A police car with a siren of frequency `8 KHz` is moving with uniform velocity `36 Km//hr` towards a ball building which reflects the sound waves. The speed of sound in air is `320 m//s`. The frequency of the siren heard by the car driver is

Options

A. `8.50 kHz`
B. `8.25 kHz`
C. `7.25 kHz`
D. `7.50 kHz`

Explanation

To solve the problem, we need to determine the frequency of the siren heard by the driver of the police car as it approaches a building that reflects sound waves. We will use the Doppler effect formula to find the apparent frequency.

### Step-by-Step Solution:

1. **Convert the speed of the police car from km/hr to m/s:**
\[ \text{Speed of police car} (V_s) = 36 \, \text{km/hr} = 36 \times \frac{5}{18} = 10 \, \text{m/s} \]

2. **Identify the speed of sound in air:**
\[ \text{Speed of sound} (c) = 320 \, \text{m/s} \]

3. **Identify the frequency of the siren:**
\[ \text{Frequency of siren} (f) = 8 \, \text{kHz} = 8000 \, \text{Hz} \]

4. **Calculate the apparent frequency \(f'\) heard by the wall (stationary observer):**
The formula for the apparent frequency when the source is moving towards a stationary observer is given by:
\[ f' = f \times \frac{c}{c - V_s} \]
Substituting the values:
\[ f' = 8000 \times \frac{320}{320 - 10} = 8000 \times \frac{320}{310} \]

5. **Calculate \(f'\):**
\[ f' = 8000 \times \frac{320}{310} \approx 8000 \times 1.03226 \approx 8260.65 \, \text{Hz} \]

6. **Now, calculate the frequency \(f''\) heard by the driver after the sound reflects off the wall:**
The formula for the apparent frequency when the observer (the car) is moving towards the source (the reflected sound) is:
\[ f'' = f' \times \frac{c + V_s}{c} \]
Substituting the values:
\[ f'' = 8260.65 \times \frac{320 + 10}{320} = 8260.65 \times \frac{330}{320} \]

7. **Calculate \(f''\):**
\[ f'' = 8260.65 \times 1.03125 \approx 8530.25 \, \text{Hz} \]

8. **Convert \(f''\) back to kHz:**
\[ f'' \approx 8.53 \, \text{kHz} \]

### Final Answer:
The frequency of the siren heard by the car driver is approximately **8.53 kHz**.