Waves
IGCSE Physics Topic 3 17:11 English narration · English + 中文 subtitles burned in
Chapters
Transcript
Drop a stone in a pond, and rings spread outward.
往池塘里丢一颗石子，水环就向外扩散。
But watch a leaf floating on the surface — it only bobs up and down; it does not travel with the ripples.
但看看漂在水面上的一片叶子—— 它只是上下起伏，并不随波纹一起前进。
That is the secret of every wave.
这就是每一种波的秘密。
A wave carries energy from one place to another, but it does not carry the water, the air, or any matter along with it.
波把能量从一个地方带到另一个地方，却不会把水、空气或任何物质一起带走。
Welcome to waves — from ripples on a pond, to the light in your eyes and the sound in your ears.
欢迎来到波的世界——从池塘上的涟漪，到你眼中的光、耳中的声。
They all follow the same simple rules.
它们都遵循同样简单的规则。
Let's begin.
让我们开始吧。
First, the language of waves.
先学波的语言。
A wavefront is a line joining points that move together — like the top of one ripple on a pond.
波前是连接一起运动的点的线——就像池塘上一道涟漪的顶部。
Wavelength is the distance between two neighbouring wavefronts: one full wave.
波长是相邻两个波前之间的距离：一整列波。
Frequency is how many waves pass a point each second, measured in hertz.
频率是每秒通过某点的波的数目， 单位是赫兹。
The top of the wave is a crest; the bottom is a trough.
波的顶部叫波峰，底部叫波谷。
Amplitude is the largest distance a point moves from its rest position.
振幅是一点离平衡位置的最大距离。
And wave speed is simply how fast a wavefront travels through the medium.
波速则是波前在介质中前进的快慢。
Every wave has the same parts.
每一种波都有相同的组成部分。
The wavelength is the distance from one crest to the next.
波长是从一个波峰到下一个波峰的距离。
The amplitude is the height from the middle up to a crest — a bigger amplitude means more energy.
振幅是从中间到波峰的高度——振幅越大，能量越多。
The frequency is how many waves pass each second, in hertz.
频率是每秒通过的波的数目，单位是赫兹。
And these link together in the wave equation: wave speed equals frequency times wavelength.
它们由波速公式联系起来：波速等于频率乘以波长。
So a sound wave at three hundred and forty metres per second, with a frequency of one hundred and seventy hertz, has a wavelength of two metres.
所以一列声波，速度是每秒三百四十米， 频率是一百七十赫兹，它的波长就是两米。
The top of a wave is the crest, also called the peak; the bottom is the trough.
波的顶部叫波峰，也叫峰；底部叫波谷。
Look carefully at this transverse wave diagram.
仔细看这张横波图。
Wavelength is the full distance between two crests, or between two troughs — one complete cycle.
波长是两个波峰之间、或两个波谷之间的完整距离——一个完整周期。
Amplitude is measured straight up from the rest position to a crest, not from crest to trough.
振幅是从平衡位置竖直量到波峰，不是从波峰量到波谷。
The arrow along the side shows the direction of travel.
旁边的箭头表示传播方向。
Remember: rearrange the wave equation as wavelength equals speed divided by frequency when the exam asks for lambda.
记住：考试要求波长时，把波速公式改写成波长等于速度除以频率。
There are two kinds of wave.
波有两种。
In a transverse wave, the particles wobble at right angles to the way the wave travels — up and down, while the wave moves sideways.
在横波中，粒子在与波前进方向成直角的方向上摆动——上下摆动，而波向侧面前进。
Light and water waves are transverse.
光波和水波是横波。
In a longitudinal wave, the particles wobble back and forth along the same line the wave travels, squeezing together and spreading apart.
在纵波中，粒子沿着波前进的同一条线来回摆动，一会儿挤在一起， 一会儿散开。
Sound is longitudinal.
声波是纵波。
Here are both types side by side.
这里两种波并排对比。
On a transverse wave the particles vibrate at right angles to the direction the wave travels — its propagation — making crests and troughs.
