Derivation of the 2D Wave Equation

[@ChristopherLum]

In case it is helpful, here are all my PDE videos in a single playlist kzbin.info/aero/PLxdnSsBqCrrFvek-n1MKhFaDARSdKWPnx. Please let me know what you think in the comments. Thanks for watching!

[@icee562]

These lectures are beautiful sir, thank you for sharing!!!

[@ahmedashmaig]

AE 501: "When someone finds this mess in the morning, I'll blame it on them". This part cracked me up 😂 Thanks for making these lectures enjoyable and fun to watch!

[@fn5002]

AE501: I really like how you made again very accessible for someone who hasn’t touch this material in quite sometime. Farouk Nejah

[@karlbalitaan]

This was not only a helpful video but extremely fun to watch. I loved how you played around with your props.

[@EfremNickel]

AE501: Thank you for making these lecture videos fun to watch as much as they are informative. Makes it a much easier watch. And I appreciate that I can come back to any of these lectures right here on youtube!

[@keyshawnb4845]

AE 501: I'm excited to Solve the 2-D wave equation! Also the use of props makes this format of video both hilarious and easy to visualize! :)

[@minaanderberg884]

Cutting out the towel definitely helped visualize how you were going to derive the 2D wave equation.

[@matthew-bennett13]

AE 501: I'm really glad that you're taking the time to get into depth on the derivation of the equations. I have in the past had professors who tended to skip through equation derivations very quickly or left more up to the student to figure out from text alone. I appreciate you going through this thoroughly.

[@jasonfranklin4614]

AE501- the methods are really the gold in these lectures. This does a great job of picking out the importance of assumptions and applicability. It's almost surprising how easily these expand to higher dimensions

[@mattpierucci7647]

Helpful extension of the 1D wave equation to another dimension. This also has to be the funniest video you've had this quarter!

[@ChristopherLum]

Glad it was entertaining!

[@DominicChongShengLim]

AE501: Somehow understood the derivation better as soon as the piece of cloth came about, but serious note a very detailed and easy to follow understanding of the derivation of 2D wave equation!

[@KennethWright-k2h]

AE501: Thank you for helping visualize the 2D wave equation with a diagram. Derivation made sense! Thanks!

[@ayaabushmeis8049]

[AE 501] I really appreciate the demonstration in the beginning, it's hard to visualize surfaces with sketches but this made it very clear!

[@rajveerniranjan1809]

Woah!!!!! the visualization is great, now I'm able to understand it much better.

[@ChristopherLum]

I'm glad it was helpful thanks for watching!

[@rajveerniranjan1809]

@@ChristopherLum today at 9:30 I have exam of partial differential equations so it is going to be best for me..... thank you and keep on going...

[@siddharthsingh6393]

The one thing that I liked the most is that you tell all the assumptions taken at each step. I would just like you to explain how those assumptions don't affect the physical reality of the situation a little bit more.

[@KarlaPkva]

AE501 - I really enjoyed this video. The props made it easier to understand the 2D wave equation, and gave me a good laugh especially once the dA patch had to come out of the towel.

[@timproby7624]

[AE 501] 2:57 You always find simple but effective demos!

[@connorbaldwin5845]

AE 501. This was a very helpful lecture, I did not go into 2D wave equations in my undergrad so this was very informative.

[@carlydunford2546]

AE 501: Normally derivations are harder for me to grasp but I like the way you simplified this one.

[@mitchellhubbard5727]

Great examples. I like that you show a simple model before diving into the derivations.

[@sumeshrajurkar5922]

Great. I like the way you made a complex derivation fun to watch. Cleaning up the mess after your video is also a great service to science, something that your wife must be knowing!!

[@ChristopherLum]

I'm glad it was helpful. There are other similar videos on the channel please feel free to check them out. Thanks for watching!

[@ryanmeinhardt81]

AE501 : Very helpful to have the props and having the diagrams drawn on them. Also found the callbacks to the 1D wave equation helpful

[@KevinKdep]

AE501: Another great demonstration with clever creativity.

[@HantaoCui]

My favorite line is “if you look at it long enough, you will…” 😄

[@adrianbirge7493]

Thank you for the in depth explanation!

[@MagdaleneRachelleShelton]

AE501: Once again- I appreciate all the creativity with the visuals , it really helps! -Maggie Shelton

[@lukewideman1]

AE501: thank you for keeping these entertaining!

[@elijahleonen198]

AE501: The derivation helped my understanding of the 2D wave equation. Thank you for the great video!

