Question

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind at constant speed and you perceive the frequency as 1340 Hz. You are relieved that he is in pursuit of a different driver when he continues past you, but now you perceive the frequency as 1300 Hz.What is the speed of the police car?

Answer 1

40.13491 m/s

Step-by-step explanation:

`v_r` = My speed = 35 m/s

v = Speed of sound in air = 343 Hz

`v_s` = Speed of the police car

When the car is approaching

`f=f'(v-v_r)/(v-v_s)\\\Rightarrow 1340=f'(343-35)/(343-v_s)`

When the car is receding

`f=f'(v+v_r)/(v+v_s)\\\Rightarrow 1300=f'(343+35)/(343+v_s)`

Dividing the equations

`(1340)/(1300)=(f'(343-35)/(343-v_s))/(f'(343+35)/(343+v_s))\\\Rightarrow (1340)/(1300)=(22\left(v_s+343\right))/(27\left(-v_s+343\right))\\\Rightarrow -36180v_s+12409740-12409740=28600v_s+9809800-12409740\\\Rightarrow (-64780v_s)/(-64780)=(-2599940)/(-64780)\\\Rightarrow v_s=(129997)/(3239)\\\Rightarrow v_s=40.13491\ m/s`

The speed of the police car is 40.13491 m/s