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8.02x - Lect 26 Traveling Waves, Standing Waves, Musical Instruments

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Traveling Waves, Standing Waves, Resonances, String Instruments, Wind Instruments, Musical Instruments Lecture Notes, Oscillating Sound Cavities - Fundamentals of Wind Instruments: http://freepdfhosting.com/e79d2b1fa9.pdf Assignments Lecture 26, 27 and 28: http://freepdfhosting.com/20495b808e.pdf Solutions Lecture 26, 27 and 28: http://freepdfhosting.com/7759a06b8d.pdf
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Text Comments (158)
Remya Krishnan (3 months ago)
in born true genius
Swan Htet (3 months ago)
You actually made me fall in love with Physics. You are the Legend, Sir!
Avinash SiNgh (3 months ago)
thank u prof
Avinash SiNgh (3 months ago)
wow prof
Akash Hegde (5 months ago)
Professor, what is it that you taught in 8.03?
Akash Hegde (4 months ago)
Haha I know that, but what kind of physics?
Karuna Meshram (5 months ago)
Sir, how is velocity of vibration of a string dependent on stress ?
watch my lectures v=sqrt(T/mu)
Diver Uzumaki (5 months ago)
thank u soo much
vidit singhal (5 months ago)
Sir what does velocity mean in standing waves... for example fn=nv/2L whose v is this in this formula?
vidit singhal (5 months ago)
Got it .. thank you sir....... Awesome lecture!!
It's the propagation speed of a traveling wave. Two of those waves in opposite direction produce a standing wave.
Mary Shittu (6 months ago)
Sir, you are the bēst, i am writing msc thesis on standīng waves and travelling of violin strings, is there anything you can do to help me, i am a very good violin player. my email is marydot2k@yahoo.com
The web can help you - I cannot.
Abijith (7 months ago)
This is the first Walter Lewin lecture I have ever seen and this is the best lecture I came across in my entire life. Now I know why you are famous :D Cheers from India! ❤❤❤
five 505 (7 months ago)
Sir, I have a question about standing wave, if wave (when it reflects from the wall) changes its phase for 180 degrees shouldnt then the reflected and the coming wave be out of phase and cancel each other
watch my 8.01 and 8.03 lectures on standing waves. cancellation ONLY accurs at the nodes of the standing waves.
Damien Blue (7 months ago)
Sir I need the transcript, where do I get it
There are no transcripts of my talks.
Damien Blue (7 months ago)
Sir actually I was talking notes so I need the transcript of this video , where do I get it
question unclear
Hitesh Pandharkar (8 months ago)
Amazing amazing amazing
Aryan Mehta (8 months ago)
Sir can standing waves occur when two waves have a phase difference of π ?
Aryan Mehta (8 months ago)
Yes sir , I did the maths of it ...the answer obtained is the same , since sin π + x) = sin X ... Is it correct ? What if phase difference is not π but some other value will it remain the same ?
two waves with the same freq and wavelength = in opposite direction add up to a standing wave. Do the math. Add phase angle pi to one and add them up again. You will then have your answer.
Subramanian NK (9 months ago)
Prof Lewin, Flute is closed at one end and through the other end, air is blown. How do we hear music? Isn't the wave trapped inside the flute? How does the music escape? Just one line from you from would suffice. Hope my dumb questions doesn't cause irritation/annoyance. I am just trying to make an analogy with antenna as I've an engineering degree.
Subramanian NK (9 months ago)
Lectures by Walter Lewin. They will make you ♥ Physics. Thanks prof, I think I have got the answer.
<<< How do we hear music?>>> we have brains! use google
David Williams (10 months ago)
At 42:38, Sir, how did you convert the sound wave to an electric signal such that it could be observed on a cro.
feed the output of a microphone to an oscilloscope.
Cesare Borgia (11 months ago)
The simple mention of the fact that, in the standing wave equation, the spatial and temporal information is not interlinked makes for a great tool for understanding how standing waves aren't being shifted left or right (speaking purely in terms of vertical vs. horizontal displacement). Excellent explanation of the standing wave professor. Thank you!