[@LilanieAlfredaAbdur-Rahman]

AE501: Very clear Professor Lum. I just hope this derivation extends as logically to the heat equation.

[@evansteele7874]

AE501: Thanks for the practical demonstrations, they really do help visualize the concepts and help with understanding!

[@GiovanniRiggi-j2q]

AE501 - Johnny Riggi. Easy to understand breakdown of a complex topic, especially with the lecture notes. Learned a good bit about double Fourier series as well!

[@robertdelossantos1936]

Definitely helpful to get a visualization of what the 2D wave equation is solving.

[@KevinCastaneda21]

AE501: I really enjoy and appreciate the initial demos with real objects to set the stage for derivations and problem solution it really allows me to tie the two together. It would be very interesting to explore a beam that has resistance to bending and its reaction or different eigenmodes.

[@alexsteahr8458]

Very cool visual demonstration!

[@gautomdeka581]

You are doing so good not only this rather all concept is 😍

[@lienchang8391]

The visualization for the derivation helped a lot!

[@matthewbajamundi8774]

Enjoyed your towel example. It really helped me visualize this concept.

[@christophersanchez2256]

Thanks for the video! I really liked the example.

[@alvinardiansyah7615]

It's very helpful. I have take home exam about this material

[@sethwhittington28]

AE501: Professor Lum, similar to in your one dimensional video, I am confused about the assumptions made regarding small angle approximations when summing vertical forces. REF timestamp 17:30. You noted that since theta was small, we could assume that the Cos(small angle) = 1, and as a result, the horizontal forces cancel out. By that logic it seems to me like a similar argument could be made to the vertical forces such that SIN(small angle) = 0, meaning that the vertical forces would also cancel out and the sum of the forces in the vertical direction = 0. Am I missing something?

[@ChristopherLum]

Hi Seth, the small angle approximation is that cos(theta) =1 and sin(theta) = theta. You can see why if you plot sin and cos and look at the functions at small values of theta.

[@sethwhittington28]

@@ChristopherLum Okay yes, that makes sense. Thanks.

[@sethwhittington28]

@@ChristopherLum I am also confused about how density * area = mass. Typically we see density * volume = mass but in this lecture it looks like we have density * delta x * delta y = mass.

[@ChristopherLum]

@@sethwhittington28 In this case we define density as mass per unit area. You are correct that this is non-standard but is how the problem is setup.

[@sethwhittington28]

@@ChristopherLum okay yeah I thought you might be doing something along those lines.. thanks for the response.

[@ThePrimeMetric]

Thank you, you did a great job helping me visualize the problem. I was reading the derivation for it in Frank Bowman's Introduction to Bessel functions and I couldn't understand where the partial derivative with respect to x (or y) was coming from. It only had one 2d picture that wasn't particularly helpful.

[@charlesharmon9065]

Thanks for the derivation and for including the towel visualization.

[@sajeew]

This is showed us how to derive the 2D wave equation.Thank you

[@helentat121]

Great visual of the bounded membrane

[@paxtonschipper1926]

AE501: Great video, I always struggle with derivations and this helped me a lot.

[@Andrew_Bruns]

AE501: It was very helpful to see and understand what is happening with the physical towel example.

[@jasondorn3514]

The outcome of the derivation was expected but it was great to see the steps to get there.

[@mrassbandit23]

Thanks for this and the solution to the 2-D wave equation!

[@daniellerogers5959]

Another great, easy to follow video. Thanks!

[@tonykuenzli2182]

AE501 - Your demonstration really showed the importance that out of plane deflections are small 😂

[@MuhammadSalman-xr7of]

Best explanation ever Thank you

[@ChristopherLum]

Hi, 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

[@mitchellnakaki7900]

interesting how added an additional dimension does not introduce too much more complexity

[@ThienNguyen-vx1td]

AE501: Great demonstration and a mess to clean up.

[@HIEPNGUYEN-wb7yg]

Great video. Visualization does help too! Thanks.

[@almightysapling]

"this garbage down here" I'm so happy to learn I'm not the only person who talks about their equations like this

[@adamyousri4903]

AE 501: Thanks Professor great video!

[@Tamanaaaa1]

AE 501: Very helpful! Thank you!

[@thomasireson1427]

The 3D graph was very helpful in trying to understand this.

[@solomondawit8866]

AE501: Your teaching style is appealing in many ways. But if I had to choose only one, I would go with those illustrations that aid in creating mental images.

