In case it is helpful, here are all my PDE videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrFvek-n1MKhFaDARSdKWPnx.html. Please let me know what you think in the comments. Thanks for watching!
So I looked up dozens and dozens of articles on this derivation and none explained why tension would have to be taken same but this video summed it up pretty nicely for me , thank you .
Appreciate the step by step breakdown of how the 1D wave equation is derived! Gives me a clear sense of where things come from and how they are applied!
Hi, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris
Sir if you ever see this, just wanna let you know the solution was an astounding proof. I was stuck on this, for how we got the differential equation. It wasn't derived in my school class, it was told to just learn it and the derivation would come later. I had the bug for it, and then I found this video. Great job!
AE501: I had never seen the derivation of the 1D wave equation. This explanation makes me appreciate the work and theory that goes into derivations. Thanks!
AE501: QUESTION: Chris, when solving for the tension vector in the vertical direction around timestamp 17:00, it seems like the tension in the vertical direction should be 0 by inspection, right? No further free bodies or equations required. You previously drew on the assumption that alpha and beta angles are very small in order to say that the horizontal components of T are equal. Since the alpha and beta angles are very small, you stated that cosine(small angle) = 1. By that argument, i would claim that sine(small angle) = 0, making the vertical component of T = 0 by obvious inspection. I haven't finished the video yet, so maybe you address this soon, but at the moment i am pretty confused about the seemingly conflicting information. After finishing the video, we never simplified the equation by claiming that the vertical component of T, (or T*sine(small angle)) was equal to zero. Can you elaborate?
Seth, let me know if this still seems off by the end of the video. If so, perhaps we should set up a time to talk as I think it would be easier to talk over teleconference rather than UA-cam comments since your question is a bit more involved.
@@issarice The best way to formalize this step is by considering the taylor series of sine and cosine and retain only the lowest order terms in the angle. For the cosine is one and for cosine is the angle itself.
The remaning terms are negligible comparing to these ones. For cosine we would have 1 + (small_angle^2 )/2 + ... , for sine small_angle. Now notice that small_angle^2 is much smaller than small_angle. like 0.001^2 = 0.000001
@@firemaniac100nice argument, there is a small mistake in the first part of the explanation though, it should be -> For the cosine is one and for the sine is the angle itself.
I search lot of things about 1D wave equation in online no one explain like you sir .this video is very helpful for my understanding about wave equation. thank you so much for giving such a excellent video.
Hi Anitha, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching! -Chris
Your explanation of this was really helpful. Your derivation from a point of view of the sum of forces in the x and y directions was very different from what I see in textbooks and other videos. Question: at about 15:54 you divide by T but give no reason. Is this meant to get us to tan(b) - tan(a)?
Hi, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching! -Chris
AE 501 - Seeing the derivation for the equation was extremely helpful as I never saw that in undergrad. It was very easy to follow how you got to the equation from the FBD.
I"m glad it was helpful. There are a lot of other PDE videos on the channel. Please feel free to check them out and let me know what you think, thanks for watching!
I'm glad it was helpful. There are several related videos on the channel (including how to solve the 1d wave equation) . Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!
Hi Jerome, Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris
AE501: It's great to learn this material, as it is the foundation for so much more. I am curious as to how the violations of these assumptions change the wave form, but I'm sure it gets much more complicated.
Hi, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching! -Chris
AE501: Jesse Perez - Looking at the notes first, followed by this breakdown of the 1D wave equation, helped me understand follow-on videos on solving the 1D wave equation. Interesting to see that this PDE can model a vibrating string. Great video that is concise and easy to follow.
Hi Sarah, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris
So if slopes are small is an assumption: that means that du/dx~0. Wouldn't that make d2u/dx2 even more 0? Why would we remove du/dx from the equation but not it's second partial w/r/to x?
Look at a sinusoidal wave u(x)=sin(kx). du/dx=kcos(kx), d2u/dx2=-k^2sin(kx), i.e. if k>1, then the second derivative is numerically larger than the first. The physical interpretation is that the string is long compared to the wavelength of the waves propagating on it.
AE 501: This is excellent presentation on derivation of 1D wave equation. I was not convinced with the mass representation , which is given as (rho *delta X) though.
Hi Ishan, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions you might have about any of the videos on Patreon. Thanks for watching! -Chris
In case it is helpful, here are all my PDE videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrFvek-n1MKhFaDARSdKWPnx.html. Please let me know what you think in the comments. Thanks for watching!
Sir please tell me that why the tension is created over there on the two points please reply 🙏🙏🙏🙏
So I looked up dozens and dozens of articles on this derivation and none explained why tension would have to be taken same but this video summed it up pretty nicely for me , thank you .
I'm glad it was helpful thanks for watching!
Appreciate the step by step breakdown of how the 1D wave equation is derived! Gives me a clear sense of where things come from and how they are applied!
This video has helped me understand more about the 1d wave equation. Thank you for posting it.
