8.03 - Lect 8 - Traveling Waves, Standing Waves, Longitudinal Waves, Energy in Waves
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- Traveling Waves - Boundary Conditions - Standing Waves - Longitudinal Waves - Energy in Waves
Assignments Lecture 8 and 9: freepdfhosting....
Solutions Lecture 8 and 9: freepdfhosting....
Of course, a 'Thank you' is a small word to express my gratitude for your amazing lectures. Your lectures and enthusiasm have always helped me(and all of us) during my Bachelor's, Masters's in Physics. I am studying standing gravitational waves during my Ph.D. It was really nice to revise nodes, antinodes and flow of energy. I saw in my work that particles are getting attracted to the antinodes(due to the accumulation of gravitational energy). Whenever I feel low or the research equations get too complicated, I come to see your lectures and they re-energize me. Thank you for making me fall(and keep falling) in love with Physics :)
How is your research going now? Just wondering :)
57:10 We do a similar analysis in quantum mechanics, since the Wavefunction should be continuous and smooth it won't have any breaks and kinks. Using this we determine the coefficients of our eigenfunction.
Dear Prof. Lewin, I am very much grateful for your generosity to share your excellent explanation about many difficult notions in physics. I feel very lucky to be born in this era, where my country is in peace, most of the world is in peace, where electronics devices are more accessible for most of us, and the internet has become so abundant, and where you are here to explain Physics for us.
Depth of your physics lectures are unbeatable. I blessed to learn from you sir
Amazing lecture like always. I guess I have another sleepless night ahead of me :)
W. L : "you may not sleep tonight!"
And really, it is 5 a.m. and I am here having my daily dose of physics!
I love those videos!!
:)
2:30AM here :)
1:03:14 how did you get this for Atr/Ai
Edit:This was resolved at 1:06:37
I want to listen to your classes lively.
In the last few minutes, R = 1 and Tr = 2 only if we're talking in terms of limits as V2 approaches infinity and u2 approaches 0 ( consider the vacuum of free space having 1 hydrogen per unit volume ) , but R = 1 is not exactly true, R is just very slightly less than 1 and this slightest decrease would contribute to Tr = 2 ( which is also not exactly 2 , slightly greater than it) , but if we just equate u2 = 0 then, V2 won't be infinity, no it will not be a defined quantity, as 1/0 isn't infinity it's undefined ; So, Tr in itself would become an indefinable quantity.
Just my thoughts on it, if you don't agree then comment what you think it is.
I cannot add anything to the clarity of this lecture. I suggest you watch it again.
The videos of this channel are of better quality than those of the so called "For the allure of Physics" channel.
Yes the resolution of my 94 course lecture is higher here. In addition, I posted homework assignments (and solns), my exams (and solns), my Lecture Notes and 140+ videos of problem solving. This channel also has all my non-course talks and lectures (talks for kids, 8 talks for NHK TV in Japan).
Lectures by Walter Lewin. They will make you ♥ Physics. Thanks for the videos😄
Where can I get your lecture notes?
@@admiralhyperspace0015 pdf files below the video thumbnails
When you pluck a string, the oscillation will be a superposition of normal modes. The resulting oscillation is still called a standing wave? Or is only the normal modes of the string that are considered to be standing waves? Also, every time there are two waves, each one going in one direction, is some sort of standing wave formed?
+299792458 m/s all resonant frequencies create standing waves and all standing waves are the result of resonant frequencies. Look at the demo I do with the very long "spring" in front of the class (with the help of a student)
+Lectures by Walter Lewin. They will make you ♥ Physics. I understood that resonant frequencies create standing waves. But my doubt is on the "definition" of what a standing wave is. For example, a wave on a guitar string (fixed on both ends) is not travelling, but it's not any ONE of the normal modes of the string, it's a superposition of many. My doubt is if the vibration of a guitar string, for example, is called a standing wave or not.
+299792458 m/s If you pluck a guitar it will ONLY oscillate in a linear combination of normal modes (resonant standing waves). Watch my 8.03 ;lecture on Fourier Analysis.
sir I was thinking like energy that incident amplitude is greater of all like initial energy some of initial amplitude lost into reflection and some in transmission why this isn't so
energy is a separate issue.
The continuity ONLY requires that the string at the junction does not break.
Standing wave is a forced phenomenon ,and we try to get to the natural frequency(any harmonics) of the string and then the resonance occurs(standing wave formation).
Am i right professor?
I am wondering that Energy expression has tension T in it. Does tension remain constant ?
In 53:02 to get the power why the T is not cancelled? that period that you called v/lamda is another different period than the T you have upstairs in the equation of power?
Thanks.
watch my lecture again. T is tension, period = v/lambda. I cannot improve on that.
Sorry, my mistake. You are right, thank you.
