Two coherent narrow slits emitting sound of wavelength

Question:

Two coherent narrow slits emitting sound of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $2 \lambda$. The sound is detected by moving a detector on the screen $\Sigma$ at a distance $D(>>\lambda)$ from the slit $S_{1}$ as shown in figure. Find the distance $x$ such that the intensity at $P$ is equal to the intensity at $O$.

Solution:

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