横波中粒子在传播方向的垂直方向振动，形成波峰和波谷。
On a longitudinal wave they vibrate along the travel direction, making compressions — particles packed close together — and rarefactions — particles spaced further apart.
纵波中粒子沿着传播方向振动，形成压缩区——粒子挤得很近——和稀疏区——粒子分得较开。
Light and water sit in the top picture; sound sits in the bottom one.
光波和水波属于上面那种；声波属于下面那种。
The exam loves that contrast, so keep it sharp.
考试很爱考这个对比，一定要分清。
All waves can do three things.
所有波都能做三件事。
They reflect, bouncing off a barrier.
它们会反射，从障碍物上弹回。
They refract, bending as they speed up or slow down in a new material.
它们会折射， 在进入新材料、速度改变时发生弯折。
And they diffract, spreading out after passing through a gap.
它们还会衍射，穿过缝隙后向外扩散。
The spreading is greatest when the gap is about as wide as one wavelength.
当缝隙的宽度大约等于一个波长时，扩散最明显。
Diffraction is waves spreading out after they pass a gap or go around an edge.
衍射是波穿过缝隙或绕过边缘后向外扩散。
Straight plane wavefronts hit a barrier with a narrow opening, and beyond the gap they curve into arcs.
笔直的平面波前碰到带窄缝的挡板， 过缝后弯成弧形。
Spreading is strongest when the gap is about one wavelength wide.
当缝宽大约等于一个波长时，扩散最强。
A much wider gap means weaker diffraction; a much narrower gap also changes the pattern.
缝宽得多，衍射就弱； 缝窄得多，图样也会变。
Remember: every kind of wave can diffract — water, sound, and light.
记住：每一种波都能衍射——水波、声波和光波都行。
A ripple tank is a shallow tray of water with vibrating dippers that make waves you can watch.
波纹水槽是一个浅水盘，振动的点拨器在水面上激起可观察的波。
Two dippers make circular ripples that overlap into a pattern of bright and dark lines.
两个点拨器 产生圆形涟漪，重叠后形成明暗条纹。
You can also put barriers in the water to show reflection, change the depth to show refraction, and open a gap to show diffraction.
你也可以在水中放挡板看反射， 改变水深看折射，开一道缝看衍射。
It is the classic school lab for wave behaviour.
这是学校里研究波行为的经典实验。
Let's look closer at light.
我们来仔细看看光。
When light hits a mirror, we measure its angle from the normal — a line at right angles to the surface.
当光照到镜子上时，我们从法线量它的角度—— 法线是与表面成直角的一条线。
The law of reflection is simple: the angle of incidence equals the angle of reflection.
反射定律很简单：入射角等于反射角。
A flat mirror makes an image that is the same size, as far behind the glass as the object is in front, and virtual — you cannot catch it on a screen.
平面镜所成的像大小相同，像在镜后的距离等于物在镜前的距离，而且是虚像—— 你无法把它接到屏幕上。
On this ray diagram, the dashed line is the normal.
在这张光线图上，虚线是法线。
The angle of incidence is between the incoming ray and the normal; the angle of reflection is between the outgoing ray and the normal.
入射角是入射线与法线之间的角；反射角是 反射线与法线之间的角。
They are equal.
它们相等。
Never measure from the mirror surface itself — that is a common way to lose the mark.
千万不要从镜面本身量角——那是丢分的常见原因。
A plane mirror image is also laterally inverted: left and right swap, as in a bathroom mirror.
平面镜像还有左右颠倒：左边和右边对调，就像浴室镜子里一样。
Now watch light cross from air into glass.
现在看光从空气进入玻璃。
It slows down, and bends towards the normal.
它慢下来，并向法线弯折。
This bending is refraction.
这种弯折就是折射。
How much it bends is measured by the refractive index — the sine of the angle going in, divided by the sine of the angle coming out.
弯折的程度用折射率来量——入射角的正弦，除以折射角的正弦。
For a ray entering glass at sixty degrees and refracting to thirty-five, the refractive index is about one point five.
