$y=y_1+y_2$

or $y=A \sin \left(k x-\omega t+\frac{\pi}{6}\right)+A \sin \left(k x-\omega t-\frac{\pi}{6}\right)$

or $y=2 A \sin (k x-\omega t) \cdot \cos \left(\frac{\left(\frac{\pi}{6}+\frac{\pi}{6}\right)}{2}\right)$

or $y^{\prime}=2 A \frac{\sqrt{3}}{2} \sin (k x-\omega t)$

$\therefore y^{\prime}=A \sqrt{3} \sin (k x-\omega t)$