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

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- (A) 90° (B) 100° (C) 120° (D) 110°

Tardigrade Admin · Accepted Answer

I = I 1+ I 2+2 √ I 1 I 2 cos φ 7 I 0= I 0+9 I 0+2 √9 I 02 cos φ 7 I 0= I 0+9 I 0+2 × 3 I 0 cos φ (-3 I 0/60)= cos φ cos φ=(-1/2) φ=120°

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-

$9 0^{\circ}$

$10 0^{\circ}$

$12 0^{\circ}$

$11 0^{\circ}$

$I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
$7 I_{0} = I_{0} + 9 I_{0} + 2 9 I_{0}^{2} cos ϕ$
$7 I_{0} = I_{0} + 9 I_{0} + 2 \times 3 I_{0} cos ϕ$
$\frac{- 3 I _{0}}{6 _{0}} = cos ϕ$
$cos ϕ = \frac{- 1}{2}$
$ϕ = 12 0^{\circ}$

Q. Two waves of same frequency and of intensity I0​ and 9I0​ produces interference. If at a certain point the resultant intensity is 7I0​ then the minimum phase difference between the two sound waves will be-

90∘

100∘

120∘

110∘