Constructive/destructive interference:

$$\begin{eqnarray*}y & = & A\sin(kx-\omega t)+A\sin (kx-\omega t-\phi )\\ & = &2A\cos(\phi /2)\sin (kx-\omega t-\phi /x) \end{eqnarray*}$$

- constructive when $\phi = 0, \pm 2\pi , \pm 4\pi$, (in phase)
- destructive when $\phi = \pm\pi , \pm 3\pi , \pm 5\pi$ ($180^\circ$ out of phase)