Watch your? Wut, is Walter Lewin who controls this channel? I thought it was some random who wanted to keep those videos to the public.
30:36 Sir, why did you sketch 6 nods in the tube, but in order to calculate lambda you measured distance between 1st and 5th node? Why you skipped 6th node and why in this case measured distance was 2*lambda?
In watched it again and I cannot add to the clarity of my lecture. Watch it again and make an effort to understand it.
Respected sir,
Kindly tell if you have dealt with thermodynamics in any of your lecture..
I shall be highly obliged for that.. if not can you suggest me a good book for thermodynamics.. (for exam like jee adv)
thank you
only 1 8.01 lecture covers some thermodynamics - search online MIT OCW EdX, Coursera
at 28:49 we have pressure wave equation in which we get two cos terms and in transverse wave equation we get both sine and cos terms my quetion is do we get same curve in longitudnal wave as we get in sinosoidal wave (i mean up and down curve we get in transverse wave due to cos and sine term but in longitudanal pressure equation we have only two cos terms ) thank you for reply sir you give new vision to think thank you again from bottom of my hear
The behavior of a transverse wave and a longitudinal wave are very similar. All you have to do is to replace the displacement in y-dir by that in the x-dir (including the signs).
+Lectures by Walter Lewin. At the end of the lecture, when the coefficient of reflection is 1 and the coefficient of transmition is 2, I think there is no incongruency with the conservation of energy because there would be no mass in medium 2, so there would be no energy flowing throught there. Would it be similar to the case of the phase velocity larger than the speed of light? In which there is no energy flow when the phase velocity goes to infinity. Thank you.
+Alexander Garzón Díaz How many minutes into the lecture?
+Lectures by Walter Lewin. They will make you ♥ Physics. At 1:15:17, the last minute of the lecture.
+Alexander Garzón Díaz mu_2=0 thus v2=infinity, thus lamda2 is infinity, thus the Energy in one wavelength is zero.
sir , could you please explain the reason why Tr = 2 at the end of the lecture ? (what does that physically signify ) ?
at 1:07:29 when v1=v2 we have no junction and just assume the whole one string my question is in lecture 7 at 1:16:31to 1:17 you have demonstrated the same demonstration but with single string but at that time mountain comes back as mountain but with double amplitude so why in this lecture we get R=0 because i think both are now same situation for the case when v1=v2 .
In both demos (lect 7 and 8) the boundary conditions are met. If you attach two strings each with propagation speed v, then there is no reflection at the junction. I suggest you watch both lect 7 and 8 again.
At 56.44 can you please tell me what are the y1 and y2 you are talking about? in the video you say the y on the board must be equal to the y right THERE. where is that there?.
watch more closely and LISTEN to what I said. It's x-tal clear what is y1 and what is y2 and it's also clear what "y-here" is.
Oh yeah that's sloppy of me.. thank you for the answer i have one more question. Why is R+tr not equal to one?
>>>>>Why is R+tr not equal to one?>>>>>
you figure that out!
Trying to find U (44:20) I write U=dm.a.h = dm.y''.y and I find that U=2.Ekinetic. It seems that I have no calculation errors. Is my starting point wrong?
I cannot add to the clarity of this lecture.
sir pressure is directly proportional to average kinetic energy of molecules so in the middle of the pipe molecules vibrate more rigorously than at the close end of the pipe. so the question is how the pressure is larger at the close end of the pipe. I was thinking of pressure at closed end zero as molecules do not move/vibrate at close end. thanks a lot
in a standing wave the "over" pressure at open end is zero, it's maximum at closed end.
sir ,do waves possessing nodes and antinodes exhibit resonance at frequencies??
yes if the wave is contained in space (like wind wood instruments) - watch my 8.01 lectures
Teacher, can you explain more about cosin term and sin term, i have a big Disturbance about them
at 1:11:25 you have in one demonstrated that mountain will come as mountain when R=1 my question is in early lecture 7 when you demonstrated with string you said mountain will come as mountain but with double amplitude so why it is not in this case when R=1 amplitude of mountain is less
watch the lecture again and pay MORE attention.
Sir, in this lecture you described a wave going to the right with f(wt-kx), but in other lectures you described the same wave (i.e. a wave going to right) with f(kx-wt). Why ?
both are correct. what counts is the sign of the ratio w/k. f(wt+kx) would go to negative values of x (which you would call "to the left")
If there is a knot on the string how is the wave form changed and is the change a permanent reflexion across the string?
a knot is a change in density per unit length and that will cause a reflection
Thank you. I conclude that the knot will change frequency throughout length of string. What if the knot was changed from something that effected the density to something that effected the movement at similar juncture. Would this change the statement?
Knot - Frequency will not change. Wavelength will change when the speed of propagation changes.
