Waves
A-Level Physics Topic 7 16:45 English narration · English + 中文 subtitles burned in
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You are standing on a street corner.
你站在街角。
An ambulance races toward you, siren wailing at a high pitch — and the instant it passes, the pitch suddenly drops.
一辆救护车朝你疾驰而来，警笛发出高亢的声音——就在它经过的那一刻， 音调突然降低。
The siren never changed.
警笛本身从未改变。
So what did?
那么改变的是什么？
The sound is a wave.
声音是一种波。
As the ambulance rushes toward you, it crowds the waves together in front — a shorter wavelength, a higher pitch.
当救护车朝你冲来时，它把前方的波挤压在一起——波长更短，音调更高。
Behind it, the waves are stretched out — a longer wavelength, a lower pitch.
在它后面，波被拉伸开——波长更长，音调更低。
This is the Doppler effect, one of many secrets hidden in a wave.
这就是多普勒效应，波中隐藏的众多秘密之一。
Waves carry energy across the world — sound, light, ripples, and radio.
波把能量传遍整个世界——声音、光、水波和无线电。
Today: the language of waves, the wave equation, the Doppler effect, the whole spectrum of light, and polarisation.
今天：波的术语、波动方程、 多普勒效应、整个光谱，以及偏振。
Let's begin.
让我们开始吧。
Start with the idea itself.
先从概念本身开始。
A progressive wave carries energy from one place to another without moving matter overall.
行波把能量从一处传到另一处，但物质整体并不跟着移动。
The particles of the medium just oscillate about fixed rest positions — only the disturbance, and its energy, propagates.
介质里的粒子只是在固定的静止位置附近振动——传播出去的，只有扰动和它的能量。
Ripples on water, a wave on a rope, a squash on a slinky spring, and sound in air are all progressive waves.
水面上的涟漪、绳子上的波、弹簧上的挤压，以及空气中的声音，都是行波。
The energy travels outward; the water, the rope, and the air stay where they are on average.
能量向外传播；水、绳子和空气平均来说都留在原地。
The three standard demonstrations are a rope, a spring and the water surface in a ripple tank: shake or touch one end, and the oscillation travels away from where it started while the medium itself stays put.
三个标准演示是绳子、弹簧和水波槽里的水面： 抖动或者触碰一端，振动就从起点传出去，而介质本身留在原地。
Six words every wave question uses.
每一道波题都会用到这六个词。
Displacement is how far a particle has moved from its rest position at a moment — it is a vector.
位移是某一时刻粒子离开静止位置有多远——它是矢量。
Amplitude is the largest displacement from rest.
振幅是离开静止位置的最大位移。
Wavelength is the shortest distance along the wave between two points that move in phase, for example two next-door crests.
波长是波上两个同相点之间的最短距离， 例如相邻的两个波峰。
Period is the time for one full oscillation of a particle.
周期是一个粒子完成一次完整振动所用的时间。
Frequency is the number of full oscillations per second — one over the period — measured in hertz.
频率是每秒完整振动的次数——周期的倒数——单位是赫兹。
Speed is how fast a crest travels along the medium.
速率是波峰沿介质传播有多快。
Every wave has a shape you must be able to read, in two different graphs.
每一个波都有一个你必须会读的形状，用两种不同的图。
Freeze the wave in space, and you see its wavelength — the distance between two matching points.
把波在空间里冻结， 你就看到它的波长——两个相同状态的点之间的距离。
The height from the middle to a peak is the amplitude.
从中线到波峰的高度就是振幅。
Now instead watch a single point over time, and you see its period — the time for one full cycle.
现在换成盯着一个点随时间变化，你就看到它的周期——完成一个完整循环所用的时间。
The number of cycles each second is the frequency.
每秒的循环次数就是频率。
A graph of particle displacement against position, at one frozen moment, looks like a sine curve for both transverse and longitudinal waves.