一条光线以六十度射入玻璃、折射到三十五度，折射率大约是一点五。
How you see it in the lab: shine a narrow ray from a ray box into a rectangular glass block standing on paper.
在实验室里怎么看到它： 用光线盒射出一条细光线，射进立在纸上的长方形玻璃砖。
Mark the ray going in and the ray coming out, remove the block, and join the marks to draw the ray inside the glass.
标出射入的光线和射出的光线，把玻璃砖拿走， 把这些标记连起来，就画出了玻璃内部的那段光线。
Then draw the normal where the ray meets the surface and measure both angles from it.
然后在光线与表面相交的地方画法线，两个角都从法线量起。
Rule of thumb for refraction.
折射的经验法则。
When light goes into a denser material — air into glass — it slows down and bends towards the normal, so the angle of incidence is bigger than the angle of refraction.
光进入较密的材料——从空气到玻璃——会变慢并向法线弯折， 所以入射角大于折射角。
When light leaves a denser material — glass into air — it speeds up and bends away from the normal.
光离开较密材料——从玻璃到空气——会变快并远离法线弯折。
The angle in the second material is called the angle of refraction.
第二种材料里的角叫做折射角。
Keep measuring both angles from the normal, not from the surface.
两个角都要从法线量，不要从表面量。
Worked example.
例题。
A ray passes from air into glass.
一束光从空气进入玻璃。
The angle of incidence is sixty degrees and the angle of refraction is thirty-five degrees.
入射角是六十度，折射角是三十五度。
The refractive index n equals sine of i over sine of r.
折射率 n 等于入射角正弦除以折射角正弦。
Sine of sixty is about zero point eight seven, and sine of thirty-five is about zero point five seven.
六十度的正弦大约是零点八七， 三十五度的正弦大约是零点五七。
Divide zero point eight seven by zero point five seven — that gives one point five.
用零点八七除以零点五七——得到一点五。
So the glass has refractive index one point five.
所以这块玻璃的折射率是一点五。
n is a ratio, so it has no unit.
n 是比值，所以没有单位。
Something surprising happens when light tries to leave glass.
当光试图离开玻璃时，会发生一件出人意料的事。
If the angle inside is too steep — bigger than the critical angle — the light cannot escape at all.
如果内部的角度太陡—— 大于临界角——光就完全无法射出。
Instead, it bounces completely back inside.
它反而会全部弹回玻璃内部。
This is total internal reflection.
这就是全反射。
It is how optical fibres work: light bounces along a thin glass thread, carrying phone calls and internet data as pulses of light.
光纤正是这样工作的：光在细细的玻璃丝里不停弹跳，把电话和互联网数据当作光脉冲一路传送。
Compare the two glass blocks.
对比这两块玻璃。
On the left the ray hits the top face below the critical angle, so some light refracts out into the air.
左边光线打在顶面时小于临界角，所以有一部分折射进空气。
On the right the angle inside is above the critical angle, so none escapes — the ray is totally internally reflected.
右边内部角度大于临界角，完全没有光射出——光线发生了全反射。
Two conditions must both be true: light must be travelling from a denser material towards a less dense one, and the angle inside must beat the critical angle.
两个条件必须同时满足：光必须从较密材料射向较疏材料，并且内部角度超过临界角。
The critical angle c is linked to the refractive index by a simple formula: n equals one over sine of c.
临界角 c 和折射率由一个简单公式联系起来：n 等于一除以 c 的正弦。
Rearrange it: sine of c equals one over n.
改写一下：c 的正弦等于一除以 n。
So denser glass with a larger n has a smaller critical angle — total internal reflection starts more easily.
所以 n 更大的密玻璃临界角更小—— 更容易发生全反射。
You only use this when light is inside the denser material, trying to get out.
只有当光在较密材料内部试图射出时，才用这个公式。
Optical fibres are thin glass threads.
光纤是细细的玻璃丝。
Light enters at one end and total internal reflection keeps bouncing it along the fibre until it shines out at the tip.
