A stationary police car emits a sound of frequency 1215 Hz that bounces off of a

Question

A stationary police car emits a sound of frequency 1215 Hz that bounces off of a car on the highway and returns with a frequency of 1280Hz . The police car is right next to the highway, so the moving car is traveling directly toward or away from it. And what frequency would the police car have received if it had been traveling toward the other car at 25.0 m/s?

I got the Speed of the moving car as 8.85. I'm just having trouble with the last question. Which is if the car is moving at 25.0 m/s.

I dont exactly know how i got 8.85 either. I set both velocities of the source and listener as 0, and i don tknow why. I thought the velocity of the listener was 0 since the police car was not moving..

Explanation / Answer

f0 = 1215 Hz, speed of sound u = 340 m/s, speed of the other car = v when the police car is stationary: the frequency the other car receives is f1 = f0*(u + v)/u the frequency the police car receives is f2 = f1*u/(u - v) = f0*(u + v)/(u - v) Given f2 = 1280 Hz so (u + v)/(u - v) = 1280/1215 got v = (1280-1215)*340/(1280+1215) = 8.86 m/s when the police car is moving with vp = 25.0 m/s toward the other car: the frequency the other car receives is f1 = f0*(u + v)/(u - vp) the frequency the police car receives is f2 = f1*(u + vp)/(u - v) = f0*(u + v)(u + vp)/[(u - v)(u - vp)] = 1215 * (340 + 8.86)(340 + 25)/[(340 - 8.86)(340-25)] = 1483 Hz

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