Nothing is as obvious as when you have revelation and see it! Thank you for the illumination! Much appreciated. Have a blessed day.
in 801 lecture of momentum.......when 2 bodies collide the speed at which they will move after the collision was derived by u......it is symmetrical to the eqs u derived at 1:01:28 ....only mass is replaced with velocity.....can u plz explain it???
question unclear
Sir can you on caption on this video -englisj autogenerated
thanks sir
Most welcome
Sir at 24:20 why don't you consider it as a 3D vibrations
Because by symmetry, the vibrations are moving the same across each cross section of the tube.
sir I want to know how to drive general equation of travelling wave which is f(x-vt)
It's covered very thoroughly in some 8.01 lectures and in my 8.03 lectures. They are all posted on this channel.
Sir
If the reflective area is harder then why the equation of reflective wave is y2= - a sin 2pi (nt+x/lamda)?
question unclear - how many minutes into the lecture?
Sir this is outside of your video.
I have read in a book that stationary wave equation can be made by 2 way and the net equation would be y= -2a sin (2*pi*x / lamda ) cos 2*pi*nt or
Y=2a cos (2*pi*x/lamda) sin 2*pi*nt .
Why this happen? I would be glad if you describe it sir.
watch this lecture. That is correct - you can always write wave eqs differently - as 1 example only, in the case of pressure waves the sin (x) => cos(x). I have no interest in checking physics books who prefer to write things differently using trigonometry.
th-cam.com/video/hElGpHTo-80/w-d-xo.html
how are stationary waves formed. is it by reflection??..
and please tell me the significance of sin and cos fynction in eqn of standing wave
use google
Lectures by Walter Lewin. They will make you ♥ Physics. i didnt find sin and cosine function meaning.
sir how to calculate the potential energy of transverse wave sir just give me a clue
I calculate it in one of my lectures. Try to find it
Isn't the unit of wave number radians per metre?
Thank you Sir.. The world needs more teachers like you.
>>>Isn't the unit of wave number radians per metre?>>>
*wavenumber is the number of waves per unit distance*
In last portion of video velocity goes to infinity which can never happened because our limit of speed is speed of light may be that the reason we get non intuitive answer may be its right
Sir
Why the changing of pressure in a longitudinal wave is highest in a node ?
There are displacement nodes and anti nodes and pressure nodes and anti nodes. The pressure nodes coincide with the displacement anti-nodes and vice versa. The pressure anti nodes coincide with the displacement nodes. Take a pipe, the closed end of that pipe will always be a displacement node and thus a pressure anti node for very obvious reasons. If this is not clear, use google
nodes ,nodes ,nodes ,nodes ,nodes ,nodes :)
In your derivation of the coefficients R and T, you implicitly divided by k2, which is not allowed if µ=0, in which case k2=0. Thus, T is undefined for this case, so the result T=2 is unphysical. By substituting insead k2=0 in the eqs in 1:02:54, one immediately gets R=1 and T=0.
I do think your idea is right. Thank you
My thoughts if μ2=0 then v2 and λ2 are infinite, so there is no energy associated with the transmitted wave. This is consistent with the fact there is no mass moving. All energy is reflected.
Hi Prof. Lewin,
At 1:15:35, what if it's a funny way of nature telling us that "NOTHING gets the amplitude of +2".
Why some videos have option for automatic English subtitles and some not?
The left question reminds me of the collision between a massive wall and an extremely light ball (lectured in 8.01). If the analogy works, then we still need energy to avoid the crisis.
Sir i would like to know can i derive the wave equation for longitudinal waves from Newton's Second Law
Thanks for it ,legendary master! Love from india
Thank you,Sir .I'm an aspirant of IIT JEE and love to build my crystal clear concepts from you.
You are most welcome
didn't get the par at 24:27 , if the molecules are moving to ward the x-direction , then why are the arrow point to the left??
yes I should have put the arrow to the right but it is irrelevant as the particles oscillate horizontally in SHM what you call +x or -x is irrelevant.
I think the answer to the question at the end of the lecture is since mu_2 is zero, the mass per unit length is zero. Therefore, although there is a wave with twice the amplitude of the incident wave (Tr = 2), the energy is zero because there is no mass.
Light has no mass but it does have energy so, mass isn't needed to have energy.
Sir can you tell me the reason for Tr = +2 because on mind only one thing comes is we can't cut infinity from (2*infinity)/infinty. Therefore please tell what is the proper reason for Tr = +2??
how many minutes into the video?
@@lecturesbywalterlewin.they9259 1:15:20
it's up to you to figure this out. Here is a hint: caculate the energy of the wave with amplitude +2 that flows into nothing.
@@lecturesbywalterlewin.they9259 thank you very much sir
Sir,
Where can I get lectures on general wave equation?🙏🙏
use google Udacity, MITX, edX, Coursera
46:11
Why strobing of light leads to slow motion? If suppose we supplant sun with a strobing light than everything around us will appear flickering and slow moving?
it can lead to *apparent* slow motion but also to *apparent* fast motion. Google "strobing*
Im Bsc student now And I'm curious about Physics from puc but after seeing your lecturing I'm crazy about Physics..
