= Phase
{disambiguate=waves}
{title2=$\phi$}
{wiki}
= Wave phase
{synonym}
= Oscillation phase
{synonym}
= Phase
{synonym}
The <wave phase> specifies position within an <oscillation> cycle. For a sinusoidal <travelling wave>,
$$
u(x,t)=A\cos\Phi(x,t),\qquad \Phi(x,t)=kx-\omega t+\phi_0,
$$
where $k$ is the <wavenumber>, $\omega$ the <angular frequency> and $\phi_0$ an initial <phase shift>. Adding $2\pi$ to $\Phi$ leaves the field unchanged; one complete cycle advances the <wave phase> by $2\pi$ radians.
A surface of equal <wave phase> is a <wavefront>. Tracking one such surface gives the <phase velocity>, whereas comparing two fields at the same point gives their <phase difference>. Two equal-<frequency> disturbances add constructively when their <wave phases> agree and can cancel when their <phase difference> is $\pi$. The sign assigned to a <phase lag> depends on the chosen time convention. In a <complex amplitude>, the <complex argument> carries this information while the <modulus> sets the <wave amplitude>.
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