Section 4.1 describes a derivation of the one-dimensional wave equation modelling the small vibrations of an elastic string.



Section 4.2 describes the units of the variables and parameter in the wave equation.



Section 4.3 uses separation of variables to find the normal modes of a finite string.



Section 4.4 uses Fourier’s method to solve an initial boundary value problem for the wave equation.



Section 4.5 describes the manner in which energy is conserved in a vibrating string.



Section 4.6 describes an elementary uniqueness theorem for an initial boundary value problem for the wave equation.


The implications of the theory for sound production in musical instruments is a central theme in the recent Oxford Mathematics Public Lecture by Professor Jon Chapman.

The external YouTube link is here: https://www.youtube.com/watch?v=I63CRjGUMGI