If you took the second-year MA20223 Vectors & PDEs course, you might remember discussing the applications of Fourier series to studying music (or more generally signal processing). There are a lot of beautiful applications of spectral and harmonic analysis to sound and music, and this project will delve into those applications.
It will be divided into two parts:
Additional reading:
[1] https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum
[2] http://www.math.udel.edu/~driscoll/research/drums.html
Pre-requisites: MA20223 is recommended but not essential. Because Part 1 will involve wrestling with some fairly heavy signal and sound processing modules, the student should be quite capable with programming and numerical algorithms. Optimally, a student who is not afraid of working with Python is desirable.