Abstract
Here, we extend the analysis of the previous chapter from many-particle coupled oscillators to continuous systems. In so doing, we will be able to describe the oscillatory motion of strings, membranes, and solid objects. We discuss both the eigenfunction and normal form solutions of the wave equation, paying particular attention to various boundary conditions and initial conditions.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
There is no consensus on the placement of the factors of \(2\pi \) in the Fourier transform. Some authors use a factor of \(1/2\pi \) in front of the definition of f(x) (with nothing in front of the definition of F(k)), while others put the factor of \(1/2\pi \) in front of the definition of F(k). We have chosen to share it evenly across both definitions, but you should check to see what convention is being used when referring to software or tables of Fourier transform pairs.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Benacquista, M.J., Romano, J.D. (2018). Wave Equation. In: Classical Mechanics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-68780-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-68780-3_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68779-7
Online ISBN: 978-3-319-68780-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)