Physics - Sound Wave Question with Solution | TestHub

The resultant intensity $I$ at a point due to the interference of two waves with intensities $I_1$ and $I_2$ and a phase difference $\varphi$ is given by:

$$I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$$

Given $I_1=I_0$, $I_2=9I_0$, and $\varphi =\frac{\pi }{2}$.

Substituting these values:

$$I=I_0+9I_0+2\sqrt{I_0\cdot 9I_0}\cos \left(\frac{\pi }{2}\right)$$

Since $\cos \left(\frac{\pi }{2}\right)=0$:

$$I=10I_0+2\sqrt{9I_0^2}\cdot 0$$

$$I=10I_0$$