某一冻结时刻，粒子位移对位置的图像，对横波和纵波都像一条正弦曲线。
From the rest axis up to a crest you read the amplitude.
从静止轴到波峰读出振幅。
Between two next-door crests you read the wavelength.
相邻两个波峰之间读出波长。
For a transverse wave the displacement axis is the real sideways motion.
对横波，位移轴就是真实的横向运动。
For a longitudinal wave it is the small back-and-forth displacement along the direction of travel — positive one way, negative the other.
对纵波，它是沿传播方向的小幅来回位移—— 正方向一边，负方向另一边。
Switch axes: particle displacement against time, at one fixed point in space.
换一组轴：在空间中一个固定点，粒子位移对时间。
Again you get a sine curve for both kinds of wave.
两种波仍然都得到正弦曲线。
From rest to a peak is still the amplitude.
从静止到峰值仍是振幅。
Between two next-door peaks is the period — and frequency is simply one over that period.
相邻两个峰值之间是周期——频率就是周期的倒数。
Two graphs, same wave: space shows wavelength; time shows period.
两幅图，同一个波：空间显示波长，时间显示周期。
These quantities are tied together by the most important equation in waves.
这些量被波中最重要的方程联系在一起。
In one period, a wave moves forward by exactly one wavelength.
在一个周期内，波恰好向前移动一个波长。
Speed is distance over time — so speed equals wavelength divided by period.
速度是距离除以时间——所以速度等于波长除以周期。
And since frequency is one over the period, the speed is simply the frequency, times the wavelength.
又因为频率是周期的倒数， 速度就等于频率乘以波长。
A sound wave at three hundred and forty hertz, with a wavelength of one metre, travels at three hundred and forty metres per second.
一个三百四十赫兹、波长为一米的声波， 以每秒三百四十米的速度传播。
Waves come in two kinds.
波分为两种。
In a transverse wave — like a wave on a rope, or a ray of light — the vibration is at right angles to the direction the wave travels.
在横波中——比如绳子上的波，或一束光——振动方向与波传播的方向成直角。
In a longitudinal wave, like sound, the vibration is back and forth along the same direction, squeezing the medium into compressions and rarefactions.
在纵波中，比如声音，振动是沿着同一方向来回进行，把介质挤压成密部和疏部。
Watch both: the same energy carried forward, but a completely different motion.
看这两种：向前传递的能量相同，但运动方式完全不同。
Look closely at a transverse wave on a rope.
仔细看绳子上的横波。
Each piece of rope vibrates up and down, at right angles to the energy travelling along the rope.
绳子的每一小段上下振动，与沿绳传播的能量方向成直角。
A wave on a rope, every electromagnetic wave, and S-waves inside the Earth are all transverse.
绳子上的波、所有电磁波，以及地球内部的横波，都是横波。
The particles oscillate perpendicular to the direction the energy travels — that is the definition you must write in the exam.
粒子垂直于能量传播方向振动——这就是考试中你必须写出的定义。
Now a longitudinal wave on a slinky spring.
再看弹簧上的纵波。
The coils bunch into compressions — higher pressure, particles close together — and spread into rarefactions — lower pressure, particles spread out.
线圈挤成密部——压强更高，粒子靠得更近——又散成疏部—— 压强更低，粒子分开。
Each coil vibrates back and forth, parallel to the direction the energy travels.
每一圈线圈前后振动，平行于能量传播方向。
Sound in any medium, P-waves in the Earth, and the squashes on a slinky are longitudinal.
任何介质中的声音、地球中的纵波，以及弹簧上的挤压，都是纵波。
Remember the names: compression and rarefaction.
记住这两个词：密部和疏部。
Two points on a wave, or two separate waves, can be in step, or out of step.
一个波上的两个点，或两个不同的波，可以同步，也可以不同步。
This is the phase difference, measured as an angle.
这就是相位差，用角度来量度。
When two waves rise and fall exactly together, they are in phase — a phase difference of zero.
