Question

two waves of same frequency and of intensity $I_0$ and $9I_0$ produces interference. If at a certain point the resultant intensity is $7I_0$ then the minimum phase difference between the two sound waves will be

• A. ${90}^0$
• B. ${150}^0$
• C. ${120}^0$
• D. ${100}^0$

Answer 1

The correct option is C ${120}^0$

$\begin{array}{c}7I_o=I_o+a{I}_o+2\sqrt{I_o}\sqrt{x{I}_o}\cos \Delta \varphi \\ \Rightarrow 7I_o=10I_o+6\cos \Delta \varphi \\ \Rightarrow -3I_o=6\cos \Delta \varphi \\ \cos \Delta \varphi =-12\\ \Delta \varphi =\frac{2\pi }{3}=\frac{2\times 180}{3}={120}^0\\ Hence,\\ optionCiscorrectanswer.\end{array}$