A train is moving towards a stationary observer. Which of the following curve best represents the frequency recived by observer `f` as a function of time?

Options

A. `(#3DCP_V03_C19_E01_035_Q01.png" width="30%">
B. `(#3DCP_V03_C19_E01_035_Q02.png" width="30%">
C. `(#3DCP_V03_C19_E01_035_Q03.png" width="30%">
D. `(#3DCP_V03_C19_E01_035_Q04.png" width="30%">

Explanation

To solve the problem of how the frequency received by a stationary observer changes as a train moves towards and then away from them, we can break it down into clear steps.

### Step-by-Step Solution:

1. **Identify the Scenario**:
- We have a train moving towards a stationary observer. Initially, the observer hears a higher frequency as the train approaches.

2. **Understand the Doppler Effect**:
- The Doppler Effect explains how the frequency of a wave changes for an observer moving relative to the source of the wave. When the source moves towards the observer, the frequency increases; when it moves away, the frequency decreases.

3. **Define Frequencies**:
- Let the original frequency of the train be \( f \).
- When the train approaches the observer, the apparent frequency \( f_1 \) can be given by:
\[ f_1 = f \left( \frac{v_s}{v_s - v_t} \right) \]
where \( v_s \) is the speed of sound, and \( v_t \) is the speed of the train.

- When the train moves away from the observer after passing, the apparent frequency \( f_2 \) is:
\[ f_2 = f \left( \frac{v_s}{v_s + v_t} \right) \]

4. **Analyze the Frequencies**:
- Since \( v_t \) is positive when the train is approaching, \( f_1 > f \).
- After the train passes, \( f_2 < f \).

5. **Plot the Frequencies Over Time**:
- At time \( t_0 \), the frequency is \( f \).
- As the train approaches, the frequency increases to \( f_1 \).
- After the train passes the observer, the frequency decreases to \( f_2 \).

6. **Draw the Graph**:
- On the graph, the x-axis represents time, and the y-axis represents frequency.
- The curve starts at \( f \), rises to \( f_1 \) as the train approaches, and then falls back to \( f_2 \) as the train moves away.

### Conclusion:
The graph representing the frequency received by the observer as a function of time will show an increase in frequency as the train approaches and a decrease as it moves away.