Y x t A sin o t - x v A sin 2 p f t - x v. G t 2 f t m o d f t 1 1. A square wave is a non-sinusoidal periodic waveform which can be represented as an infinite summation of sinusoidal waves in which the amplitude alternates at a steady frequency between fixed minimum and maximum values with the same duration at minimum and maximum.
Furthermore any superpositions of solutions to the wave equation are also solutions because the equation is linear.
Keep a fixed vertical scale by first calculating the maximum and minimum values of u over all times and scale all plots to use those z-axis limits. This is in contrast with more familiar linear partial differential equations such as the heat equation the wave equation and the Schroedinger equation of quantum physics 1 2. SquareWavex gives a square wave that alternates between 1 and -1 with unit period. Y x t A sin o t - x v A sin 2 p f t - x v.