Apolice car parked on the side of the highway emits a 1200 hz sound that bounces off a vehicle farther down the highway and returns with a frequency of 1250 hz. how fast is the vehicle going?

Hello,

A police car parked on the side of the highway emits a 1200 Hz sound that bounces off a vehicle farther down the highway and returns with a frequency of 1250 Hz. 

How fast is the vehicle going?

Doppler equation formula: ƒL = ƒS(v - vL)/(v - vS)

The wave returns with a frequency of 1250 Hz, the echo frequency is higher; the car must be traveling towards the police car. 

The wave echo is coming back towards the police car at the same speed as the sound wave travels towards the moving car so the relative speed between the cars is half of the speed of the echo.

* speed of sound equals about 337 m/s 

2v / 337 = (1250/1200) - 1 
2v = 14.04 m/s 
v = 7.02 m/s

Thus, the vehicle is going 7.02 m/s.

Faith xoxo