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

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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, 2018 in Q&A by Tyson [ no revision ]

Recent similar question answered twice here

commented Jan 23, 2018 by igael (360 points) [ no revision ]

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!

commented Jan 24, 2018 by Mark Bugden (105 points) [ no revision ]

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.

commented Feb 7, 2018 by Pieter Kuiper (0 points) [ no revision ]

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