光从一端进入，全反射让它在光纤里不停弹跳， 直到从尖端射出。
That is how telephone calls and internet data travel as pulses of light — fast, with little energy lost.
电话和互联网数据就是这样以光脉冲传送的——又快，能量损失又小。
You can see each fibre glowing where the light finally escapes.
你可以看到每根光纤在光最终逸出的地方发光。
A converging lens is fat in the middle, and it bends parallel rays inward to meet at a single point — the principal focus.
凸透镜中间厚，它把平行光线向内弯折，会聚到一个点——焦点。
The distance from the lens to that point is the focal length.
从透镜到这个点的距离就是焦距。
A converging lens can throw a real image onto a screen; held close to the eye, the same lens works as a magnifying glass.
凸透镜能把实像投到屏幕上； 如果拿到眼睛附近，同一块透镜就成了放大镜。
A converging lens is thick in the middle.
凸透镜中间厚。
Parallel rays that pass through it meet at the principal focus; the focal length is the lens-to-focus distance.
穿过它的平行光线会聚在主焦点；焦距就是透镜到焦点的距离。
A diverging lens is thin in the middle and spreads rays out, so they only seem to come from a focus on the same side as the object.
凹透镜中间薄，会把光线散开，所以光线只是看起来像从物侧的焦点发出。
Know both shapes: fat middle converges; thin middle diverges.
两种形状都要认：中间厚会聚，中间薄发散。
Two words to get right.
有两个说法要说准。
The principal axis is the straight line through the centre of the lens at right angles to it, and the principal focus lies on that axis.
主光轴，是穿过透镜中心并且与透镜垂直的那条直线，焦点就在这条轴上。
And describe an image with three pairs of words: enlarged or diminished, upright or inverted, real or virtual.
另外，描述像要用三对词： 放大的还是缩小的，正立的还是倒立的，实像还是虚像。
An object far beyond the focus gives a diminished, inverted, real image.
物体远在焦点之外时，成的是缩小、倒立的实像。
A real image is where rays actually meet, so you can catch it on a screen — a projector and a camera both form real images.
实像是光线真正会聚的地方，所以可以接到屏幕上——投影仪和照相机都成实像。
A virtual image is where rays only seem to come from; you cannot put a screen there and see it.
虚像是光线只是看起来从那里发出的地方；你无法在那里放屏幕看到像。
When the object is very close to a converging lens, the image is virtual, upright and magnified — that is a magnifying glass held close to the eye.
当物体离凸透镜很近时，像是虚像、正立且放大——那就是靠近眼睛的放大镜。
Hold a converging lens away from your eye and look through it at distant houses.
把凸透镜拿离眼睛，透过它看远处的房子。
The image appears upside down — that is a real image formed by the lens.
像是倒立的——这是透镜成的实像。
Rays from each point on the house really meet again after the lens, so the picture is inverted.
房子上每一点发出的光线在透镜后真正会聚，所以画面是倒的。
Bring the lens close to your eye instead, and you get the upright magnified view of a magnifying glass.
若把透镜靠近眼睛，就得到放大镜那种正立放大的像。
Send white light through a prism, and it fans out into a rainbow — red bends the least, violet the most.
让白光穿过棱镜，它就展开成一道彩虹——红光弯折最少，紫光最多。
This splitting is called dispersion.
这种分解叫做色散。
But visible light is only a tiny slice of a much bigger family: the electromagnetic spectrum.
但可见光只是一个更大家族里的一小片：电磁波谱。
In order: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
按顺序是：无线电波、微波、红外线、 可见光、紫外线、X射线和伽马射线。
They all travel at the same speed in a vacuum.
它们在真空中都以相同的速度传播。
But moving from radio to gamma, the wavelength shrinks while the frequency and energy rise — and so does the danger.
但从无线电波到伽马射线，波长变短，而频率和能量升高——危险性也随之升高。
A glass prism refracts violet light most and red light least, so white light spreads into a spectrum.
