How Does the Doppler Effect Explain Frequency Changes in Moving Cars?

[Elias Waranoi]

Homework Statement

A stationary police car emits a sound of frequency 1200 Hz that bounces off a car on the highway and returns with a frequency of 1250 Hz. The police car is right next to the highway, so the moving car is traveling directly toward or away from it. (a) How fast was the moving car going? Was it moving toward or away from the police car?

Homework Equations

ƒ_L = ƒ_S(v - v_L)/(v - v_S)

The Attempt at a Solution

The returning frequence is larger so its wave length has to be smaller which tells us that the car is moving towards the police car.

v_S = v - vƒ_S/ƒ_L = 13.76 m/s
The correct answer is 7.02 m/s.
What am I doing wrong?

 

[Doc Al]

Hint: You need to apply the Doppler formula twice.

1) What frequency does the moving car "observe"? (That's the frequency it will reflect.)
2) What frequency does the police car observe?

 

[haruspex]

Homework Equations

Where f_L is what, exactly? Is that the frequency that the police will hear?

Edit: pipped by The Doc.

 

[Elias Waranoi]

Hint: You need to apply the Doppler formula twice.

1) What frequency does the moving car "observe"? (That's the frequency it will reflect.)
2) What frequency does the police car observe?

Thanks! I got it right now.