8.03 - Lect 12 - Dispersion, Phase Velocity, Group Velocity

Dispersion - Phase Velocity - Group Velocity
Assignments Lecture 11 and 12: freepdfhosting.com/b1eb3c492d.pdf
Solutions Lecture 11 and 12: freepdfhosting.com/6320080896.pdf

[@perfectlyimperfect6849]

Best series of lectures to clear our concepts.... 😀 Thankyou so much professor 🙏

[@kithvilla5442]

this is the best lecturer for physics.i don't think anyone going to doubt that .thank you sir

[@lecturesbywalterlewin.they9259]

+Kith Villa Thank you Kith

[@stauffap]

This is great! Some years ago i was fascinated with slow motion videos of guitar strings and i was wondering how a string could ever produce sound with different harmonics/frequencies. After all initially i expected a string to simply swing up and down like a first harmonic standing wave, when i pluck it in the middle. In my mind this could only produce sound(pressure oscilations) of one frequency. Later on i speculated that since, when you pluck a string you start out with a triangular shape, that this shape might split into its different fourier components and that this causes the higher harmonics, that i was recording on my computer. But i was never really sure if i was on the right track. So this lecture answers a lot of questions! Very interesting. I'd love to see this behavior on a real string though. Maybe it's possible with modern slow motion cameras.

[@lecturesbywalterlewin.they9259]

:)

[@victorenriquetumepalacios3046]

Wonderful lecture!!

[@bharathreddygudibandi492]

extraordinary lecture!!!!!!!!!!!!

[@MathewVarughese]

You have really inspired me professor in the feld of physics. Planning to do higher stdies in Optics after a long gap of job.

[@lecturesbywalterlewin.they9259]

GREAT!

[@PymGordonArthur]

Thank you sir so so much. Hello from Serbia❤

[@alexpacini]

How to pass the corona virus lock-down safely? Staying at home and watching Lewin's physics lectures!

[@pedbag2813]

Absolutely superb! Thank you :D I also read through your book "For the Love of physics" the free press edition, and loved your notes on electromagnetism and quite liked the photographs specially black hole pictures. Loved it! Tasty little intellectual morsel!

[@lecturesbywalterlewin.they9259]

+Ped Bag Thank you Ped.

[@eladmileikowsky738]

Hi, Does anyone have any information about the full derivation of the dispersion relation of a string and deep water waves?

[@marziavalli7511]

Dear Prof. Lewin, thank you for your inspiring lecture. I would like to ask a question: At about 51’:55’’ you say that the dephasing of the component waves, which induces the destruction of the squared wave profile, is due the fact that . Now, on a string having fixed extremes, the waves should be standing because the stationarity is a consequence of the superposition of each incident and reflected component wave in correspondence of the extremes (whether the string is dispersive or not). Therefore the travelling speed should be zero. Wouldn’t be preferable to affirm that the squared profile vanishes since the higher frequencies are no longer integer multiples of the fundamental and, hence, tend to lose the phase coherence during their oscillations?

[@hannaedwards5197]

I wished i could go back in time and be your student . These days i would appreciate it so much .

[@lecturesbywalterlewin.they9259]

Hanna - What is special about "These days"? are you OK? My 94 MIT course lectures are on my KZbin channel, thus you can be my student. I answer all questions! You may also like my Bi-Weekly Physics Math Problems.

[@hannaedwards5197]

Lectures by Walter Lewin. They will make you ♥ Physics. And this is truly wonderful of you and i am glad you understood my non-question after all ;) . With "these days" i meant as opposed to 16 years ago when i was a student that did not appreciate.

[@lecturesbywalterlewin.they9259]

😊 🌈 😊

[@sanjaybishtphysics461]

Very engrossing lecture dear sir. The physical interpretation of phase velocity and group velocity is spot on. Your passion and penchant for Physics is exemplary. You have gone fairly deep into the matter and still kept the lecture very lucid and energetic.Love, light and energy to Dr. Walter. Lewin.

[@charlesb3300]

😮

[@realcygnus]

clearly thE best of the best !

