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Old Apr 15th 2017, 02:25 PM   #1
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Is there something fishy about the wave equation?

Been watching some youtube videos about the derivation of the PDE wave equation Uxx = c^2*Utt




It seems to me they made a lot of unrealistic assumptions when deriving it, namely:
  • Vibration amplitudes are small
  • The tension in the wave is the same everywhere
  • Vertical displacement only

Given that a lot of physics (eg: QM, Maxwell's equations, etc) is built around Uxx = c^2*Utt being law doesn't this make all the conclusions a bit dodgy?
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Old Apr 15th 2017, 03:28 PM   #2
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Originally Posted by kiwiheretic View Post
Been watching some youtube videos about the derivation of the PDE wave equation Uxx = c^2*Utt

It seems to me they made a lot of unrealistic assumptions when deriving it, namely:
  • Vibration amplitudes are small
  • The tension in the wave is the same everywhere
  • Vertical displacement only

Given that a lot of physics (eg: QM, Maxwell's equations, etc) is built around Uxx = c^2*Utt being law doesn't this make all the conclusions a bit dodgy?
You are absolutely right. The wave equation (which normally does a fine job) is full of variety of assumptions. Most of Physics depends on a number of unnatural assumptions, three of which you have already mentioned. The problem is that if we write a more realistic equation it is harder to solve. Replace too many assumptions for more realism and you will wind up with an unsolvable problem.

Here's a "down and dirty" look at the non-linear wave equation.

-Dan
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