Good job presenting the material in a concisely. It helps the students a lot.
Thanks for another informative lecture. I laughed when you threw the pens everywhere by mistake :D Fun.
Wow! Just wow! Words cannot describe how grateful I am to you for making this video. Thank you!
Hi,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!
-Chris
It's very good, i had this point unclear when studying schrödinger equation and because of you, now I understand :)
I'm glad this was helpful, thanks for watching!
Sir if you ever see this, just wanna let you know the solution was an astounding proof. I was stuck on this, for how we got the differential equation. It wasn't derived in my school class, it was told to just learn it and the derivation would come later. I had the bug for it, and then I found this video. Great job!
I'm glad it was helpful thanks for watching!
@@ChristopherLum 😇😊
It's undoubtedly outstanding sir
I'm glad it was helpful thanks for watching!
best Video so far on deriving the wave equation! Thank youu!
AE501: I had never seen the derivation of the 1D wave equation. This explanation makes me appreciate the work and theory that goes into derivations. Thanks!
great vid i feel like 26 mins was enough to explain it in detail without being too short or too long, really helped me out!
AE501: I don't think I've ever seen such a detailed explanation of this derivation before. Thank you!
AE501:
QUESTION:
Chris, when solving for the tension vector in the vertical direction around timestamp 17:00, it seems like the tension in the vertical direction should be 0 by inspection, right? No further free bodies or equations required. You previously drew on the assumption that alpha and beta angles are very small in order to say that the horizontal components of T are equal. Since the alpha and beta angles are very small, you stated that cosine(small angle) = 1. By that argument, i would claim that sine(small angle) = 0, making the vertical component of T = 0 by obvious inspection. I haven't finished the video yet, so maybe you address this soon, but at the moment i am pretty confused about the seemingly conflicting information.
After finishing the video, we never simplified the equation by claiming that the vertical component of T, (or T*sine(small angle)) was equal to zero. Can you elaborate?
Seth, let me know if this still seems off by the end of the video. If so, perhaps we should set up a time to talk as I think it would be easier to talk over teleconference rather than UA-cam comments since your question is a bit more involved.
@@ChristopherLum I have this same question and watching the whole video didn't resolve it.
@@issarice The best way to formalize this step is by considering the taylor series of sine and cosine and retain only the lowest order terms in the angle. For the cosine is one and for cosine is the angle itself.
The remaning terms are negligible comparing to these ones. For cosine we would have 1 + (small_angle^2 )/2 + ... , for sine small_angle. Now notice that small_angle^2 is much smaller than small_angle. like 0.001^2 = 0.000001
@@firemaniac100nice argument, there is a small mistake in the first part of the explanation though, it should be -> For the cosine is one and for the sine is the angle itself.
Thanks. This is a wonderful explanation for those who find ODE PDE a bit difficult.
Thanks Chris. Simple enough to understand! Keep them coming...
Thanks for watching! If you're interested in the solution of the 1D wave equation, you can check out ua-cam.com/video/lMRnTd8yLeY/v-deo.html.
It is amazing how simple the final form becomes yet with so much complexity embedded
Excellent presentation. Best derivation of the wave equation I've seen with every step clearly explained.
"Here on Earth this guy Newton apparently I think this guy Newton came up with"
I search lot of things about 1D wave equation in online no one explain like you sir .this video is very helpful for my understanding about wave equation. thank you so much for giving such a excellent video.
Hi Anitha,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching!
-Chris
You are the best. Thank you so much for giving your time to make videos like these !
You're welcome, I'm glad you found it useful!
This is the best class i have took related to waves
faboulous explanation and way of teaching
Mahi, thanks for watching and for the nice comment. Please let me know what you think about some of the follow up videos as well.
Your explanation of this was really helpful. Your derivation from a point of view of the sum of forces in the x and y directions was very different from what I see in textbooks and other videos. Question: at about 15:54 you divide by T but give no reason. Is this meant to get us to tan(b) - tan(a)?
yes since you can equate T with terms that will cancel out T1 and T2 and create tangents.
AE 501: This was a great explanation on the derivation on the 1-D wave equation!
My favourite equation!!! Crystal clear explanation!!!Excellent derivation
Hi,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching!
-Chris
Thanks for breaking down how to solve the 1D wave equation in an understandable fashion.
AE501: Great video, it offers a concise and insightful breakdown of the mathematical steps, making the derivation of the 1D wave equation.
Thank you for the clear and nice interpretation of the deriving wave equation!!!! :)
Great to hear from you again, I'm glad it was helpful. Thanks for watching and let me know what you think of the other PDE videos.
Very clear content, and nicely paced. Very helpful!
Excellent derivation! I had been looking for a good version of this derivation for a while. Very clear
That was a beautiful demonstration thanks Chris
AE 501 - Seeing the derivation for the equation was extremely helpful as I never saw that in undergrad. It was very easy to follow how you got to the equation from the FBD.
Nice demo on the "non-string" wave medium.
great into and demonstration. it's great to be able to rewatch these for review.
