when a source is going away from a stationary observer with the velocity equal to that of sound in air , then the frequency heard by observer is `n` times the original frequency . The value of `n` is

Options

A. `0.5`
B. `0.25`
C. `1.0`
D. No sound is heard

Explanation

To solve the problem of finding the frequency heard by a stationary observer when a source is moving away from them at the speed of sound, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Scenario**:
- We have a source of sound moving away from a stationary observer.
- The speed of the source (Vs) is equal to the speed of sound in air (C).

2. **Identify the Variables**:
- Let the original frequency emitted by the source be \( F \).
- The frequency heard by the observer will be denoted as \( F' \).
- The speed of sound in air is \( C \).

3. **Use the Doppler Effect Formula**:
- The formula for the frequency heard by a stationary observer when the source is moving away is given by:
\[ F' = F \times \frac{C}{C + V_s} \]
- Since \( V_s = C \) (the source is moving away at the speed of sound), we can substitute this into the equation.

4. **Substitute the Values**:
- Plugging in \( V_s = C \):
\[ F' = F \times \frac{C}{C + C} = F \times \frac{C}{2C} \]
- This simplifies to:
\[ F' = F \times \frac{1}{2} = 0.5F \]

5. **Relate to the Given Frequency**:
- According to the problem, the frequency heard by the observer \( F' \) is \( n \) times the original frequency \( F \):
\[ F' = nF \]
- From our previous calculation, we have:
\[ 0.5F = nF \]
- Dividing both sides by \( F \) (assuming \( F \neq 0 \)):
\[ n = 0.5 \]

6. **Conclusion**:
- The value of \( n \) is \( 0.5 \).

### Final Answer:
The value of \( n \) is \( 0.5 \).