Two vehicles, each moving with speed `u` on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity `w`. One of these vehicles blows a whistle of frequency `f_(1)`. An observer in the other vehicle hears the frequency of the whistle to be `f_(2)`. the speed of sound in still air is `V_C`. The correct statement `(s)` is (are)

Options

A. (a)If the wind blows from the source to the observer `f_(2) gt f_(1)`
B. (b)If the wind blows from the observer to the source, `f_(2) gt f_(1)`
C. (c)If the wind blows from observer to the source, `f_(2) lt f_(1)`
D. (d)If the wind blows from the source to the observer `f_(2) lt f_(1)`

Explanation

To solve the problem, we need to analyze the situation involving two vehicles moving towards each other, the effect of wind, and how it influences the frequency of the sound heard by the observer in the other vehicle.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let the speed of each vehicle be \( u \).
- The frequency of the whistle blown by the source vehicle is \( f_1 \).
- The frequency heard by the observer in the other vehicle is \( f_2 \).
- The speed of sound in still air is \( V_C \).
- The speed of the wind is \( w \).

2. **Case 1: Wind Blowing from Observer to Source**:
- In this case, the effective speed of sound towards the observer is increased by the wind speed \( w \).
- The frequency heard by the observer can be calculated using the Doppler effect formula:
\[ f_2 = f_1 \left( \frac{V_C + w}{V_C - u} \right) \]
- Here, \( V_C + w \) is the speed of sound plus the wind speed (moving towards the observer), and \( V_C - u \) is the speed of sound minus the speed of the source (moving towards the observer).
- Since both vehicles are approaching each other, \( f_2 \) will be greater than \( f_1 \).

3. **Case 2: Wind Blowing from Source to Observer**:
- Here, the effective speed of sound towards the observer is decreased by the wind speed \( w \).
- The frequency heard by the observer is given by:
\[ f_2 = f_1 \left( \frac{V_C - w}{V_C + u} \right) \]
- In this case, \( V_C - w \) is the speed of sound minus the wind speed (moving towards the observer), and \( V_C + u \) is the speed of sound plus the speed of the source (moving towards the observer).
- Again, since both vehicles are approaching each other, \( f_2 \) will still be greater than \( f_1 \).

4. **Conclusion**:
- In both cases, the frequency \( f_2 \) is greater than \( f_1 \):
\[ f_2 > f_1 \]
- Therefore, the correct statements regarding the frequency heard by the observer are that in both scenarios (wind blowing from observer to source and from source to observer), the frequency \( f_2 \) is greater than \( f_1 \).

### Final Answer:
The correct statements are:
- If the wind blows from the source to the observer, \( f_2 > f_1 \).
- If the wind blows from the observer to the source, \( f_2 > f_1 \).