当两个波完全一起起伏时，它们同相——相位差为零。
When one is a full half-cycle behind, they are in anti-phase — a phase difference of one hundred and eighty degrees, or pi radians.
当一个整整落后半个周期时， 它们反相——相位差是一百八十度，或者说派弧度。
Phase difference is the fraction of a cycle by which one oscillation leads or lags another.
相位差是一个振动比另一个超前或落后多少分之一个周期。
Give it in radians — a full cycle is two pi — or in degrees, where a full cycle is three hundred and sixty.
用弧度表示——一整周是二派——或用角度，一整周是三百六十度。
Two points one wavelength apart are in phase: phase difference zero, or two pi.
相距一个波长的两点同相：相位差为零，或二派。
Two points half a wavelength apart are exactly out of phase: phase difference pi.
相距半个波长的两点完全反相：相位差是派。
Same idea as anti-phase — just said in terms of distance along the wave.
这和反相是同一个意思——只是用波上的距离来说。
A wave carries energy, and how concentrated that energy is, is called the intensity — the power passing through each unit of area.
波携带能量，而这些能量有多集中，就叫做强度——穿过每单位面积的功率。
As a wave spreads out from a source, the same power covers a bigger and bigger area, so the intensity falls.
当波从一个源向外扩散时，同样的功率覆盖越来越大的面积，所以强度下降。
And here is a key link: the intensity is proportional to the amplitude squared.
这里有一个关键联系：强度与振幅的平方成正比。
Double the amplitude, and you get four times the intensity.
振幅加倍，强度就变成四倍。
For a point source sending energy equally in all directions, the wavefronts are spheres.
对一个向所有方向均匀发出能量的点源，波前是球面。
The surface area at distance r is four pi r squared, so intensity equals the power over four pi r squared — intensity falls as one over r squared.
距离为 r 处的表面积是四派 r 的平方，所以强度等于功率除以四派 r 的平方—— 强度按 r 的平方的倒数下降。
Doubling the distance cuts the intensity to a quarter.
距离加倍，强度降到四分之一。
And because intensity is proportional to amplitude squared, that means the amplitude is halved.
又因为强度与振幅的平方成正比，这意味着振幅减半。
Unit of intensity: watts per square metre.
强度的单位：瓦每平方米。
A lamp emits sixty watts of light equally in all directions.
一盏灯向所有方向均匀发出六十瓦的光。
Find the intensity two point zero metres away.
求二点零米处的强度。
Intensity is power over four pi r squared.
强度是功率除以四派 r 的平方。
Put the numbers in: sixty, divided by four pi times two squared.
代入数字：六十，除以四派乘以二的平方。
That is sixty over sixteen pi, which is about one point two watts per square metre.
也就是六十除以十六派，大约是一点二瓦每平方米。
Notice the units — watts on top, square metres below — exactly intensity.
注意单位——上面是瓦，下面是平方米——正好是强度。
To measure a wave in the lab, we use a cathode-ray oscilloscope, a CRO.
要在实验室里测量一个波，我们使用阴极射线示波器（CRO）。
It draws the wave on a screen.
它把波画在屏幕上。
The time-base sets how much time each square across stands for — so you can read the period, and from it the frequency.
时基决定横向每一格代表多少时间——这样你就能读出周期，再由它得到频率。
The y-gain sets how much voltage each square up stands for — so you can read the amplitude.
Y增益决定纵向每一格代表多少电压——这样你就能读出振幅。
Count the squares, and the wave gives up its secrets.
数一数格子，波就交出它的秘密。
Here is a real exam-style CRO trace.
这是一道考试风格的示波器波形。
The time-base is five milliseconds per division, and one full cycle takes four divisions across.
时基是每格五毫秒，一个完整周期占横向四格。
So the period is four times five milliseconds — twenty milliseconds.
所以周期是四乘以五毫秒——二十毫秒。
Frequency is one over the period: one over zero point zero two seconds, which is fifty hertz.
