A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall 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 :

Let the frequency of the siren be f = 8 kHz = 8 × 10³ Hz.
The speed of the police car is v = 36 km/hr = 36 × (5/18) m/s = 10 m/s.
The speed of sound in air is v_s = 320 m/s.
The police car is moving towards the building. The sound waves are reflected from the building and reach the driver.
The frequency of the sound waves reaching the building is given by the Doppler effect formula:
f' = f (v_s / (v_s - v))
where f' is the frequency of the sound waves reaching the building, f is the frequency of the siren, v_s is the speed of sound, and v is the speed of the car.
f' = (8 × 10³) (320 / (320 - 10)) = (8 × 10³) (320 / 310) Hz
The building acts as a stationary source emitting sound waves at frequency f'.
These waves are received by the car driver moving towards the building.
The frequency heard by the car driver is given by:
f'' = f' (v_s + v) / v_s
f'' = [(8 × 10³) (320 / 310)] (320 + 10) / 320
f'' = (8 × 10³) (320 / 310) (330 / 320) = (8 × 10³) (330 / 310) Hz
f'' = (8 × 10³) (1.0645) Hz ≈ 8516 Hz
f'' ≈ 8.516 kHz ≈ 8.5 kHz
Therefore, the frequency of the siren heard by the car driver is approximately 8.5 kHz.