Question

Sounds from two identical sources $S_{1}$ and $S_{2}$ reach a point $P$. When the sounds reach directly, and in the same phase, the intensity at $P$ is $I_{0}$. The power of $5$ , is now reduced by $64 \%$, and the phase difference between $S_{1}$ and $S_{2}$ is varied continuously. The maximum and minimum intensities recorded at $P$ are now $I_{\max }$ and $I_{\min }$. The value of $\frac{I_{\max }}{I_{\min }}$ is _____

Answer 1

When waves are in phase resultant intensity is $I_{0}=4 I_{1}$
Where $I_{0}$ is intensity by each source.
If $I_{2}=0.36 I_{1}$.
Then we have $\frac{I_{\max }}{I_{\min }}=\left(\frac{\sqrt{I_{1}}+\sqrt{I_{2}}}{\sqrt{I_{1}}-\sqrt{I_{2}}}\right)^{2}$
$=\left(\frac{1.6}{0.4}\right)^{2}=16$