Derivation of the 1D Wave Equation

In this video, we derive the 1D wave equation. This partial differential equation (PDE) applies to scenarios such as the vibrations of a continuous string. This video focuses on the derivation of the governing PDE only, other videos in this series discuss how to solve this PDE.

Additional videos in this series:

Associated videos on software tools relevant to PDEs include:

You can see all the videos related to partial differential equations at

[shivaniits]

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 .

[anthonyz]

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!

[matthewbajamundi]

This video has helped me understand more about the 1d wave equation. Thank you for posting it.

[mitchellhubbard]

Good job presenting the material in a concisely. It helps the students a lot.

[atharvarai]

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!

[anithabarani]

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.

[asn]

Wow! Just wow! Words cannot describe how grateful I am to you for making this video. Thank you!

[petergsaad]

It's very good, i had this point unclear when studying schrödinger equation and because of you, now I understand :)

[ricomajestic]

Excellent presentation. Best derivation of the wave equation I've seen with every step clearly explained.

[himanshu]

Thanks. This is a wonderful explanation for those who find ODE PDE a bit difficult.

[whyargon]

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!

[mattpierucci]

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.

[kidslearningbymadhankarthi]

My favourite equation!!! Crystal clear explanation!!!Excellent derivation

[niharrayalu]

This is the best class i have took related to waves

[mitchellnakaki]

It is amazing how simple the final form becomes yet with so much complexity embedded

[atruonuw]

[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

[brianas]

AE501: GREAT explanation.haven’t found a better explanation of this derivation. Looking forward to how to find the solutions of this PDE

[robertdelossantos]

Thanks for breaking down how to solve the 1D wave equation in an understandable fashion.

[LorraineB_]

Thanks for another informative lecture. I laughed when you threw the pens everywhere by mistake :D Fun.

[dakshitha]

Thanks Chris. Simple enough to understand! Keep them coming...