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

Answer: 16.0

When waves are in phase resultant intensity is $I_0=4I_1$
Where $I_0$ is intensity by each source.
If $I_2=0.36I_1$.
Then we have $\frac{I_{\max }}{I_{\min }}={\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)}^2$
$={\left(\frac{1.6}{0.4}\right)}^2=16$