MANIKANTT M (11 months ago)
Professor WALTER LEWIN are you even human , Physics is a beautiful sound of nature in varying harmonics and you are by all practical purposes the resonating column for it. Sir can you please tell me how you can be so good.
souptik dandapat (6 months ago)
Lectures by Walter Lewin. They will make you ♥ Physics.
Prashant Shukla (11 months ago)
thank you professor and flute is an Indian instrument
lol lolzi (1 year ago)
16:34 if you only have walf a wavelength shouldnt lambda be 0,5L?
This is a full wave ^v. ^ is half a wave. Thus the fundamental wavelength is 2L.
I watched at 16:43 my lecture is x-tal clear. I cannot improve on that. The wavelength of the fundamental is 2L. I suggest you watch it again.
lol lolzi (1 year ago)
please explain since that part is the only thing confusing me
>>>shouldnt lambda be 0,5L?>>> NO
phoenix (1 year ago)
8.03 seems as exciting
bubayou (1 year ago)
I am so confused !
bubayou (1 year ago)
You are a great professor it's just that my input data rate is alot slower than your output rate. My Input FIFO has overflowed. The great thing with having things on video is that I can watch it over and over until I get it.
Toothless ! (1 year ago)
Sir you explained standing waves to me! My physics teacher had confused me. Thank you so much!! You are the best physics teacher I will ever see. I KNOW IT
Paulo Constantino (1 year ago)
This is the most beautiful presentation ever. For the first time I realize that a standing wave is nothing more than a cosine modulating the amplitude of a sine wave. Amazing. I love you!
Paulo Constantino (1 year ago)
This is so beautiful. God damnit. Why are you so marvellous! Unbelievable. My hero forever !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Freyd (1 year ago)
Anyone else notice that he played Epona's song from The Legend of Zelda Ocarina of Time at 33:50?
Pulak Roy (1 year ago)
"Sound" sounds very very interesting because of YOU, Sir.......
Mohan R (1 year ago)
is 2pi/3 angle or dis
kabir (1 year ago)
first time i understood standing waves,
Amit Khare (1 year ago)
well the last 2 min were really appreciable,he can do anything for physics awesome professor👍👍👍👍
Arkadipta Ghosh (1 year ago)
professor,what is the energy equation for sound wave????
question ill-defined - use google
Arkadipta Ghosh (1 year ago)
is y=sinX a standing wave????
Arkadipta Ghosh (1 year ago)
Lectures by Walter Lewin. They will make you ♥ Physics. thank you sir.. .
a standing wave is both position and time dependent. Yours is not time dependent this it's not a standing wave.
Arkadipta Ghosh (1 year ago)
Lectures by Walter Lewin. They will make you ♥ Physics. No time term....no VT in there... so should I consider this as a standing wave???
where is the time dependence?
Hmm. Interesting (1 year ago)
After i watched this lecture i downloaded a software oscilloscope(for microphone) and a frequency generator and i am testing various frequency's and harmonics to find nodes and i am sliding with my chair slowly away from the speakers to find nodes ..its really fun when i find a node i feel a drop in pressure..its been 2 hours i have been doing this LOL and not bored at all! thankyou prof. lewin
Ayush Nema (1 year ago)
Thnx a lot :)
Ayush Nema (1 year ago)
could you please share the source to download the software? I would really appreciate it. I too am interested in trying it on my piano and having some fun
Ajay (1 year ago)
Thank you Proff. Lewin for this lecture, now I can give my exams without any fear:-)
YD (1 year ago)
In case of fundamental frequency, we always get high amplitude as compared to other harmonics so is it safe to say that if we want to have destructive resonance then fundamental frequency is the most suitable option for it?
This will often be true. However, it's in principle possible for objects to break much easier in the second harmonic than in the fundamental. Suppose you took a glass rod of length L which is thinner (thus weaker) near L/4 and 3L/4.. It may then be easier to break it when you excite it in first harmonic above the fundamental than in the fundamental. There may be many objects (including bridges and glass wear) that are more vulnerable at res freq above the fundamental than at the fundamental.
YD (1 year ago)
In case of wine glass, there is only one resonance frequency which if a speaker matches with then we get resonance....... Other objects also like Tacoma bridge also have only one resonance frequency but why strings and woodwind instruments have more than one resonance frequency?