玻璃棱镜对紫光折射最多、对红光折射最少，所以白光展开成光谱。
The colour order is red, orange, yellow, green, blue, indigo, violet.
颜色顺序是红、橙、黄、绿、蓝、靛、紫。
Red has the longest wavelength and the lowest frequency; violet is the opposite — shortest wavelength, highest frequency.
红光波长最长、频率最低； 紫光相反——波长最短、频率最高。
Light of a single pure frequency is called monochromatic — one colour only.
单一纯频率的光叫单色光——只有一种颜色。
Here is a real prism doing the same job.
这是真实棱镜做的同一件事。
A narrow beam of white light enters the glass and fans out into a bright band of rainbow colours on a dark background.
一束窄白光进入玻璃，在深色背景上展开成明亮的彩虹色带。
Same physics as the diagram: different wavelengths refract by different amounts, so the colours separate.
和示意图同一套物理：不同波长折射程度不同，颜色就分开了。
Learn a use and a danger for each band.
每一段都要记住一个用途和一个危险。
Radio waves carry radio and TV signals.
无线电波传送广播和电视信号。
Microwaves run mobile phones, satellite TV and cooking, but too much heats body cells.
微波用于手机、卫星电视和烹饪，但过多会加热人体细胞。
Infrared is for remote controls, thermal imaging and grills — excess causes skin burns.
红外线用于遥控器、 热成像和烤架——过量会灼伤皮肤。
Visible light lets us see.
可见光让我们看见东西。
Ultraviolet sterilises water and checks bank notes, but can cause skin cancer and eye damage.
紫外线消毒水和检查钞票， 但可能导致皮肤癌和眼睛损伤。
X-rays make medical and security scans, yet damage cells.
X射线做医学和安检扫描，却会损伤细胞。
Gamma rays sterilise equipment and treat cancer, but can mutate cells.
伽马射线消毒设备和治疗癌症，但可能使细胞突变。
From radio to gamma, frequency and energy climb, so danger climbs too.
从无线电到伽马， 频率和能量上升，危险也上升。
All travel at three times ten to the eight metres per second in a vacuum.
它们在真空中都以每秒三乘以十的八次方米传播。
Radio waves and microwaves carry information as signals.
无线电波和微波以信号形式携带信息。
An analogue signal varies continuously and can take any value.
模拟信号连续变化，可以取任意值。
A digital signal is a stream of just two values — high or low, one or zero.
数字信号只是两个值的序列——高或低，一或零。
Modern systems prefer digital for two exam reasons.
现代系统偏爱数字，考试有两个理由。
First, a higher rate of data transmission.
第一，更高的数据传输速率。
Second, a greater range: a weak digital signal can be regenerated back to a clean one or zero, because only two levels must be told apart, so noise is stripped away.
第二，更远的传输距离：微弱的数字信号可以再生为 干净的一或零，因为只需区分两个电平，噪声就被去掉。
Analogue noise cannot be cleaned like that, so it builds up.
模拟噪声无法这样清理， 所以会不断累积。
Finally, sound.
最后是声音。
A vibrating object squeezes the air into compressions, and stretches it into rarefactions — a longitudinal wave.
振动的物体把空气挤成压缩区，又把它拉成稀疏区——这是一列纵波。
Because sound needs a material to travel through, it cannot cross empty space.
因为声音需要靠材料来传播，所以它无法穿越真空。
A bigger vibration is louder; a faster vibration is higher in pitch.
振动越大，声音越响； 振动越快，音调越高。
And a reflected sound is an echo.
反射回来的声音就是回声。
Clap eighty-five metres from a wall; if the echo returns in half a second, the sound travelled one hundred and seventy metres — so its speed is three hundred and forty metres per second.
在离墙八十五米处拍一下手， 如果回声在半秒后传回，声音就走了一百七十米——所以声速是每秒三百四十米。
Humans hear frequencies from about twenty hertz up to twenty thousand hertz.
人能听到大约二十赫兹到两万赫兹的频率。
Below that is infrasound; above it is ultrasound.
