Question

Interference pattern can be observed due to superposition of the following waves:
A. \(y = a \sin \omega t\)     B. \(y = a \sin 2\omega t\)
C. \(y = a \sin(\omega t - \phi)\)      D. \(y = a \sin 3\omega t\)
Choose the correct answer from the options given below.

• A. B and C
• B. B and D
• C. A and C
• D. A and B

Answer 1

The Correct Option is C

To observe interference patterns, the superposition of waves must meet certain criteria. The key requirement is that the waves should be coherent, meaning they have the same frequency and a constant phase difference. Let's analyze the given options:

• A. \(y = a \sin \omega t\)
• B. \(y = a \sin 2\omega t\)
• C. \(y = a \sin(\omega t - \phi)\) 
• D. \(y = a \sin 3\omega t\)

Let's evaluate each pair of waves mentioned in the options:

1. A and C: These two waves, \(\omega t\) and \(\omega t - \phi\), have the same frequency \( \omega \) and a phase difference \( \phi \). Being coherent, they can form a stable interference pattern.
2. B and C: These waves have different frequencies, \(2\omega\) and \(\omega\), respectively, and thus cannot produce a stable interference pattern.
3. B and D: Both of these waves have different frequencies, \(2\omega\) and \(3\omega\), and interfere destructively, not forming a stable pattern.
4. A and B: Again, the waves have different frequencies, \(\omega\) and \(2\omega\), making them unsuitable for stable interference.

Thus, the correct choice is A and C, which fulfill the criteria for coherent waves needed to observe an interference pattern. Therefore, the correct answer is:

Option C: A and C