Linear Wave Propagation

trapezoidal method, waves, Fourier transform

An introduction to studying linear surface waves on an infinite domain. In particular, the problem of finding the time evolution of a small perturbation of the surface of an inviscid and incompressible fluid.

  Modeling Atoms, Molecules, and Crystals in One Dimension

spin, hemmer, eigenenergy, eigenstate, schrödinger equation, waves

Solving the time independent Schrödinger equation in one dimension using matrix diagonalisation for five different potentials.

  Simple Sound Filtering

discrete fourier transform, nyquist-shannon sampling theorem, music, sound filtering, beat

Programming with sounds and using Fourier transforms to filter sound signals.

  Sloshing

simpson's method, newton, euler, eigenvalue, poisson's equation, integration, interpolation

Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.

  Doppler Effect

speed of sound, doppler, discrete fourier transform

Calculating the speed of a passing train by Fourier analysis of the corresponding sound file.