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 $I=4m$. Resultant intensity at $D$ will be:

• A. $4I_0$
• B. $2I_0$
• C. $I_0$
• D. zero

Answer 1

The correct option is B $2I_0$

Intensity of waves arriving at $D$ from two coherent sources $S_1$ and $S_2$ is $I_0$.
The wavelength of the wave is $\lambda =4m$
Path difference,
$\Delta x=S_{2}D-S_{1}D$
$\Delta x=\left(\sqrt{3^2+4^2}\right)-4$
$\Delta x=5-4$
$\Delta x=1m$

We know that: $\varphi =\frac{2\pi }{\lambda }\Delta x$
Phase difference,
$\varphi =\frac{2\pi }{\lambda }\Delta x=\left(\frac{2\pi }{\lambda }\right)1=\frac{\pi }{2}$

Now, $I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$
Here, $l=$ resultant intensity
$\varphi =$ phase difference
$I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$
$I=I_0+I_0+2\sqrt{I_0{I}_0}\cos \frac{\pi }{2}$
$I=2I_0$

Final Answer: (c)