Question

In the figure the intensity of waves arriving at D from two coherent source $S_1$ & $S_2$ is $I_0$. the wavelength of the wave is $\lambda =4m.$ Resultant intensity at D will be

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

Answer 1

The correct option is C $2I_0$

$S_{2}P=\sqrt{S_1{P}^2+S_1{S}_2^2}$

$=\sqrt{4^2+3^2}$

$=5m$

$\Delta x=S_{2}P-S_{1}P=5-4=1m$

$\Delta \Phi =\frac{2\pi }{\lambda }\Delta x$

$=\frac{2\pi }{4}\left(1\right)=\frac{\pi }{2}$

Now $I_0=4I_0{\cos }^2\left(\frac{\Delta \Phi }{2}\right)=4I_0{\cos }^2\frac{\pi }{4}=2I_0$