The graph between distance between source and observer and apparent frequency in the case of Doppler's effect will be

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Explanation

To solve the problem of determining the relationship between the distance between the source and observer and the apparent frequency in the case of the Doppler effect, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Doppler Effect:**
The Doppler effect describes how the frequency of a wave changes for an observer moving relative to the source of the wave. When the source and observer are moving towards each other, the observed frequency increases, and when they are moving apart, the observed frequency decreases.

2. **Identify the Variables:**
- Let \( f_0 \) be the actual frequency emitted by the source.
- Let \( v \) be the speed of sound in the medium.
- Let \( v_o \) be the speed of the observer.
- Let \( v_s \) be the speed of the source.
- Let \( d \) be the distance between the source and the observer.

3. **Apparent Frequency Formula:**
The apparent frequency \( f' \) can be expressed using the formula:
\[ f' = f_0 \frac{v + v_o}{v - v_s} \]
- If the source is stationary (\( v_s = 0 \)), the formula simplifies to:
\[ f' = f_0 \frac{v + v_o}{v} \]

4. **Distance Independence:**
The key point here is that the apparent frequency \( f' \) does not depend on the distance \( d \) between the source and the observer. Instead, it depends on their relative velocities. Thus, as the distance changes, the apparent frequency remains constant if the speeds of the source and observer do not change.

5. **Graph Representation:**
When plotting the graph of distance \( d \) (on the x-axis) versus apparent frequency \( f' \) (on the y-axis), since \( f' \) remains constant regardless of \( d \), the graph will be a horizontal line. This indicates that as the distance between the source and observer increases or decreases, the apparent frequency does not change.

### Conclusion:
The graph between the distance between the source and observer and the apparent frequency in the case of the Doppler effect will be a horizontal line, indicating that the apparent frequency is independent of the distance.

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