[@Account-fi1cu]

Wow youre great ! thank you so much, you made it so simple

[@ChristopherLum]

I'm glad it was useful, thanks for watching!

[@peteralbertmadakson]

AE501: Thank you Chris for the amazing illustration using the towel. Constraining the edges reminds me of drum making as a kid. Could this approach be used to relate the deflection on a hand drum to the notes produced?

[@ChristopherLum]

Absolutely, it would be even better if we had gotten to the discussion on circular membranes as these more closely resemble drums.

[@jacobgivens2000]

AE501: I liked the graphs and visual elements in your lectures. I find it really hard to follow along with theory if there isn't something physical to see in order to understand the material!

[@paulpietrowicz3683]

AE501- Easy to understand the derivation with the visual to start out. Makes sense.

[@mylesdeluca8789]

Great video! Helped a lot!

[@ryancazin5930]

Interesting and clear derivation - thanks!

[@alviehaider4559]

AE 501 very helpful video to understand the derivation of 2d wave equations

[@TriMartz-f4x]

[AE501] I wonder what ever happened to the delta x-y patch.

[@RajChhabraUW]

AE501: Is there any issue with the fact that when the simplification is made from [u_x (x+deltax,y1),u_x(x,y2)]/deltax to u_x_x that y1 and y2 don't necessarily equal each other? Is it because y1 and y2 are assumed some average or constant value? Similar potential issue for u_y_y?

[@jonathonlaird6279]

the demo was helpful. thanks

[@painting_cg]

Sir, which book that you preferred

[@kuralmalar4483]

sir could u post a video for three dimensional wave equation

[@jesusespinoza2349]

Good demonstration

[@jasonwhyte4162]

Great video!

[@masontelander3847]

Great video

[@garrettdavis4665]

What if density is not uniform for the material?

[@calebwatson6331]

AE501: Really funny video! I don't remember doing this in undergrad so this was interesting

[@ChristopherLum]

I'm glad it was entertaining and it is good to see you getting a jump on next week's videos!

[@calebwatson6331]

@@ChristopherLum I've finally got the routine down. Sundays are lecture day. Ready to start the next HW on Tuesday!

[@SScook206]

Thanks Chris!

[@lorianacouturier5038]

What are some real world applications of this 2d wave equation? I look online but all I can find is the example of a drum head, are there any less obvious applications? And if so would they all take this exact form but with a different value for c^2 ? Thanks :)

[@ChristopherLum]

Hi Loriana, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on KZbin due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

[@selamhendrix5252]

the funny demo actually helped understand the derivation

[@samanisrar1242]

Great

[@trevorubrown]

Great vid

[@selwild2050]

Merci, c'est très clair.

[@joewalker5753]

Very Good!

[@bryanmasserang5190]

Interesting derivation

[@LorraineB_0911]

Love the visuals every time. #AE501

[@holidayplatform2570]

I wish you were my current teacher(undergraduate) .

[@ChristopherLum]

I'm glad it was helpful. There are other similar videos on the channel, please let me know what you think, thanks for watching!

[@kylekearsley800]

Great video.

[@lauraramlal4189]

Very informative

[@atruon17uw]

[AE501] The cloth was a innovative way to manipulate the shape of the function

[@tm89681]

Nice 👍

[@vanshikasinghal4948]

In writing the Horizontal and Vertical forces (when we start the derivation) why have we not considered the T del x forces?

[@harshavardhan9399]

he didn't derive because he considered x and y are symmetric

[@andrewsegundo7977]

Intuitively this just means that the membrane is secure and won’t slide off. That’s what he means by no horizontal motion. It also means the membrane won’t tear.

[@TheBudids]

can you help me for describe a deriviting wave equation from paper Mario ootaviani (1971)-Elastic wave propagation in two evenly-welded quarter-spaces

[@ardacetken9090]

AE501: Arda Cetken - Digging the shirt!

[@nghihoang2952]

great example (AE501)

[@jeetubais5507]

Beautiful❤😍

[@marissalamadrid8190]

replacement towels from williams-sonoma? :)

[@ChristopherLum]

Haha, good idea :)

[@jakegalleryn6200]

Loved the bead-mess

[@MrThegonz1]

great video, This is Martin Gonzalez, credit plz

[@antoniogomez4241]

Hahahahaha when he says he´d blame his kids and dog for the mess

[@renowhitcomb5505]

AE 501. Fall 2020. Which kid did you blame the mess on lol

[@ChristopherLum]

I actually like to blame things on the dog, he can't disagree with my version of events 😀.