ALL objects (NO exception ) have many resonance freq. That includes wine glasses, bridges, plates of any shape, strings and sound cavities. If you excite them (pluck, strike, bang them, blow air . . .), in general the object will oscillate in a combination of its res freq. All musical instruments do that (I demonstrated several instruments in class). If you drive them with any of their res freq they will start to oscill in ONLY that freq. The bridge was NOT driven at one of its res freq. The reason why it only oscillated in at a low res freq (maybe even the lowest) is that it would have taken more power than was available to also drive at the same time a higher res freq. If you drive the wine glass with a sound freq that is the glasses first harmonic above the fundamental it will start to oscill in that freq but the glass will probably not break as that would require more power than we had. End of story
YOU still miss the point. I cannot help you anymore. I tried to explain this to you more than 3 times referring to my 8.03 lectures. This is my last msg on this topic. ALL answers are in my lectures.and in previous msgs
YD (1 year ago)
So all objects react to only those resonance frequency that we drive them to(eg. Tacoma bridge, Wine Glass)..... Is this an exception for the musical instruments?
ALLLLLL objects have many resonance frequencies. If you drive them with one of their res freq they will "react" accordingly, but that does not mean that you can destroy them. Look at my great demo of the many resonance freq of a disc (Chladni plates). I search for the res freq and you see the results !!! Lect https://www.youtube.com/watch?v=GFR8UJK3Mzc&index=1&list=PLyQSN7X0ro218ZADJkvINBhTUAQeDMHf- It's even more impressive to do this with a square plate https://www.youtube.com/watch?v=Qf0t4qIVWF4
YD (1 year ago)
So is it safe to say that every object in the world can have more than one resonance frequency ie fundamental and several other harmonics even if we can't match it(as you said in case of wine glass)?
Josh YD (1 year ago)
In case of you oscillating the string, which is oscillator and what is external force?
It's explained in my 8.03 lectures.
YD (1 year ago)
I got this definition of oscillation from web..... "Resonance can be defined as the condition in which force is applied to an oscillator at the point of maximum amplitude. In this way, the motion of the outside force is perfectly matched to that of the oscillator, making possible a transfer of energy." How will you explain this?
It depends on your definition. If you call an oscillator the source of the energy (circuit) that causes oscillations, then I am the oscillator as I move the string. It's really irrelevant for me - what counts is that you understand how you can make an object oscillate.
YD (1 year ago)
In case of you oscillating the string in your lecture, what's the oscillator?
in what?
Spammish Repitition (1 year ago)
Your videos are excellent. However, you don't get into the mathematics behind all of it. do you have lectures elsewhere where you do? thanks
ashutosh sharma (1 year ago)
Sir, can you please explain how a antenna radiates?
watch my 8.03 lectures and/or use google
Thanks Professor Lewin you make your lectures very interesting. Thus makes us love physics.
Sayantan Sengupta (1 year ago)
in case of generating resonant frequencies,if intially the string is fixed at x=0 and x=L how can the frequencies be given?
Sayantan Sengupta (1 year ago)
Sir, I m not able to clearly imagine what is the scenario in case of a longitudunal wave like sound??Its a stupid question but it really means a lot in understanding standing/stationary longitudunal waves and its applications in organ pipes.Plz help............
Sayantan Sengupta (1 year ago)
extremely grateful to you sir!!! nd u r really making us love physics
The resonances wavelengths are the easy. If you knew the mass per unit length and the tension, you can then also calculate the speed of propagation and that will allow you then to calculate the resonance frequencies (as you know the resonance wavelengths).
Massimiliano Maggioni (1 year ago)
You are definitely a GENIUS
Sanchar Chattopadhyay (1 year ago)
Sir, I guess I may be asking something a bit off topic. But I think you are the best person to answer it. My question is, when we consider a subatomic particle as a wave, then which parameter of the wave is related to the mass of the particle?
It is not in this classical equation. It's in Schroedinger's eq.
Sanchar Chattopadhyay (1 year ago)
I didn't quite understand it. I know that the wave function of a particle is expressed as (psi)=e^i(kx-(omega)t).......where can I find the mass of the particle in this equation?
