The correct answer is Option C: A and C. Here's why:

Interference occurs when two waves superpose, resulting in a new wave with an amplitude that varies depending on the phase difference between the original waves. Let's analyze the given options:

Option A: y = a sin ωt and Option C: y = a sin (ωt - φ)

These two waves have the same frequency (ω) and amplitude (a), but they differ in phase by φ. This phase difference is crucial for interference. When waves with the same frequency and different phases superpose, they create an interference pattern with alternating regions of constructive and destructive interference.

Option B: y = a sin 2ωt and Option D: y = a sin 3ωt

These waves have different frequencies (2ω and 3ω). While superposition occurs, it doesn't lead to a stable interference pattern. The waves will not consistently reinforce or cancel each other out because their frequencies are not synchronized.

In summary, interference patterns are observed when two waves have the same frequency (or a very small difference in frequency, called "beats") and a phase difference. Options A and C satisfy these conditions, leading to interference.