A train is moving on a straight track with speed `20ms^(-1)`. It is blowing its whistle at the frequency of `1000 Hz`. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound `= 320 ms^(-1)`) close to :

Options

A. `12%`
B. `6%`
C. `18%`
D. `24%`

Explanation

To solve the problem, we will use the Doppler effect formula for sound waves. The frequency heard by an observer when the source is moving towards the observer and when it is moving away from the observer will be calculated separately.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Speed of sound, \( V = 320 \, \text{m/s} \)
- Speed of the train (source), \( V_s = 20 \, \text{m/s} \)
- Frequency of the whistle (source frequency), \( f = 1000 \, \text{Hz} \)

2. **Calculate the Frequency Heard When the Train Approaches:**
- When the source is moving towards the observer, the formula for the observed frequency \( f' \) is:
\[ f' = f \cdot \frac{V}{V - V_s} \]
- Substituting the values:
\[ f' = 1000 \cdot \frac{320}{320 - 20} = 1000 \cdot \frac{320}{300} = \frac{320000}{300} = \frac{3200}{3} \approx 1066.67 \, \text{Hz} \]

3. **Calculate the Frequency Heard When the Train Moves Away:**
- When the source is moving away from the observer, the formula for the observed frequency \( f'' \) is:
\[ f'' = f \cdot \frac{V}{V + V_s} \]
- Substituting the values:
\[ f'' = 1000 \cdot \frac{320}{320 + 20} = 1000 \cdot \frac{320}{340} = \frac{320000}{340} = \frac{3200}{34} \approx 941.18 \, \text{Hz} \]

4. **Calculate the Change in Frequency:**
- The change in frequency \( \Delta f \) is given by:
\[ \Delta f = f' - f'' \]
- Substituting the values:
\[ \Delta f = 1066.67 - 941.18 \approx 125.49 \, \text{Hz} \]

5. **Calculate the Percentage Change in Frequency:**
- The percentage change in frequency is calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{\Delta f}{f} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage Change} = \left( \frac{125.49}{1000} \right) \times 100 \approx 12.55\% \]

### Final Answer:
The percentage change in the frequency heard by a person standing near the track as the train passes him is approximately **12.55%**.