An Important Property of Waves: Superposition

The wave equation is linear, and hence it is easy to show that if $y_1(x,t)$ solves the wave equation and $y_2(x,t)$ (independent of $y_1$) also solves the wave equation, then:

$$y(x,t) = A y_1(x,t) + B y_2(x,t)$$ (107)

solves the wave equation for arbitrary (complex) $A$ and $B$.

This property of waves is most powerful and sublime.