频率是周期的倒数：一除以零点零二秒， 就是五十赫兹。
Always convert to seconds before you invert.
取倒数之前一定先换成秒。
The y-gain would give you the amplitude in volts the same way: peak height in divisions, times volts per division.
Y 增益用同样的方法给出振幅的电压值： 峰值占几格，再乘以每格多少伏。
In the lab the screen looks like this — a modern digital oscilloscope with a grid, control knobs, and probe leads into the input sockets.
在实验室里屏幕就是这样——一台现代数字示波器，有网格、控制旋钮， 以及插在输入插座上的探头线。
For sound, a microphone feeds the voltage signal.
对声音，麦克风送入电压信号。
The grid lets you read the period and the amplitude directly.
网格让你直接读出周期和振幅。
Same two controls: time-base across, y-gain up.
还是那两个控制：横向时基，纵向 Y 增益。
Count the squares, apply the scale, and you have T, f, and A.
数格子，乘以标度，你就得到了周期、频率和振幅。
Now we can explain the siren with a formula.
现在我们可以用一个公式来解释警笛。
When a source moves toward a stationary observer, the observed frequency is the source frequency, times the wave speed, divided by the wave speed minus the source's speed.
当一个声源朝着静止的观察者移动时， 观测到的频率等于声源频率，乘以波速，再除以波速减去声源的速度。
Moving toward you, subtract, and the frequency rises.
朝你而来时，用减，频率升高。
Moving away, add, and it falls.
离你而去时，用加，频率降低。
That sudden drop as the ambulance passes is this formula, flipping its sign.
救护车经过时那突然的音调下降，就是这个公式在改变它的符号。
Picture the wavefronts.
想象这些波前。
The source moves to the right at speed v-sub-s.
声源以速度 v 下标 s 向右运动。
Ahead of it the circles bunch closer — shorter wavelength, higher heard frequency.
在它前方，圆圈挤得更近—— 波长更短，听到的频率更高。
Behind, they spread out — longer wavelength, lower frequency.
在后方，它们散开——波长更长，频率更低。
You only need the case of a stationary observer.
你只需要观察者静止这一种情况。
Choose the sign on the bottom of the formula to match the physics: minus when the source moves toward the observer, plus when it moves away.
在公式分母上选符号以匹配物理： 声源朝观察者来用减，离去用加。
A car horn at eight hundred hertz moves at thirty metres per second toward a still listener.
一个八百赫兹的汽车喇叭，以每秒三十米朝静止的听者驶来。
Speed of sound is three hundred and forty metres per second.
声速是每秒三百四十米。
Observed frequency is the wave speed times source frequency, over wave speed minus the source speed — toward, so subtract.
观测频率是波速乘以声源频率，再除以波速减去声源速度—— 朝向，所以用减。
Three hundred and forty times eight hundred, over three hundred and forty minus thirty.
三百四十乘以八百，除以三百四十减三十。
That is two hundred and seventy-two thousand over three hundred and ten, about eight hundred and seventy-seven hertz.
也就是二十七万二千除以三百一十，大约八百七十七赫兹。
Higher than eight hundred, as expected.
比八百高，正如所料。
Light is just one member of a huge family: the electromagnetic spectrum.
光只是一个庞大家族中的一员：电磁波谱。
From radio waves, metres or more across, through microwaves, infrared, visible light, ultraviolet, X-rays, and finally gamma rays, smaller than an atom.
从波长几米甚至更长的无线电波， 经过微波、红外线、可见光、紫外线、X射线，直到最后比一个原子还小的伽马射线。
They are all transverse waves, and in empty space they all travel at the same speed — the speed of light.
它们全都是横波，而在真空中它们都以相同的速度传播——光速。
Only a thin slice, from four hundred to seven hundred nanometres, is visible to your eyes.
只有很窄的一段，从四百到七百纳米，是你的眼睛能看见的。
Learn the orders of magnitude.
