A traffic policeman blows a whistle to halt an approaching car-driver. The car-driver fails to stop and later argues in court that, due to the Doppler shift, the frequency of the whistle reaching him could have exceeded the audible limit of 20 kHz , making it impossible to hear. Tests revealed that the whistle produces sound at a frequency close to 16 kHz . Assuming the driver's argument is correct, what was the spee

Step-by-step solution

The frequency heard by the approaching driver is given by the Doppler effect formula: f' = f ( v + v_c v ) where f' is the apparent frequency, f is the actual frequency, v is the speed of sound, and v_c is the speed of the car. Given f' = 20 kHz , f = 16 kHz , and v = 330 m s ⁻¹ , substituting these values: 20 = 16 ( 330 + v_c 330 ) 5 4 = 1 + v_c 330 v_c 330 = 1 4 v_c = 330 4 = 82.5 m s ⁻¹ Converting the speed from m s ⁻¹ to km h ⁻¹ : v_c = 82.5 18 5 km h ⁻¹ = 297 km h ⁻¹