Wave equation

This shows the time evolution of a solution for the wave equation u_tt = α²u_xx given an initial condition, and subject to the boundary conditions of the left and right endpoints being fixed.

Click and drag to adjust the current wave displacement at different points along the curve. The light grey lines are different terms of the Fourier series at the current moment — the linear combination of these gives the black line.

Try creating standing waves, for instance picking out a single Fourier mode.

Try creating small impulses and see how they reflect off of the boundaries.

Try creating the shape you would imagine a string would be when it is about to be plucked.

©2016 Kyle Miller