[@lecturesbywalterlewin.they9259]

thank you

[@GuilherHast]

01:07:00 The speed of light in the water is about 0.75 C

[@yajatagarwal5809]

hello sir i wanted to ask that when you have used lambda in deep water waves, which wavelength are we talking about.Is it the envelope wavelength or something else

[@zachgeldenhuis]

Your dotted line drawing skills are an inspiration! The dispersion stuff was helpful to haha

[@lecturesbywalterlewin.they9259]

+Zach Geldenhuis try this kzbin.info/www/bejne/qJLYo59qqJWjoLc

[@zachgeldenhuis]

Hahaha that is absolutely fantastic! The sound makes it!

[@zachgeldenhuis]

On another note, the reason I was watching the video is because I'm a tad stuck on a question in my revision notes, can't hurt to ask I guess! That's the question, if you could help me in any way that would be amazing! If not, keep drawing those lines and I'll be happy haha Demonstrate that there is a standing wave at the Brillouin zone boundary for the case of waves on a row of masses, m, with spacing a, and connected by springs of elastic constant, β, for which the dispersion relation is 𝜔= (4𝛽 / M)^0.5 |sin(𝑘𝑎 / 2)|

[@lecturesbywalterlewin.they9259]

+Zach Geldenhuis I am unaware of this. I suggest you search the web. In the mean time you may have to settle for my dotted lines. Ben jij Nederlander? Geldenhuis is een Nederlandse naam; kom je nergens anders tegen. .

[@zachgeldenhuisqwerty]

+Lectures by Walter Lewin. They will make you ♥ Physics. Ah well, it was worth a try :) Suid Afrikaans Ek is bang, maar hulle is baie soortgelyk

[@MathPhysicsFunwithGus]

At the beginning I was thinking how am I going to always remember that, then he said I don't expect you to remember that, then I calmed down😂

[@monkfoobar]

A labor of love

[@rajiballiashayar]

Best lecture sir

[@yogeshkumar-zv1ix]

Sir for lambda < 1cm Vg should be 3/2 Vp but you said that Vg = 1/2Vp... is it correct ?

[@france8607]

Sir, my teacher told me that when refraction takes place, the emergent ray has the same speed as the incident one, but then he told that Refractive index is inversely proportional to wavelength Till then, so far so good!! But then he said that wavelength changes because frequency remains constant. I straight away asked if refractive index changes with wavelength and wavelength decreases inside the glass, then refractive index inside the glass slab will be lower and hence the speeds of emergent and incident rays are not the same

[@carultch]

The emergent ray is what we call it, after it exits the optically dense medium, and returns to its original medium (or lack thereof), which therefore has the same speed as the incident ray. The refracted ray is what you haven't mentioned, which is the ray that travels in the optically dense medium at a lower speed than the incident ray. Frequency remains unchanged as waves transition between media. Wavelength is "sacrificed" to a reduce wavespeed. It would mean big problems for causality and conservation of energy, if frequency changed instead. When we plot refractive index as a function of wavelength, what we really mean is the free space wavelength, rather than the wavelength in that particular medium. It would be more accurate to plot it as a function of frequency or period, but you cannot measure these values directly at IR frequencies and above. So we measure the free space wavelength to quantify the color of light.

[@pollofeliz6792]

Professor Lewin, When we talk about the dispersion relation, we find very often the relation in the form omega = f(k). Is that not misleading? Actually, omega of the wave is not changing... Would not be better to give k (oder lambda) = f (omega) or simply v = f(omega) ? Each given omega has a different k in a dispersive medium compared to vacuum but not each given k in a dispersive medium has a different omega compared to vacuum... Like 8.01 and 8.02, 8.03 lectures are fantastic... Thank you so much to be able to explain in such a wonderful way so non intuitive concepts..

[@lecturesbywalterlewin.they9259]

+Pollo Feliz k = 2pi/lambda. The higher omega, the smaller lambda. omega for blue light is higher than for red light. Thus the wavelength of blue light is smaller than that of red light.

