Derivation of the 2D Wave Equation

In this video we derive the 2D wave equation. This partial differential equation governs the motion of waves in a plane and is applicable for thin vibrating membranes. This video focuses on the derivation of the governing PDE only, other videos in this series discuss how to solve this PDE.

Associated videos on software tools relevant to PDEs include:

[karlbalitaan]

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

[minaanderberg]

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

[keyshawnb]

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! :)

[fn]

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

[jasonfranklin]

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

[matthew-bennett]

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.

[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!

[ayaabushmeis]

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

[carlydunford]

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

[siddharthsingh]

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.

[mitchellhubbard]

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

[connorbaldwin]

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

[GiovanniRiggi-jq]

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!

[MagdaleneRachelleShelton]

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

[timproby]

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

[mattpierucci]

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

[KevinKdep]

AE501: Another great demonstration with clever creativity.

[KevinCastaneda]

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.

[evansteele]

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

[robertdelossantos]

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