Question

Four independent waves are represented by equations :
(1) $X_{1}=a_{1} \sin \omega t$
(2) $X_{2}=a_{1} \sin 2 \omega t$
(3) $X_{3}=a_{1} \sin \omega_{1} t$
(4) $X_{4}=a_{1} \sin (\omega t+\delta)$
Interference is possible between waves represented by equations :

• A. 3 and 4
• B. 1 and 2
• C. 2 and 3
• D. 1 and 4

Answer 1

Answer: (D)

To see interference, we need two sources with the same frequency and with 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 a constant phase difference $\delta$, so interference is possible between them.
For.$X_{1}=a_{1} \sin \omega t$
and $X_{2}=a_{2} \sin 2 \omega t$,
frequency is not equal and there is no constant phase difference. For
$X_{1}=a_{1} \sin \omega t$,
and $X_{3}=a_{1} \sin \omega_{1} t$,
frequency is different and there is no constant phase difference.