[@The_Green_Man_OAP]

​​​@@lecturesbywalterlewin.they9259 c=ω/κ=(2π/T)/(2π/λ). I use android greek language extension for my tablet on screen keyboard and an ascii android app. Quite handy! 😁

[@sachinnarang7727]

at 1:06:00 ....professor is it a case of anomalous dispersion?

[@arijitchattopadhyay2045]

Sir , sometimes it turns out that phase velocity exceeds the speed of light although the group velocity lies way bellow it . I asked that to my teacher and he said that it's only the group velocity that matters because energy travels at group velocity . But why ? Can u please explain why energy travels at the group velocity not the phase velocity and why it's not alarming when phase velocity exceeds the speed of light .

[@lecturesbywalterlewin.they9259]

your teacher is right. I derive all this in my 8.03 lectures.

[@mhmdchamseddine5749]

Dear professor Lewin, first of all thank you for your great lectures :) If you permit me, I would like to ask you some questions to clarify a few things in my mind. 1) At 1:11:46 , what is the physical reason behind the light not being able to go through the opening for long wavelengths? Aside from the mathematical calculation, what happens physically to the wave when it reaches the opening so that it cant go through? 2) In your previous lecture, we saw that any solution to the vibrating string is a superposition of its normal modes, and we cant have other frequencies because of the boundary condition, but what happens if I drive one end of the rope at a frequency different from any of its natural frequencies? 3)Final question, you previously stated that systems love to oscillate in their natural frequencies, is this due to the fact that any fourier decomposition of the original shape of the string is ALWAYS made up of fourier modes that also correspond to the string's normal modes? I hope I get a reply from you, and thank you in advance :)

[@lecturesbywalterlewin.they9259]

1. E-field drives current in comb 2. solve the diff eqs. 3. yes

[@Jirayu.Kaewprateep]

From previous lecture, the light travel into the blackhole does not change the traveling speed. Is it chage a phase velocity? Is it chage the light inyensity? The phase velocity changed then the frequency change and light intensity change?

[@lecturesbywalterlewin.they9259]

use google and learn a lot more about black holes

[@mechanical4642]

Sir I am not able to download Assignments. It shows the requested URL /b1eb3c492d.pdf was not found on this server.

[@naujojimokykla1517]

Professor Lewin, Could You please tell my why physically a wave can not pass through a gap which is smaller than half of its wavelength? Or could You guide me to where I could find this information. Thank You! P.S. love Your lectures.

[@lecturesbywalterlewin.they9259]

I derived it! What more do you want?

[@naujojimokykla1517]

I want to understand what is physically happening when a wave is going through two parallel plates.

[@naujojimokykla1517]

The picture I have in my mind is a string in space representing a single photon, this string has a wave propagating down it with wavelength, lets say 1 meter, but the amplitude of the wave is 1 mm. So even with a wavelength of 1 meter it seems to me that the string can easily fit through any hole of size 1 mm or greater. I'm sure this analogy is wrong, but I don't understand why

[@lecturesbywalterlewin.they9259]

amplitude is NOT what matters. Wavelength is what matters. Maybe this helps you. Suppose you want to generate a standing wave in a string between fixed points. If the distance between those points is smaller than half the wavelength that you generate, a standing wave is not possible, However, any parallel between EM radiation and string strictly fails.

[@shreyashmeshram5351]

does wave equation also changes when Vp and Vg are different???

[@lecturesbywalterlewin.they9259]

question unclear. Vp=w/k Vg=dw/dk

[@ManojKumar-cj7oj]

@@lecturesbywalterlewin.they9259 profassor: In case of a dispersive medium ,Do we have to make changes in our wave equations too??

[@subrajitpuhan4125]

Can we distinguish phase velocity and group velocity by dropping stone into a still water🤔...I can't find it

[@Jirayu.Kaewprateep]

That is different kind of wave, would you try to increase light intense by rotate light switch?

