A person observes two moving trains.'A' reaching the station and 'B' leaving the station with equal speed of `30m/s`.If both trains emit sounds with frequency `300Hz`,(Speed of sound : `330m/s` ) approximate difference of frequencies heard by the person will be :

Options

A. `33Hz`
B. `80Hz`
C. `10Hz`
D. `55Hz`

Answer

To solve the problem, we need to calculate the apparent frequencies of the sounds emitted by the two trains as heard by the observer. We will use the Doppler effect formula for sound.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency of sound emitted by the trains, \( f_0 = 300 \, \text{Hz} \)
- Speed of sound, \( v = 330 \, \text{m/s} \)
- Speed of the trains, \( v_s = 30 \, \text{m/s} \)

2. **Calculate the Apparent Frequency for Train A (reaching the station):**
- For a source moving towards the observer, the formula for apparent frequency \( f_a \) is:
\[ f_a = \frac{v}{v - v_s} \times f_0 \]
- Substituting the values:
\[ f_a = \frac{330}{330 - 30} \times 300 \]
\[ f_a = \frac{330}{300} \times 300 = 330 \, \text{Hz} \]

3. **Calculate the Apparent Frequency for Train B (leaving the station):**
- For a source moving away from the observer, the formula for apparent frequency \( f_b \) is:
\[ f_b = \frac{v}{v + v_s} \times f_0 \]
- Substituting the values:
\[ f_b = \frac{330}{330 + 30} \times 300 \]
\[ f_b = \frac{330}{360} \times 300 \]
\[ f_b = \frac{11}{12} \times 300 = 275 \, \text{Hz} \]

4. **Calculate the Difference in Frequencies:**
- The difference in frequencies heard by the observer is:
\[ \Delta f = f_a - f_b \]
- Substituting the values:
\[ \Delta f = 330 - 275 = 55 \, \text{Hz} \]

### Final Answer:
The approximate difference of frequencies heard by the person is \( 55 \, \text{Hz} \).

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