Two waves of equal amplitude and frequency interfere each other. The ratio of intensity when the two waves arrive in phase to that when they arrive 90° out of phase is

Question

Two waves of equal amplitude and frequency interfere each other. The ratio of intensity when the two waves arrive in phase to that when they arrive 90° out of phase is (A) 1: 1 (B) √2: 1 (C) 2: 1 (D) 4: 1

Tardigrade Admin · Accepted Answer

Resultant intensity I=4 I0 cos 2(φ / 2) ⇒ (I1/I2)=( cos 2(φ1 / 2)/ cos 2(φ2 / 2)) =( cos 2 0/ cos 2(90 / 2))=(2/1)

Q. Two waves of equal amplitude and frequency interfere each other. The ratio of intensity when the two waves arrive in phase to that when they arrive $9 0^{\circ}$ out of phase is

1 : 1

$2 : 1$

2 : 1

4 : 1

Resultant intensity $I = 4 I_{0} cos^{2} (ϕ /2)$
$\Rightarrow \frac{I _{1}}{I _{2}} = \frac{c o s ^{2} ( ϕ _{1} /2 )}{c o s ^{2} ( ϕ _{2} /2 )}$
$= \frac{c o s ^{2} 0}{c o s ^{2} ( 90/2 )} = \frac{2}{1}$

Q. Two waves of equal amplitude and frequency interfere each other. The ratio of intensity when the two waves arrive in phase to that when they arrive 90∘ out of phase is