5
votes
Galilean invariance of the wave equation
You derived the wave equation assuming the material was stationary, and that is the only case for which that equation is valid. When you transform reference frames you no longer have a stationary ...
3
votes
Galilean invariance of the wave equation
A simple derivation of the wave equation from Newton’s second law is to consider harmonic oscillators in series:
$$
\ddot u_n = (u_{n+1}+u_{n-1}-2u_n)
$$
with $u$ the displacement and normalized mass ...
- 13.1k
1
vote
Accepted
What is the mathematical support for the formula $f_n = n f_1$, used to calculate the frequency of a standing wave?
Let's start with a quick answer: the boundary conditions fix the frequencies of the harmonics. It's worth emphasizing that boundary conditions come from physics, not mathematics. Below, I'll consider ...
- 51.2k
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