Question

Four independent waves are represented by equations \[ X_1 = a_1 \sin \omega t, \, X_2 = a_2 \sin 2 \omega t, \, X_3 = a_3 \sin \omega t, \, X_4 = a_4 \sin (\omega t + \delta) \] Interference is possible between waves represented by equations

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

Hint:

For interference to occur, waves must have the same frequency and a phase difference.

Answer 1

The Correct Option is D

Step 1: Interference condition.
Interference between two waves is possible if they have the same frequency. Here, equations 3 and 4 both represent waves with frequency \( \omega \) but with a phase difference \( \delta \). Hence, interference is possible between them.

Step 2: Conclusion.
Therefore, the correct answer is option (D).

Final Answer: \[ \boxed{\text{(D) 3 and 4}} \]