Any wave traveling at a speed of v along the x-axis should obey the wave equation
One way to show this is by comparing the two sides of the equation using the
general form of a wave function,
y(x,t) = f(x ± vt). We know from math note 1, that any wave traveling at constant speed can be written as a function
of x-vt (f(x-vt) moving to the right), or x+vt (f(x+vt) moving to the left).
The two sides are equal.