记住数量级。
In free space, radio waves are longer than a tenth of a metre — up to many kilometres.
在自由空间中，无线电波长于十分之一米——可达许多千米。
Microwaves sit from a millimetre to a tenth of a metre.
微波从一毫米到十分之一米。
Infrared runs from about seven times ten to the minus seven, up to a millimetre.
红外大约从七乘以十的负七次方到一毫米。
Visible light is four hundred nanometres, violet, to seven hundred nanometres, red.
可见光是四百纳米的紫光到七百纳米的红光。
Ultraviolet is shorter still; X-rays around ten to the minus eleven to ten to the minus eight metres; and gamma rays shorter than ten to the minus eleven.
紫外更短； X 射线大约十的负十一次方到十的负八次方米；伽马射线短于十的负十一次方。
All of them travel at c equals three point zero zero times ten to the eight metres per second in a vacuum.
在真空中它们都以光速传播——三点零零乘以十的八次方米每秒。
Use c equals f lambda to change between wavelength and frequency.
用光速等于频率乘以波长在波长和频率之间换算。
The boundaries are not sharp.
区域边界并不锐利。
One last property, unique to transverse waves.
最后一个性质，是横波所独有的。
Normally light vibrates in every direction at once.
通常光在每一个方向上同时振动。
A polarising filter lets through only the vibrations in one direction — the light is now polarised.
一个偏振滤片只让一个方向上的振动通过——现在光被偏振了。
Send it through a second filter, turned at an angle, and Malus's law tells you how much survives: the original intensity, times the cosine of the angle, squared.
让它穿过第二个转了一个角度的滤片， 马吕斯定律就告诉你有多少能通过：原来的强度，乘以角度的余弦，再平方。
Turn the second filter to ninety degrees, and no light gets through at all.
把第二个滤片转到九十度，就没有光能通过了。
Polarisation means making a transverse wave oscillate in one plane only.
偏振意味着让横波只在一个平面内振动。
Unpolarised light vibrates in many planes at once.
非偏振光同时在许多平面内振动。
After a polarising filter, only one plane remains — plane-polarised light.
经过偏振滤片后，只剩一个平面——平面偏振光。
Only transverse waves can be polarised, because the oscillation is perpendicular to travel, so different planes are real choices.
只有横波能被偏振，因为振动垂直于传播方向，不同平面才是真实的选择。
Longitudinal waves — sound — cannot be polarised: the oscillation is along the travel direction, so there is no other plane.
纵波——声音——不能偏振：振动沿传播方向，没有别的平面。
So polarisation is a test: if a wave can be polarised, it must be transverse.
所以偏振是一个检验：如果一种波能被偏振，它一定是横波。
Two filters in a row make this vivid.
两个滤片排成一列， 把这点表现得很清楚。
When their transmission axes are parallel, polarised light passes through.
当它们的透光轴平行时，偏振光通过。
When they are crossed — at right angles — no light passes.
当它们交叉——成直角——时， 没有光通过。
Malus's law at angle zero gives the full original intensity; at sixty degrees, intensity falls to a quarter, because cosine of sixty squared is one quarter; at ninety degrees, zero.
马吕斯定律在角度为零时给出全部原来的强度； 在六十度时强度降到四分之一，因为六十度余弦的平方是四分之一；在九十度时为零。
Plane-polarised light of intensity twelve watts per square metre meets a polarising filter whose axis is at thirty degrees to the plane of polarisation.
强度为十二瓦每平方米的平面偏振光，遇到透光轴与偏振面成三十度的偏振滤片。
Find the transmitted intensity.
求透射强度。
Malus says intensity times cosine squared of the angle.
马吕斯说：强度乘以角度余弦的平方。
Cosine of thirty degrees is root three over two, and that squared is three quarters.
三十度的余弦是根号三除以二， 平方是四分之三。
Twelve times zero point seven five is nine point zero watts per square metre.
十二乘以零点七五是九点零瓦每平方米。
After the first filter the polarisation lies along that filter's axis — measure the next angle from there.
