Two separated sources emit sinusoidal travelling waves but have the same wavelength `lambda` and are in phase at their respective sources . One travels a distance `l_(1)` to get to the observeration point while the other travels a distance `l_(2)` . The amplitude is minimum at the observation point , `l_(1) - l_(2)` is an

Options

A. odd integral multiple of `lambda`
B. even integral multiple of `lambda`
C. odd integral multiple of `lambda//2`
D. odd integral multiple of `lambda//4`

Explanation

To solve the problem, we need to analyze the conditions for destructive interference of two waves emitted from separate sources. The key points to consider are the path lengths traveled by the waves and the conditions for minimum amplitude at the observation point.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two sources emitting waves that are in phase. The distances traveled by the waves to the observation point are \( l_1 \) and \( l_2 \). The difference in these distances is \( \Delta l = l_1 - l_2 \).

**Hint**: Identify the path difference between the two waves.

2. **Condition for Minimum Amplitude**:
The problem states that the amplitude is minimum at the observation point. This indicates that the waves are interfering destructively.

**Hint**: Recall the conditions for constructive and destructive interference.

3. **Destructive Interference Condition**:
For destructive interference to occur, the path difference must be an odd multiple of half the wavelength. Mathematically, this can be expressed as:
\[ \Delta l = l_1 - l_2 = \left(2n - 1\right) \frac{\lambda}{2} \]
where \( n \) is an integer (0, 1, 2, ...).

**Hint**: Remember that \( n \) can take any integer value, and the factor \( (2n - 1) \) ensures that the path difference is odd.

4. **Conclusion**:
Since the amplitude is minimum at the observation point, we conclude that the path difference \( l_1 - l_2 \) must be an odd integral multiple of \( \frac{\lambda}{2} \). Therefore, the answer to the question is:
\[ l_1 - l_2 = (2n - 1) \frac{\lambda}{2} \]

**Hint**: Verify that the answer matches the conditions for destructive interference.

### Final Answer:
The path difference \( l_1 - l_2 \) is an odd integral multiple of \( \frac{\lambda}{2} \).