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physics question help- doppler shift when reflection takes place

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. 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? (b) What frequency would the police car have received if it had been traveling toward the other car at 20.0 m/s?

I understand the question to be
1. Doppler shift, is the frequency observed by the car that will help us in part 2
2. Doppler shift, the reflected frequency onto the stationary observer

What I am unsure about is what the initial equation will be as we need the frequency from the source but do not have its velocity. I tried setting up two simultaneous equations but that gave me 13m/s when the answer is about 7m/s. How should the first part be approached? What is the missing value and how do I understand it?
Original post by billybob1111
Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. 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? (b) What frequency would the police car have received if it had been traveling toward the other car at 20.0 m/s?

I understand the question to be
1. Doppler shift, is the frequency observed by the car that will help us in part 2
2. Doppler shift, the reflected frequency onto the stationary observer

What I am unsure about is what the initial equation will be as we need the frequency from the source but do not have its velocity. I tried setting up two simultaneous equations but that gave me 13m/s when the answer is about 7m/s. How should the first part be approached? What is the missing value and how do I understand it?


The police car is the source of the initial sound wave. Is it the source of the reflected?
Reply 2
(Original post by Joseph McMahon)The police car is the source of the initial sound wave. Is it the source of the reflected?

yes
Original post by billybob1111
(Original post by Joseph McMahon)The police car is the source of the initial sound wave. Is it the source of the reflected?

yes


"A stationary police car emits..."

"that bounces off a car on the highway...so the moving car is..."

I would have a closer think at the underlying Physics here: the source of the initial waves is stationary. But given the difference in frequency of the emitted and reflected waves then a Doppler shift has occurred. How can the stationary vehicle be the source of both the unshifted and shifted waves?

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