低于这是次声波；高于这是超声波。
Sound needs a medium — a material — so there is no sound in a vacuum.
声音需要介质——一种材料——所以真空中没有声音。
Pump the air out of a jar and the sound stops.
把罐子里的空气抽掉，声音就停了。
It travels much slower than light: about three hundred and forty metres per second in air, and faster in liquids and solids than in gases.
它比光慢得多：空气中大约 每秒三百四十米，在液体和固体中比在气体中更快。
Larger amplitude means greater loudness; higher frequency means higher pitch.
振幅越大响度越大； 频率越高音调越高。
A microphone converts those air vibrations into an electrical signal.
麦克风把空气振动转换成电信号。
Ultrasound is sound above twenty thousand hertz — too high for humans to hear.
超声波是频率高于两万赫兹的声音——人听不见。
Its uses all rely on reflection.
它的用途都靠反射。
Sonar measures water depth.
声呐测量水深。
Medical scanning images a baby or soft tissue.
医学扫描给胎儿或软组织成像。
Non-destructive testing finds cracks inside metal without cutting it open.
无损检测在不切开金属的情况下找裂纹。
Like an echo, an ultrasound pulse travels there and back, so you halve the total distance.
和回声一样，超声脉冲走去又回来，所以总距离要除以二。
Worked example: a sonar pulse returns from the seabed in zero point one zero seconds; sound in water is one thousand five hundred metres per second.
例题：声呐脉冲 零点一秒后从海底返回；水中声速是每秒一千五百米。
Distance there and back is one hundred and fifty metres, so the sea is seventy-five metres deep.
来回距离是一百五十米， 所以海水深七十五米。
Three marks to secure.
锁住三个分。
First, always measure angles from the normal, not from the surface.
第一，永远从法线量角度，而不是从表面。
Second, sound needs a medium, so it cannot travel through a vacuum — but light can.
第二，声音需要介质， 所以它无法穿越真空——但光可以。
Third, total internal reflection happens only going from a denser material to a less dense one, when the angle beats the critical angle.
第三，全反射只在光从较密的材料射向较疏的材料、 并且角度超过临界角时才发生。
Learn these, and waves are yours.
把这些记牢，波就是你的了。
Three more.
再记三条。
Learn the wave equation: wave speed equals frequency times wavelength — and be ready to rearrange it.
学会波速公式：波速等于频率乘以波长——并会改写。
Transverse waves vibrate across the direction of travel, like light and water; longitudinal waves vibrate along it, like sound.
横波在传播方向的垂直方向振动，如光和水波；纵波沿传播方向振动，如声波。
Going into a denser material light bends towards the normal; leaving it, light bends away.
进入较密材料时光向法线弯折；离开时远离法线弯折。
And know the electromagnetic spectrum order: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
还要记住电磁波谱顺序： 无线电、微波、红外、可见、紫外、X射线、伽马。
Correcting sight is the standard application.
矫正视力是标准的应用题。
A person with short-sightedness sees near things clearly but distant things are blurred, because the eye focuses the light in front of the retina; a diverging lens spreads the rays out first, so they focus on the retina instead.
近视的人看近处清楚、看远处模糊，因为眼睛把光聚焦在视网膜前面； 凹透镜先把光线发散一些，于是它们正好聚焦在视网膜上。
Long-sightedness is the other way round — the light would focus behind the retina — and a converging lens brings it forward.
远视正好相反——光线会聚焦在视网膜后面——凸透镜把焦点往前拉。
And communication with artificial satellites mainly uses microwaves, because they pass through the atmosphere: some satellite phones use satellites in low orbit, while direct broadcast television uses a geostationary orbit, where the satellite stays above the same point on the Earth so the dish never has to move.
另外，与人造卫星的通信主要用微波，因为微波能穿过大气层： 有些卫星电话用低轨道卫星， 而卫星电视直播用地球同步轨道， 卫星停在地球同一个点的上空，所以接收天线不用转动。