Question

In the figure the intensity of waves arriving at $D$ from two coherent sources $S_{1}$ and $S_{2}$ is $I_{0}$. The wavelength of the wave is $\lambda=4 m$. Resultant intensity at $D$ will be:

• A. $4 I_{0}$
• B. $I_{0}$
• C. $2 I_{0}$
• D. zero

Answer 1

Answer: (C)

Path differences, $\Delta x=S_{2} D-S_{1} D=5-4=1\, m$
$\therefore $ The corresponding phase difference will be
$\phi=\frac{2 \pi}{\lambda} \Delta x=\frac{2 \pi}{4} \cdot 1=\frac{\pi}{2}$
Using $I=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos \phi$
$I=I_{0}+I_{0} +2 \sqrt{I_{0} I_{0}} \cos \frac{\pi}{2}=2 I_{0}$