Two stationary sources of sound, `S_(1)` and `S_(2)` having an equal frequency are fixed some distance apart. The position A is left of `S_(1)` , position B in the middle of the two sources and positionC is to the right of `S_(2)`. An observer starts moving with velocity `V_(0)` from position A towards `S_(1)`, then

Options

A. beats for three position A,B and C will be heard
B. beats will be heard from A and C but not in case of B
C. beats will be not heard for A and C but will be heard for B
D. beats will be not heard for three position of A,B and C

Answer

To solve the problem, we need to analyze the situation involving two stationary sound sources, \( S_1 \) and \( S_2 \), and an observer moving towards \( S_1 \) from position A. We will use the principles of the Doppler effect and the concept of beats.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two stationary sound sources, \( S_1 \) and \( S_2 \), which emit sound waves of equal frequency \( f \).
- The observer starts from position A (to the left of \( S_1 \)) and moves towards \( S_1 \).

2. **Doppler Effect at Position A**:
- As the observer moves towards \( S_1 \), the apparent frequency \( f' \) heard by the observer can be calculated using the Doppler effect formula:
\[ f' = f \left( \frac{v + v_0}{v} \right) \]
where \( v \) is the speed of sound in air, and \( v_0 \) is the velocity of the observer towards the source.
- Since the observer is also moving towards \( S_2 \), the apparent frequency from \( S_2 \) can be calculated similarly:
\[ f'' = f \left( \frac{v + v_0}{v} \right) \]
- Since both sources have the same frequency and the observer is moving towards both sources, the change in frequency (or beat frequency) will be:
\[ \Delta f = f' - f'' = 0 \]
- Therefore, at position A, the beats are unheard (as there is no difference in frequency).

3. **Doppler Effect at Position B**:
- At position B (the midpoint between \( S_1 \) and \( S_2 \)), the observer is moving towards \( S_1 \) and away from \( S_2 \).
- The frequency from \( S_1 \) will increase:
\[ f' = f \left( \frac{v + v_0}{v} \right) \]
- The frequency from \( S_2 \) will decrease:
\[ f'' = f \left( \frac{v - v_0}{v} \right) \]
- The change in frequency (beat frequency) will be:
\[ \Delta f = f' - f'' = f \left( \frac{v + v_0}{v} \right) - f \left( \frac{v - v_0}{v} \right) = f \left( \frac{2v_0}{v} \right) \]
- Thus, at position B, beats will be heard.

4. **Doppler Effect at Position C**:
- At position C (to the right of \( S_2 \)), the observer is moving away from both sources.
- The frequency from \( S_1 \) will decrease:
\[ f' = f \left( \frac{v - v_0}{v} \right) \]
- The frequency from \( S_2 \) will also decrease:
\[ f'' = f \left( \frac{v - v_0}{v} \right) \]
- The change in frequency (beat frequency) will be:
\[ \Delta f = f' - f'' = 0 \]
- Therefore, at position C, the beats are unheard.

5. **Conclusion**:
- The beats are unheard at positions A and C, and heard at position B.
- Therefore, the correct answer is that beats will be heard at position B and not at positions A and C.

### Final Answer:
The beats will be heard at position B, but not at positions A and C.