Two waves of the same frequency meet at a point…

Superposition: where waves meet, their displacements add, $y = y_1 + y_2$. Two waves of amplitudes $a_1$ and $a_2$ with a phase difference $\phi$ give $A^2 = a_1^2 + a_2^2 + 2a_1a_2\cos\phi$; for equal amplitudes, $A = 2a\cos(\phi/2)$. A path difference $\Delta x$ is a phase difference $\phi = \dfrac{2\pi}{\lambda}\Delta x$. Intensity $I \propto A^2$.