The speed at which a source of sound should move so that a stationary observer finds the apparent frequency equal to `11//12` of the original frequency

Options

A. `V//2`
B. `2V`
C. `V//4`
D. `V//11`

Explanation

To solve the problem of finding the speed at which a source of sound should move so that a stationary observer finds the apparent frequency equal to \( \frac{11}{12} \) of the original frequency, we can use the principles of the Doppler effect.

### Step-by-Step Solution:

1. **Understand the Doppler Effect**: The Doppler effect describes the change in frequency (or wavelength) of a wave in relation to an observer moving relative to the source of the wave. In this case, the source is moving away from a stationary observer.

2. **Set Up the Relationship**: According to the problem, the apparent frequency \( f' \) is equal to \( \frac{11}{12} f_0 \), where \( f_0 \) is the original frequency emitted by the source.

\[ f' = \frac{11}{12} f_0 \]

3. **Doppler Effect Formula**: The formula for the frequency observed when the source is moving away from a stationary observer is given by:

\[ f' = \frac{v}{v + v_s} f_0 \]

where:
- \( v \) is the speed of sound,
- \( v_s \) is the speed of the source.

4. **Substitute the Known Values**: We can substitute \( f' \) into the Doppler effect formula:

\[ \frac{11}{12} f_0 = \frac{v}{v + v_s} f_0 \]

5. **Cancel \( f_0 \)**: Since \( f_0 \) is common on both sides, we can cancel it out:

\[ \frac{11}{12} = \frac{v}{v + v_s} \]

6. **Cross-Multiply**: To eliminate the fraction, we can cross-multiply:

\[ 11(v + v_s) = 12v \]

7. **Distribute**: Distributing the 11 gives us:

\[ 11v + 11v_s = 12v \]

8. **Rearrange the Equation**: Now, we can rearrange the equation to isolate \( v_s \):

\[ 11v_s = 12v - 11v \]
\[ 11v_s = v \]

9. **Solve for \( v_s \)**: Finally, divide both sides by 11 to find the speed of the source:

\[ v_s = \frac{v}{11} \]

### Conclusion:
The speed at which the source of sound should move so that a stationary observer finds the apparent frequency equal to \( \frac{11}{12} \) of the original frequency is \( \frac{v}{11} \), where \( v \) is the speed of sound.