A police car moves away from the accident scene at a constant speed with its siren on. A paramedic at the accident observes a 7% drop in the frequency of the sound of the siren in comparison to when the car was standing still. Speed of sound in air on that day is 335 m.s^-1
1) calculate the speed of the car.
First, we need to calculate the actual frequency of the siren when the car is moving.
Let the frequency of the siren when the car is standing still be f1, and the observed frequency when the car is moving be f2.
The observed frequency when the car is moving can be calculated using the formula:
f2 = f1 * (1 - v_source / v_sound)
Where v_source is the speed of the source (the police car) and v_sound is the speed of sound in air.
Given that v_sound = 335 m/s and the observed drop in frequency is 7%, we can set up the equation as:
f2 = f1 * (1 - v_source / v_sound)
f2 = 0.93 * f1
Since the speed of sound in air is constant, the change in frequency is due to the Doppler effect caused by the moving police car. Therefore, we can assume that the speed of the car is directly proportional to the change in frequency.
This means that the speed of the car is 7% of the speed of sound in air:
v_source = 0.07 * v_sound
v_source = 0.07 * 335
v_source = 23.45 m/s
Therefore, the speed of the car is 23.45 m/s.