[AE501] I don't remember having to derive this out and I'm glad it got covered now, really helps getting to know why instead of what something is
AE501: Really nice explanation of a 1D Wave Equation derivation. I like the step by step method used. Farouk Nejah
AE501: GREAT explanation.haven’t found a better explanation of this derivation. Looking forward to how to find the solutions of this PDE
15:53 Why do we divide by T here?
AE501: Great video! At 12:30, I think that should be assumption 4, not 3?
AE 501: Very easy to follow derivation, thanks for the video!
Great video
Christopher Lum, helped me a lot. Thank you
I"m glad it was helpful. There are a lot of other PDE videos on the channel. Please feel free to check them out and let me know what you think, thanks for watching!
Nice explanation for the derivation of the 1D wave equation, far more understood now!
Good work Mr. Christopher Lum...
Marvelous explanation ❤️
This was an enjoyable derivation of the 1D wave equation. thanks for posting. It has helped a lot.
I'm glad it was helpful. There are several related videos on the channel (including how to solve the 1d wave equation) . Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!
@@ChristopherLum I sure will.welcome.
Great video for explaining the 1D Wave Equation. thanks!
Thank you for this video. I learned a lot and it helped my homework too.
Thankful for your great efforts
Why did you take sin and not cos in vertical components of force
It all makes sense now! Thank you so much.
This was a fun derivation. Thanks!
Great and simple explanation! Thanks!
Hello, thanks for putting this online! This video was very clear! Will definitely look at your other videos for my physics needs.
Hi Jerome,
Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!
-Chris
Very lucid, thanks!
AE501. Great video. Thanks for explaining the actual derivation and not just "how to solve". Appreciate the clear explanation!
AE501 9:32 If the vertical deflections are small, would it still be possible to have nodes anywhere but the ends?
We assume they are small but non-zero so we will indeed have nodes in the middle of the domain.
AE501: It's great to learn this material, as it is the foundation for so much more. I am curious as to how the violations of these assumptions change the wave form, but I'm sure it gets much more complicated.
Very methodical, easy to understand walkthrough
Keep up the good work!!!
Super informative and easy to follow. Thank you very much!
Hi,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching!
-Chris
AE501: Jesse Perez - Looking at the notes first, followed by this breakdown of the 1D wave equation, helped me understand follow-on videos on solving the 1D wave equation. Interesting to see that this PDE can model a vibrating string. Great video that is concise and easy to follow.
Thanks for the derivation, looking forward to applying/ solving the 1D wave equation
that was nice and clear! thanks
I'm glad it was helpful thanks for watching!
Great explanation. There is a little error in writing @12:47--it should be "for A4 to hold" instead of "A3"
Mark, thanks for pointing this out. Please let me know if you encounter any other typos in the future. Thanks for watching!
I like your teaching style
Great explanation of the derivation!
It is really an impressive lesson that had given me a lot of time to understand
Breaks things down nicely.
excellent derivation 😊
Good stuff. Thanks Chris!
Thanks! Very easy to understand video.
I'm glad it was helpful, thanks for watching!
Thanks for this video. You explained very well
[AE 501 7:07]
Hahaha the pens
I'm glad it was entertaining :)
Thanks Chris for the helpful derivation
Good work 👏
Well done
great video and demonstration! Thanks,
AE501: Very good video on this derivation.
Amazing explanation!! thanks
Hi Sarah,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!
-Chris
Good to see where these equations come from
So if slopes are small is an assumption: that means that du/dx~0. Wouldn't that make d2u/dx2 even more 0? Why would we remove du/dx from the equation but not it's second partial w/r/to x?
Look at a sinusoidal wave u(x)=sin(kx). du/dx=kcos(kx), d2u/dx2=-k^2sin(kx), i.e. if k>1, then the second derivative is numerically larger than the first. The physical interpretation is that the string is long compared to the wavelength of the waves propagating on it.
Great derivation!
AE 501: This is excellent presentation on derivation of 1D wave equation. I was not convinced with the mass representation , which is given as (rho *delta X) though.
Neat derivation,,,,,,it is so helpfull,,,
AE501: Having the graphs drawn out for the derivation was very helpful.
Great ... Master! thank you very much...
Thanks for the video! It was very helpful.
You are brilliant! Thanks a lot. Very helpful.
I'm glad it was helpful thanks for watching!
nice explaenation..thanks from india
شكرا جزيلا 🎉
it was amazing sire , thank you....
AE501: I enjoyed this video and it really helped with understanding the 1d wave equation.
AE 501: Great video thank you!
Thanks for the wonderful explanation of the wave Equation Sir
great video, This is Martin Gonzalez, credit plz
What is the use of this equation?
Could you please tell some applications briefly
Quantum mechanics
@@BlockStahIn Quantum mechanics, where & how? Give one example
Thank you so much for this amazing explanation
Hi Ishan,
Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions you might have about any of the videos on Patreon. Thanks for watching!
-Chris
Great video