Two coherent waves represented by  $y_1=A\sin (\frac{2\pi x_1}{\lambda }-\omega t+\frac{\pi }{4})$  and  $y_2=A\sin (\frac{2\pi x_2}{\lambda }-\omega t+\frac{\pi }{6})$  are superposed. The two waves will produce

Path difference  $\Delta \varphi =\{\frac{2\pi }{\lambda }{x}_1-wt+\frac{\pi }{4}-(\frac{2\pi }{\lambda }{x}_2-wt+\frac{\pi }{6})\} \Delta \varphi =\frac{2\lambda }{\lambda }(x_1-x_2)+\frac{\lambda }{12}$

For constructive interference,  $\frac{2\lambda }{\lambda }(x_1-x_2)+\frac{\pi }{12}=2n\pi x_1-x_2=(2n-\frac{1}{12})\frac{\lambda }{2} x_1-x_2=\frac{23\lambda }{24} n=1,2,3$

For destructive interference,  $\frac{2\pi }{\lambda }(x_1-x_2)+\frac{\pi }{12}=(2n-1)\pi x_1-x_2=(2n-1-\frac{1}{12})\frac{\lambda }{2}$

For, n=1
 
$x_1-x_2=\frac{11}{24}\lambda$