A source of sound of frequency `1.8kHz` moves uniformly along a straight line at a distance `250m` from observer. The velocity of source is `0.8C` where `C` is the velocity of sound. Find out the frequency of sound received by observer (in kHz) at the moment when the source gets closest to him.

Explanation

To solve the problem, we need to find the frequency of sound received by the observer when the source of sound is closest to him. We will use the Doppler effect formula for sound.

### Step-by-step Solution:

1. **Identify Given Values:**
- Frequency of the source, \( f_s = 1.8 \, \text{kHz} \)
- Velocity of sound, \( c \) (assumed to be \( 343 \, \text{m/s} \) for calculations)
- Velocity of the source, \( v_s = 0.8c = 0.8 \times 343 \, \text{m/s} = 274.4 \, \text{m/s} \)
- Distance from the observer to the path of the source, \( L = 250 \, \text{m} \)

2. **Determine the Condition When the Source is Closest:**
- At the moment the source is closest to the observer, the angle \( \theta \) is such that the sound waves are emitted directly towards the observer. Thus, \( \cos \theta = \frac{L}{\sqrt{L^2 + x^2}} \) where \( x \) is the horizontal distance traveled by the source.

3. **Using the Doppler Effect Formula:**
- The observed frequency \( f_o \) when the source is moving towards the observer is given by:
\[ f_o = f_s \frac{c}{c - v_s} \]
- Here, since the source is moving towards the observer, we will use the formula directly.

4. **Substituting Values:**
- Substitute \( f_s = 1.8 \, \text{kHz} \) and \( v_s = 0.8c \):
\[ f_o = 1.8 \, \text{kHz} \cdot \frac{c}{c - 0.8c} = 1.8 \, \text{kHz} \cdot \frac{c}{0.2c} \]
- Simplifying this gives:
\[ f_o = 1.8 \, \text{kHz} \cdot 5 = 9 \, \text{kHz} \]

5. **Final Calculation:**
- The frequency of sound received by the observer when the source is closest is:
\[ f_o = 9 \, \text{kHz} \]

### Final Answer:
The frequency of sound received by the observer is **9 kHz**.