1. Tardigrade
  2. Question
  3. Physics
  4. Two waves of same frequency and of intensity I 0 and 9 I 0 produces interference. If at a certain point the resultant intensity is 7 I 0 then the minimum phase difference between the two sound waves will be-

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two waves of same frequency and of intensity $I _{0}$ and $9 I _{0}$ produces interference. If at a certain point the resultant intensity is $7 I _{0}$ then the minimum phase difference between the two sound waves will be-

Solution:

$I = I _{1}+ I _{2}+2 \sqrt{ I _{1}\, I _{2}} \cos \phi$
$7 I _{0}= I _{0}+9 I _{0}+2 \sqrt{9 I _{0}^{2}} \cos \phi$
$7 I _{0}= I _{0}+9 I _{0}+2 \times 3 I _{0} \cos \phi$
$\frac{-3 I _{0}}{6_{0}}=\cos \phi$
$\cos \phi=\frac{-1}{2}$
$\phi=120^{\circ}$