Look at Schroedinger's equation
dipesh rathi (2 years ago)
thanks sir as you said in above lecture that the wave y= asinwt is not travelling at all is it standing wave?
y= asinwt is not a wave at all as there is no dependence on x. Any object that oscillates as a SHO can be written as y=A*sin(wt + theta).
>>>y= asinwt is not travelling at all is it standing wave?>>> It is not a standing wave. Traveling and standing waves MUST depend BOTH on x and y (and t). y=sin(kx)*cos(wt) is a standing wave. k = 2pi/lambda. It has nodes (y=0) at x=0, lambda/2, lambda, etc. y=cos(wt-kx) is a traveling wave.
dipesh rathi (2 years ago)
Then what type of wave that is ?
dipesh rathi (2 years ago)
is V= V(0)sin(wt+theta) travelling wave or not here V is for voltage
This is NOT a traveling wave. It's V as a function of time. theta is a phase angle.
JunYu Lei (2 years ago)
Hello, Professor Lewin. My textbook used cosine to represent standing wave instead of sine. So, y1 + y2 = 2ysin(kx)sin(wt). I felt confused. Are they the same? Can you explain it to me?
+JunYu Lei If the string is closed at both sides, then at x=0 and at x=L the displacement must always be zero. As long as your solution meets those conditions it does not matter whether you have sin or cos. If the string is closed at one end but open at x=L, then your solution should give a displacement of 0 at x=0 at all times and dy/dx must be zero at all times. As long as your solution meets those conditions it does not matter whether you have sin or cos.
shivang raina (2 years ago)
sir, how does resonance work if the object is not already vibrating???how did the glass break even if its not already vibrating??thank u in advance..
shivang raina (2 years ago)
+Lectures by Walter Lewin. They will make you ♥ Physics. THANK U SO MUCH SIR....I`M REALLY INFATUATED WITH YOUR TEACHING................
+shivang raina There has to be a driving force. Wind can be a driving force (Tacoma Bridge disaster). In the case of the wine glass sound is the driving force.
tecktonikboy13 (2 years ago)
may I ask what piece of music was tom playing on his violin? at 43:31 it sounds beautiful.
tecktonikboy13 (1 year ago)
nice, thank you very much! :)
jcheattai (1 year ago)
Ysaye violin sonata, I'm almost sure that it is n°3
Nikola Vulinovic (2 years ago)
I have a question about the traveling wave equation y=2sin3(x-6t). When I search on the internet I always find that the equatin is y=2sin(wt-kx). When we write equation for AC voltage it's also u(t)=U*sin(wt + "theta" ). So I'm not sure which one is correct. Please forgive me if I am missing something obvious, thank you in advance.
Nikola Vulinovic (2 years ago)
+Lectures by Walter Lewin. They will make you ♥ Physics. Thank you so much for clearing that up for me and answering so quickly. I see now that I need to study a bit more before asking a question. I would just like to take the opportunity to say that I love your lectures they're so interesting and helpful, Thank you again very much.
+Lectures by Walter Lewin. They will make you ♥ Physics.  u(t)=U*sin(wt + "theta" This is not a traveling wave.
+Nikola Vulinovic TRAVELING WAVES y=2sin3(x-6t) = 2sin(3x-18t). Thus k = 3 (lambda = 2.1m) and omega is 18 rad/sec. y=2sin(wt-kx) => y=-2sin(18t-3x). Again lambda = 2.1 m and omega = 18 rad/sec. The - sign is a phase change of 180 degrees. NO PROBLEM!  These are TRAVELING WAVES!
Hussain Mujahid (2 years ago)
i dont understand what u did at #5:22 sir. How can a rotating wheel make a string oscillate ?
+Hussain Mujahid I attach a string to a rotating disk. A wave will pro;palate in the string.
Gian Lukmana (2 years ago)
umm in the beginning,, so 18 is the omega.. but isn't omega suppose to have pi or at least a degree symbol in it..?? I don't get why the omega can be just an integer without any degree symbol..
+GThinks the unit of omega is radians per sec. thus 1/sec.
Enrique Morell (2 years ago)
Dr. Lewin, I've watched several of your lectures since the start of my first year in my physics major and I just wanted to take the time today to thank you for all your dedication you put into these lectures. Thank you for your amazing teaching and making me love physics.
