Final answer:
The phenomenon described in this question is known as the Doppler effect, which involves a change in the frequency or pitch of a sound wave as the source and observer move relative to each other. By applying the equation for the Doppler effect, we can find that the speed of the police car is approximately 74.088 m/s.
Step-by-step explanation:
The phenomenon described in this question is known as the Doppler effect. The Doppler effect refers to the change in frequency or pitch of a sound wave as the source of the sound moves relative to an observer.
In this case, as the police car approaches you, the frequency of the siren that you hear is higher than the actual frequency of the siren, which is 510 Hz. This is because the sound waves get compressed as the police car moves towards you.
When the police car passes you and moves away, the frequency you hear decreases to 400 Hz. This is because the sound waves get stretched as the police car moves away from you.
To determine the speed of the police car, we can use the equation for the Doppler effect:
(f2 - f1) / f1 = v / c
Where f2 is the frequency observed after the police car passes you (400 Hz), f1 is the frequency observed before the police car passes you (510 Hz), v is the speed of the police car, and c is the speed of sound (approximately 343 m/s).
Plugging in the values, we can solve for v:
v = (f2 - f1) / f1 * c
v = (400 - 510) / 510 * 343
v ≈ -0.216 * 343
v ≈ -74.088 m/s
Since the speed of the police car is given as a positive value, we take the absolute value of v:
speed of the police car ≈ 74.088 m/s