Is there a way to derive the wave equation for a classical string using coordinate free differential geometry?

+ 0 like - 1 dislike
94 views
Can wave equations such as that for a string be formulated without partial differential equations with respect to space and time coordinates?
asked Jan 22 in Q&A

Recent similar question answered twice here

I'm a bit confused by what you mean here. How do you expect to get a wave equation without using PDEs? The wave equation IS a partial differential equation!

There is a nice argument by PG Tait that derives the speed of propagation without calculus. It turns out that arbitrary waveforms will propagate (not only functions). Even knots would propagate. It is in an old Encyclopedia Brittanica. If that is an answer, I could write it up here.

Your answer

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysicsOverfl$\varnothing$wThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.