，这些就是各次谐波。
Here is the classic question.
这是一道经典题。
A guitar string fixed at both ends is sixty-five centimetres long, and waves travel along it at two hundred and sixty metres per second.
一根两端固定的吉他弦长六十五厘米，波在弦上的传播速度是每秒二百六十米， 求它的最低音。
Find its lowest note. That note is the fundamental, and it fits exactly half a wavelength between the ends, so the wavelength is twice the length: one point three metres.
最低音是基频，它在两端之间恰好容纳半个波长， 所以波长是弦长的两倍：一点三米。
The frequency is the speed divided by the wavelength: two hundred hertz.
频率等于波速除以波长，算得二百赫兹。
Waves also bend around edges.
波也会绕过边缘弯折。
Send a wave through a gap and it spreads out on the far side: diffraction.
让波穿过一个缝，它会在另一侧扩散开，这就是衍射。
How much it spreads depends on the size of the gap compared with the wavelength. A gap about as wide as one wavelength fans the wave right out. A much wider gap hardly bends it at all.
扩散的程度取决于缝宽与波长的比较：缝宽与波长相当时，波会扇形散开； 缝宽得多时，几乎不弯折。
That is why sound bends round a doorway, while light needs a far thinner slit.
这就是为什么声音能轻易绕过门口，而光需要比头发还细的缝。
Beyond the gap, waves from different parts of the opening interfere into bright and dark bands.
在缝的后面，来自开口不同部分的波相互干涉，形成明暗相间的条纹。
Now use two slits.
现在改用两条缝。
Light spreads from each, and the two sets of waves overlap.
光从每条缝散开，两组波相互重叠。
Where the paths differ by a whole number of wavelengths, the waves arrive in step: a bright fringe. Where they differ by half a wavelength they interfere destructively and cancel: a dark one.
当两条路径相差整数个波长时，波同步到达，你会看到一条亮纹； 相差半个波长时则相互抵消，成为暗纹。
It only works because the two sets of waves are coherent — locked in step, with a fixed phase relationship.
这只有在两组波相干时才成立——它们步调锁定，位相差固定。 这个图样正是光具有波动性的证据。
That pattern proves light is a wave. Add thousands of slits and you have a diffraction grating — sharper lines, and white light fanned into a rainbow: the shimmer on a disc.
把缝增加到成千上万条，就成了衍射光栅：亮线更锐利，白光被展开成彩虹—— 光盘上的那层闪光就是这样来的。
And the soap bubble from the start is thin film interference: light reflecting off the front and back surfaces of a thin film travels different distances, so some colours cancel and the ones left over are what you see.
开头那个肥皂泡则是薄膜干涉：光在薄膜的前表面和后表面分别反射， 两条路径的长度不同，于是有些颜色相互抵消，剩下的就是你看到的颜色。
Light of six hundred nanometres falls on two slits, two tenths of a millimetre apart. Where is the first bright fringe?
波长六百纳米的光照到相距零点二毫米的两条缝上，第一条亮纹在哪里？
A bright fringe needs a path difference of one whole wavelength, so the slit spacing times the sine of the angle equals the wavelength.
亮纹要求光程差恰好是一个完整波长，所以缝间距乘以角度的正弦等于波长。
That makes the sine of the angle three thousandths, and the angle about zero point one seven degrees.
由此角度的正弦是千分之三，角度约为零点一七度。
Tiny — which is why the screen sits far away.
非常小——这正是屏幕必须放得很远的原因。
Now we can answer the bubble.
现在我们可以回答泡泡的问题了。
Light hitting the film reflects twice: once from the top surface, once from the bottom.
光照到薄膜上会反射两次：一次来自上表面，一次来自下表面。
The two travel different distances, and the one off the denser surface flips by half a wavelength.
这两束反射波走过的距离不同，而从较密介质表面反射的那一束还会翻转半个波长。
So for each colour the two either add or cancel. It depends on the film's thickness there.
于是对每一种颜色来说，两束波要么相加、要么抵消，取决于该处薄膜的厚度。
The colours you see are the ones that add.
你看到的颜色就是相加的那些。
Turn that around and you get an antireflection coating. It is a quarter-wavelength layer, and its two reflections cancel.
反过来运用这个道理，就得到增透膜： 一层四分之一波长厚的薄层，让两束反射波相互抵消。
Three marks to lock in.
三个必须拿稳的分。
First, when a wave enters a new medium, the frequency never changes. The speed and the wavelength do.
第一，波进入新介质时频率永远不变，改变的是速度和波长。
Second, the path difference decides. Constructive interference needs a whole number of wavelengths. Destructive needs an odd number of half wavelengths.
第二，相长干涉要求光程差是整数个波长，相消干涉要求是奇数个半波长。
Third, on a string fixed at both ends the fundamental fits half a wavelength.
第三，两端固定的弦，基频恰好容纳半个波长。
Get those right and this unit is yours.
把这三点做对，这一单元就是你的了。