[@inamulhaq5064]

💕 for physics

[@siddharthaagnihotri9918]

sir if group velocity can greater than phase velocity than how van particle velocity will be eqal to group velocity............because phase velocity is already greater than speed of light

[@lecturesbywalterlewin.they9259]

Information does NOT move with the phase velocity; it moves with the group velocity. In your frame of reference the speed of a particle can be very very close to c but it cannot be c, but photons travel with the speed c (in vacuum); photons have no mass.

[@sandipchakraborty184]

Love you Sir..I am from India so i will not get the chance to meet you and touch your feet and this is the only wish that will remain unfulfilled in my life..

[@lecturesbywalterlewin.they9259]

maybe some day we will meet in Cambridge, MA USA

[@sandipchakraborty184]

@@lecturesbywalterlewin.they9259 You replied me Sir, that's the greatest honor i received ever.😍😍.. Hope your words become reality..

[@prakharbhalla9461]

Sir, is there any physical significance of group velocity for a single travelling wave ?

[@lecturesbywalterlewin.they9259]

you can send a msg with the group velocity

[@prakharbhalla9461]

@@lecturesbywalterlewin.they9259 sir if there is a single travelling wave then what is the difference between phase velocity and group velocity?

[@lecturesbywalterlewin.they9259]

@@prakharbhalla9461 I cover that in great detail in my 8.03 lectures. Phase velocity can sometimes be larger than c.

[@prakharbhalla9461]

@@lecturesbywalterlewin.they9259 sir I meant to ask the physical significance as phase velocity means velocity of propagation. But what is physical significance of group velocity if it's a single travelling wave and not superimposition of waves. As in case of deep water wave example you gave at 57:30. There you gave value of group velocity and phase velocity. But what is their physical significance.

[@garvitsethi8649]

Stiffness of the wire is due to the tension generated in it.. I mean that if a wire is not stretched why would it respond.... So how are stiffness and tension different??

[@lecturesbywalterlewin.they9259]

use google

[@cana5312]

I am so sorry to ask a stupid question. At 33:33 why is the lambda_10=2/10 rather than 1/10? Since the length is 1 shouldn't we have 1/10?

[@lecturesbywalterlewin.they9259]

I watched the lecture near 33.33 my lecture is very clear and I cannot add annythng to it.

[@cana5312]

@@lecturesbywalterlewin.they9259 Okay, thank you so much for your answer!! I will try to make sense of it myself!!!!!:) I can not get a good grade on my course without your video!! It is absolutely wonderful thank you so much!

[@saurabhjha4535]

sir,how does phase velocity being greater than c does not violate str?

[@lecturesbywalterlewin.they9259]

no violation as no information can travel with phase velocity

[@saurabhjha4535]

@@lecturesbywalterlewin.they9259 Then, what is travelling with phase velocity?

[@siddharthaagnihotri9918]

sir i think that there is a misunderstanding in my question...........i asked how can group velocity be equal to particles velocity.......because in many cases group velocity can be greater than phase velocity ..and phase velocity is already greater than speed of light....

[@lecturesbywalterlewin.they9259]

Particles cannot travel with the speed of light let alone with a speed larger than c. Only massless "particles" can like photons travel with speed c in vacuum. .

[@Rishabhkumar-gp9tg]

1:00:03 is it true that the group velocity is half the phase velocity for wavelength less than 1 cm.

[@lecturesbywalterlewin.they9259]

en.wikipedia.org/wiki/Phase_velocity

[@Rishabhkumar-gp9tg]

You said its half the phase velocity......differentiating gave me 1.5 time the phase velocity.

[@lecturesbywalterlewin.they9259]

how many minutes into the lecture?

[@Rishabhkumar-gp9tg]

Lectures by Walter Lewin. They will make you ♥ Physics. 1:00:04

[@lecturesbywalterlewin.they9259]

I watched from 1:00:04 to 1:00:18 it's correct.

[@yohanskasaw2299]

why is it 4pi/k?

[@lecturesbywalterlewin.they9259]

why not?

[@yohanskasaw2299]

@@lecturesbywalterlewin.they9259 it should be 2pi/deltak

[@anthonybloise868]

M.