Physics is beautiful in your demonstration ❤️❤️
Pls ON the caption sir it will be easy for me to understand
captions are not available
*Epilepsy intensifies* at 21 mins of the lecture
Please turn on subtitles.🙏🙏
that's no longer possible. My 8.03 lectures were recorder in 2003
Your 8.03 lectures are great!!!
I know but they are too difficult for most of my 1.4 million viewers
@@lecturesbywalterlewin.they9259 Dear Walter, I think for someone like me, who has master's degree in mathematics, especially specialized in complex and functional analysis,more specifically the Bergman and Hardy spaces, also I have been a T.A in engineering college in Israel for 15 years in courses like calculus 1,2, ode, pde, complex analysis, harmonic analysis, etc. Also I am interested in physics, but my knowledge is restricted to the 8.01 up to 8.06 mit courses, I'm fascinated by these lectures. Salute to You sir!
Sir at 8:10 you are explaining about rope fixed at both ends. To solve that you are using the equation of standing waves formed by same amplitude. But in previous lecture you explained that reflection from fixed end would give valley if incident is mountain pulse, i.e., same amplitude but opposite in sign. So in that case kx term should come with cos function and omega*t term should come with sin function.
if you hear the previous lecture while explaining how the mountain flips into the valley at the end he says that waves flip both up and down as well as front and back , hence if a sin flips up and down and again front and back it is essentially the same wave again and hence they add up as both mountains
Hello sir ,
I have a question. When I measure the pressure with a pressure gauge inside a closed container ( example a hydraulic pipe). I dont see any difference where I put the pressure gauge It gives me the same pressure because of Pascal's law .
But when you are doing with the mic there are nodes where you dont see any pressure .
Thanks for help
question unclear
hello sir...
my question is what is the reason for the KE and PE of the the travelling wave turns out to be equal??
Follow my derivations
Lectures by Walter Lewin. They will make you ♥ Physics.
sir could u please tell me the physical reason for them being coming equal..
excellent question! I would have to watch parts of my lecture again to give you an answer. Do I not mention in class why the 2 happen to be the same?
If there was an obvious answer I would probably have mentioned it during my lecture. Are you sure I did not mention it????
Lectures by Walter Lewin. They will make you ♥ Physics.
yes sir u didn't...
1:11:00
37:27
Finally today I know what "ADO three" is.
That's 8.03
In 1:15:20 why the wavelength in two strings are n't equal, thanks Sir
mu is different
1:13:55
In which lecture do you derive the speed of a wave
Lec 7. Whilst deriving the wave equation.
in lecture 7 at 1:16:31 to 1:17
what is your question?
sir please give explanation of Tr = +2 when incident wave on vacuum from a medium i,e, last case which you left as a thrilling suspense :)
thank you for these amazing lectures sir. Love and respect from india
:)
Why is it, that the k-vector is perpendicular to the wave front and parallel to the direction of propagation. I cannot find a derivation of this fact in your lessons. Would appreciate an answer. Love your lessons.
The k-vector is not always parallel to the Pointing Vector. It depends on the material. Can you explain that, please?
how many minutes into the lecture?
I think you never mention it in any of your lectures. I choose this lesson, because the question fits here.
you have to tell how many minutes into the lecture do I introduce k and when I talk about the magnitude and direction of k.
k is in the direction of propagation. Take a longitudinal wave (sound wave). The wave front is the region with the same change in pressure. That is perpendicular to the direction of propagation. In anisotropic media, k does not have to be perpendicular to the wave front but I do not cover that in my lectures.
sir how can Ai + Ar=Atr
how many minutes into the lecture?
This is a continuity argument. At the junction Ai and Ar are on the left and Atr is on the right. If Ar+Ai were not Atr the string would break.
sir at 1.00.28
what is your question?
About amplitudes Ai+Ar=At
On the left at the junction is Ar and Ai on the right id Atr.
For reasons on continuity, Atr must be Ai+Ar; if not the string would be broken.
@@lecturesbywalterlewin.they9259 But in the follwing example is e.g. Ai=1, Atr= 2/3 and Ar=1/3.
That means Ai + Ar = 4/3. Could it be, that I have to count Ar negative, because the reflectet waves shows in the opposite direction (I mean up and downwards) than de incedend wave? :D
27:33 isn't that supposed to be sin?
no
I think he explains why it is cosine as opposed to sine immediately after
Hello sir, is sin(kx-wt) same as sin(wt-kx)?
is sin(a - b) the same as sin(b -a)?
@@lecturesbywalterlewin.they9259 İf trig is cos, then yes, It will be same.