Question

Four independent waves are represented by the following equations:
$X_1=a_1\sin \omega t...\left(1\right)$
$X_2=a_1\sin 2\omega t...\left(2\right)$
$X_3=a_1\sin {\omega }_{1}t...\left(3\right)$
$X_4=a_1\sin (\omega t+\delta )...\left(4\right)$
Interference is possible between waves represented by the equations,

• A. $3\text{and}4$
• B. $1\text{and}2$
• C. $2\text{and}3$
• D. $1\text{and}4$

Answer 1

The correct option is D $1\text{and}4$

To observe the interference, we need two coherent sources , i.e. two sources with the same frequency and a constant phase difference.

In the given waves,

$X_1=a_1\sin \omega t$, and
$X_4=a_1\sin (\omega t+\delta )$

have same frequency and a constant phase difference $\delta$, so interference is possible between them.

Hence, the correct answer is option $\left(D\right)$.