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).

__Left-hand side__

__Right-hand side__

The two sides are equal.

Additional material - Wave equation