+Enrique Morell Thanks Enrique for your kind words.
Jason Sulliman (2 years ago)
I am a professional trombonist. I really enjoyed your presentation. I have a question regarding what I believe to be standing waves. I blow air through my lips, which causes my lips to open and close rapidly. The frequency can change but it gravitates towards the harmonic series related to the length of the trombone at any particular time. If air is being displaced into the instrument, the air would also be displaced back into my body when the lips recoil back to their original position (which means my lips actually move forwards and backwards as opposed to just 'up and down'- the 'open and closed' is a byproduct of 'back and forth'). If there is also air being displaced into my body, then that would mean my body resonates like a drum. If my body resonates like a drum, then the amount of tension my body has will change the amount of resonance it can produce. Does this mean that body tension will change my overall sound (I assume amplitude)? Do you know of any information regarding body tension? I haven't really found any research addressing this type of measurement. Thanks for any help you can provide!
+Jason Sulliman your lips do not produce the 440 Hz. Of course the 440 Hz tome, sound waves produced by your trombone, propagate in all directions. Also in the directions of your ears, lips and arms but the energy in the sound waves that reach your lips, arms and ears is insufficient to act as a driving force to make your lips, arms and ears noticeably vibrate at 440 Hz.
Jason Sulliman (2 years ago)
+Lectures by Walter Lewin. They will make you ♥ Physics. But how than that be? I understand that the air inside the trombone will oscillate at 440Hz, but given the way the lips are moving air, *some* oscillation of air must happen in the other direction- I assume 440 in this example but at a different amplitude. I am interested in learning more about this phenomenon but no one seems to have done any research on it. I just don't understand how it could *not be a factor. The more relaxed I am, the louder and fuller my sound is. I would go so far as to say larger players have an easier time producing larger sounds (I think) because the mass of their bodies contributes in some way to sound ia standing waves. Am I really way off base? Thanks for getting back to me.
+Jason Sulliman If you produce a 440 Hz tone with your trombone, it's the air inside the trombone that oscillates at 440 Hz and with higher harmonics. The air in your body will not vibrate at 440 Hz.
InventTwig (2 years ago)
im a bit confused, if a violin is producing 440Hz then how is it producing much higher harmonics at the same time , aren't the frequencies for higher harmonics higher , coz length and speed are constant ?
souptik dandapat (6 months ago)
I think that if you transform the particular wave form into shm wave form you will get your answer.it may be wrong but I think so.
C (2 years ago)
+InventTwig If we displace the string in the same shape of one of the normal mode (the shape of a harmonic), it would vibrate in that mode with the respective frequency. But when we struck a string, it is usually not the case that the displacement is the same as one single mode. So depending on the shape of the displacement, the string will vibrate in the corresponding frequencies.
InventTwig (2 years ago)
+Lectures by Walter Lewin. They will make you ♥ Physics. oohh , ok thank you :))
+InventTwig It cannot choose, it has NO choice. When you strike higher harmonics will be produced. I suggest you watch my 8.03 lectures about Fourier Analysis. I derive there e.g. which harmonics are excited if I plucked a string. https://www.youtube.com/watch?v=k3byqIaULb8&index=12&list=PLyQSN7X0ro22WeXM2QCKJm2NP_xHpGV89
InventTwig (2 years ago)
+Lectures by Walter Lewin. They will make you ♥ Physics. ooh yeah ,because when hit it it can choose to vibrate at higher frequencies too, thank you professor :)
Fabrizio Tabasso (2 years ago)
Great Lecture Professor!
+Fabrizio Tabasso Thank you!
This website contains all my 94 course lectures (8.01, 8.02 and 8.03) with improved resolution. They also include all my homework problem sets, my exams and the solutions. Also included are lecture notes and 143 short videos in which I discuss basic problems.  ENJOY! 
MrExtremehustler (1 month ago)
What website?
souptik dandapat (6 months ago)
Greatest teacher
Abijith (7 months ago)
FRANK ETEMESI (1 year ago)
Lectures by Walter Lewin. They will make you ♥ Physics. Thanks

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