经过第一个滤片后，偏振沿着该滤片的轴——下一个角度从那里量起。
Here is polarisation doing something beautiful.
这是偏振做的一件漂亮事。
A clear plastic protractor sits between two crossed polarising filters.
一把透明塑料量角器放在两个交叉的偏振滤片之间。
Light only reaches your eye because the stressed plastic rotates its plane of polarisation — the rainbow colours map where the plastic is squeezed most.
光之所以能到达你的眼睛，是因为受应力的塑料旋转了偏振面—— 彩虹色标出塑料被挤压最厉害的地方。
With ordinary light it would just look clear.
在普通光下它看起来只是透明的。
Crossed filters plus stress turn invisible forces into a picture.
交叉滤片加上应力，把看不见的力变成一幅图。
Three marks to secure.
三个要拿稳的分。
First, the wave equation: speed equals frequency times wavelength — the backbone of every wave problem.
第一，波动方程：速度等于频率乘以波长——每一道波题的支柱。
Second, intensity is proportional to amplitude squared, not amplitude.
第二，强度与振幅的平方成正比，而不是与振幅成正比。
Third, polarisation only happens for transverse waves — never for sound.
第三，偏振只发生在横波上—— 声音绝不会偏振。
Master these, and waves are yours.
掌握这些，波就是你的了。
The fixed-wording definitions, one answer only.
固定措辞的定义，只给一个答案。
A progressive wave transfers energy from one place to another without transferring matter.
行波：把能量从一处传到另一处，而不传递物质。
A transverse wave oscillates perpendicular to the direction of energy transfer; a longitudinal wave oscillates parallel to it.
横波的振动方向与能量传递方向垂直；纵波的振动方向与之平行。
Displacement: the distance of a particle from its equilibrium position, in a stated direction.
位移：质点沿指定方向偏离平衡位置的距离。
Amplitude: the maximum displacement from equilibrium.
振幅：质点偏离平衡位置的最大位移。
Wavelength: the minimum distance between two points on the wave that are in phase — adjacent crests, for example.
波长：波上相位相同的两点之间的最小距离——比如相邻的两个波峰。
Period: the time for one complete oscillation, or for the wave to travel one wavelength.
周期：完成一次完整振动所需的时间，或者波传播一个波长所需的时间。
Frequency: the number of oscillations per unit time, or the number of wavefronts passing a point per unit time.
频率：单位时间内的振动次数，或者单位时间内通过某点的波前数目。
And the traps that lose marks every year.
再说每年都在丢分的那些陷阱。
A phase difference bigger than one cycle means you have not reduced it — only the fraction of a cycle matters, so four hundred and fifty degrees is ninety, and ninety degrees is pi over two radians.
相位差超过一个周期，说明你没有把它化简——只有一个周期的那一部分才有意义， 所以四百五十度就是九十度，而九十度是 π 比二弧度。
Read the wavelength from the displacement-DISTANCE graph; the displacement-time graph gives the period.
波长要从位移—距离图上读；位移—时间图给的是周期。
Doubling the amplitude does not double the intensity — the intensity goes as amplitude squared, so it is four times.
振幅加倍，强度并不是加倍——强度随振幅的平方变化，所以是四倍。
Do not choose the Doppler sign by feel: towards means minus on the bottom and the frequency goes up, away means plus and it goes down, and check the answer lies on the right side of the source frequency.
多普勒的符号不要凭感觉选： 相向运动是分母取减、频率升高，背向运动是取加、频率降低， 而且要检查答案落在波源频率的正确一侧。
After a polarising filter the light is polarised along that filter's axis, so the next angle is measured from there, not from the first.
光通过一个偏振片之后，就沿着那个偏振片的轴偏振， 所以下一个角度要从那里量起，不是从第一个量起。
And sound cannot be polarised — only transverse waves can.
另外声音不能被偏振——只有横波可以。