Question

Four light sources produce the following four waves: (i) \(y_1 = a\sin(\omega t + \phi_1)\) (ii) \(y_2 = a\sin 2\omega t\) (iii) \(y_3 = a\sin(\omega t + \phi_2)\) (iv) \(y_4 = a\sin(3\omega t + \phi_1)\) Superposition of which two waves give rise to interference?

• A. (i) and (ii)
• B. (ii) and (iii)
• C. (i) and (iii)
• D. (iii) and (iv)

Hint:

Interference requires same frequency and constant phase difference. Waves of different frequencies do not give stable interference.

Answer 1

The Correct Option is C

Step 1: Condition for interference.
For sustained interference:
- Two waves must have same frequency.
- They should maintain a constant phase difference.
- They should have comparable amplitudes.
Step 2: Compare frequencies of given waves.
(i) has frequency \(\omega\).
(ii) has frequency \(2\omega\).
(iii) has frequency \(\omega\).
(iv) has frequency \(3\omega\).
Step 3: Select pair with same frequency.
Only (i) and (iii) have same angular frequency \(\omega\).
They can maintain constant phase difference \((\phi_2-\phi_1)\).
Hence, they produce interference.
Final Answer: \[ \boxed{\text{(i) and (iii)}} \]