Definition:Wave Profile

Definition
Let $\phi$ be a wave which is propagated along the $x$-axis with velocity $c$.

At $t = 0$, let $\phi = \map f x$.

Then $\map f x$ is the wave profile of $\phi$.

This can be expressed as: $\paren {\map \phi x}_{t \mathop = 0} = \map f x$