A train, standing in a station yard, blows a whistle of frequency 400Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10m//s. Given that the speed sound in still air is `340m//s`,

Options

A. The frequency of sound as heard by an observer standing on the platform is 400 Hz.
B. The speed of sound for the observer standing on the platform is 330 `m s^(-1)`
C. The frequency of sound as heard by the observer standing on the platform will increase.
D. The frequency of sound as heard by the observer standing

Explanation

To solve the problem, we need to determine the frequency of the sound as heard by an observer standing on the platform when the wind is blowing from the yard to the station.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Frequency of the whistle (f) = 400 Hz
- Speed of sound in still air (v_sound) = 340 m/s
- Speed of wind (v_wind) = 10 m/s

2. **Determine the Effective Speed of Sound:**
Since the wind is blowing in the same direction as the sound, the effective speed of sound (v_effective) is the sum of the speed of sound in still air and the speed of the wind:
\[ v_{effective} = v_{sound} + v_{wind} = 340 \, \text{m/s} + 10 \, \text{m/s} = 350 \, \text{m/s} \]

3. **Apply the Doppler Effect Formula:**
The frequency heard by the observer (f') can be calculated using the Doppler effect formula for a stationary observer and a stationary source:
\[ f' = f \times \frac{v_{effective}}{v_{sound}} \]
Here, the observer is at rest, so we do not need to consider any motion of the observer.

4. **Substituting the Values:**
\[ f' = 400 \, \text{Hz} \times \frac{350 \, \text{m/s}}{340 \, \text{m/s}} \]
\[ f' = 400 \, \text{Hz} \times 1.0294 \approx 411.76 \, \text{Hz} \]

5. **Conclusion:**
The frequency of the sound as heard by the observer standing on the platform is approximately 411.76 Hz.

### Final Answer:
The frequency of the sound as heard by the observer is approximately **411.76 Hz**.